Journal articles on the topic 'Regression Monte-Carlo scheme'
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1
Izydorczyk, Lucas, Nadia Oudjane, and Francesco Russo. "A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems." Monte Carlo Methods and Applications 27, no. 4 (October 21, 2021): 347–71. http://dx.doi.org/10.1515/mcma-2021-2095.
Abstract:
Abstract We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest, and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads.
2
Folashade Adeola Bolarinwa, Olusola Samuel Makinde, and Olusoga Akin Fasoranbaku. "A new Bayesian ridge estimator for logistic regression in the presence of multicollinearity." World Journal of Advanced Research and Reviews 20, no. 3 (December 30, 2023): 458–65. http://dx.doi.org/10.30574/wjarr.2023.20.3.2415.
Abstract:
This research introduces the Bayesian schemes for estimating logistic regression parameters in the presence of multicollinearity. The Bayesian schemes involve the introduction of a prior together with the likelihood which resulted in the posterior distribution that is not tractable, hence the use of a numerical method i.e Gibbs sampler. Different levels of multicollinearity were chosen to be p = 0.80‚0.85‚0.90‚0.95‚0.99and 0.999to accommodate severe, very severe and nearly perfect state of multicollinearity with sample sizes taken as 10,20,30,50,100,200,300 and 500.Different ridge parameters k were introduced to remedy the effect of multicollinearity .The explanatory variables used were 3 and 7. Model estimation was carried out using Bayesian approach via the Gibbs sampler of Markov Chain Monte Carlo Simulation. The means square error MSE of Bayesian logistic regression estimation was compared with the frequentist methods of the estimation. The result shows a minimum mean square error with the Bayesian scheme compared to the frequentist method.
3
Gobet, E., J. G. López-Salas, P. Turkedjiev, and C. Vázquez. "Stratified Regression Monte-Carlo Scheme for Semilinear PDEs and BSDEs with Large Scale Parallelization on GPUs." SIAM Journal on Scientific Computing 38, no. 6 (January 2016): C652—C677. http://dx.doi.org/10.1137/16m106371x.
4
Trinchero, Riccardo, and Flavio Canavero. "Use of an Active Learning Strategy Based on Gaussian Process Regression for the Uncertainty Quantification of Electronic Devices." Engineering Proceedings 3, no. 1 (October 30, 2020): 3. http://dx.doi.org/10.3390/iec2020-06967.
Abstract:
This paper presents a preliminary version of an active learning (AL) scheme for the sample selection aimed at the development of a surrogate model for the uncertainty quantification based on the Gaussian process regression. The proposed AL strategy iteratively searches for new candidate points to be included within the training set by trying to minimize the relative posterior standard deviation provided by the Gaussian process regression surrogate. The above scheme has been applied for the construction of a surrogate model for the statistical analysis of the efficiency of a switching buck converter as a function of seven uncertain parameters. The performance of the surrogate model constructed via the proposed active learning method is compared with that provided by an equivalent model built via a Latin hypercube sampling. The results of a Monte Carlo simulation with the computational model are used as reference.
5
Gobet, Emmanuel, José Germán López-Salas, and Carlos Vázquez. "Quasi-Regression Monte-Carlo Scheme for Semi-Linear PDEs and BSDEs with Large Scale Parallelization on GPUs." Archives of Computational Methods in Engineering 27, no. 3 (April 4, 2019): 889–921. http://dx.doi.org/10.1007/s11831-019-09335-x.
6
Khan, Sajid Ali, Sayyad Khurshid, Shabnam Arshad, and Owais Mushtaq. "Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study." Journal of Mathematical Analysis and Modeling 2, no. 1 (March 29, 2021): 26–39. http://dx.doi.org/10.48185/jmam.v2i1.131.
Abstract:
In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.
7
Wang, Han, Lingwei Xu, and Xianpeng Wang. "Outage Probability Performance Prediction for Mobile Cooperative Communication Networks Based on Artificial Neural Network." Sensors 19, no. 21 (November 4, 2019): 4789. http://dx.doi.org/10.3390/s19214789.
Abstract:
This paper investigates outage probability (OP) performance predictions using transmit antenna selection (TAS) and derives exact closed-form OP expressions for a TAS scheme. It uses Monte-Carlo simulations to evaluate OP performance and verify the analysis. A back-propagation (BP) neural network-based OP performance prediction algorithm is proposed and compared with extreme learning machine (ELM), locally weighted linear regression (LWLR), support vector machine (SVM), and BP neural network methods. The proposed method was found to have higher OP performance prediction results than the other prediction methods.
8
Seo, Jung-In, Young Eun Jeon, and Suk-Bok Kang. "New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme." Mathematics 8, no. 10 (October 5, 2020): 1713. http://dx.doi.org/10.3390/math8101713.
Abstract:
This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach.
9
MORALES, MARÍA, CARMELO RODRÍGUEZ, and ANTONIO SALMERÓN. "SELECTIVE NAIVE BAYES FOR REGRESSION BASED ON MIXTURES OF TRUNCATED EXPONENTIALS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 06 (December 2007): 697–716. http://dx.doi.org/10.1142/s0218488507004959.
Abstract:
Naive Bayes models have been successfully used in classification problems where the class variable is discrete. These models have also been applied to regression or prediction problems, i.e. classification problems where the class variable is continuous, but usually under the assumption that the joint distribution of the feature variables and the class is multivariate Gaussian. In this paper we are interested in regression problems where some of the feature variables are discrete while the others are continuous. We propose a Naive Bayes predictor based on the approximation of the joint distribution by a Mixture of Truncated Exponentials (MTE). We have followed a filter-wrapper procedure for selecting the variables to be used in the construction of the model. This scheme is based on the mutual information between each of the candidate variables and the class. Since the mutual information can not be computed exactly for the MTE distribution, we introduce an unbiased estimator of it, based on Monte Carlo methods. We test the performance of the proposed model in artificial and real-world datasets.
10
Ma, Zhi-Sai, Li Liu, Si-Da Zhou, and Lei Yu. "Output-Only Modal Parameter Recursive Estimation of Time-Varying Structures via a Kernel Ridge Regression FS-TARMA Approach." Shock and Vibration 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/8176593.
Abstract:
Modal parameter estimation plays an important role in vibration-based damage detection and is worth more attention and investigation, as changes in modal parameters are usually being used as damage indicators. This paper focuses on the problem of output-only modal parameter recursive estimation of time-varying structures based upon parameterized representations of the time-dependent autoregressive moving average (TARMA). A kernel ridge regression functional series TARMA (FS-TARMA) recursive identification scheme is proposed and subsequently employed for the modal parameter estimation of a numerical three-degree-of-freedom time-varying structural system and a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudolinear regression FS-TARMA approach via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics in a recursive manner.
11
Jiang, Nan, and Yexiang Xue. "Racing Control Variable Genetic Programming for Symbolic Regression." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 11 (March 24, 2024): 12901–9. http://dx.doi.org/10.1609/aaai.v38i11.29187.
Abstract:
Symbolic regression, as one of the most crucial tasks in AI for science, discovers governing equations from experimental data. Popular approaches based on genetic programming, Monte Carlo tree search, or deep reinforcement learning learn symbolic regression from a fixed dataset. These methods require massive datasets and long training time especially when learning complex equations involving many variables. Recently, Control Variable Genetic Programming (CVGP) has been introduced which accelerates the regression process by discovering equations from designed control variable experiments. However, the set of experiments is fixed a-priori in CVGP and we observe that sub-optimal selection of experiment schedules delay the discovery process significantly. To overcome this limitation, we propose Racing Control Variable Genetic Programming (Racing-CVGP), which carries out multiple experiment schedules simultaneously. A selection scheme similar to that used in selecting good symbolic equations in the genetic programming process is implemented to ensure that promising experiment schedules eventually win over the average ones. The unfavorable schedules are terminated early to save time for the promising ones. We evaluate Racing-CVGP on several synthetic and real-world datasets corresponding to true physics laws. We demonstrate that Racing-CVGP outperforms CVGP and a series of symbolic regressors which discover equations from fixed datasets.
12
Wu, Hsiao-Chun, Shih Yu Chang, Tho Le-Ngoc, and Yiyan Wu. "Efficient Rank-Adaptive Least-Square Estimation and Multiple-Parameter Linear Regression Using Novel Dyadically Recursive Hermitian Matrix Inversion." International Journal of Antennas and Propagation 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/891932.
Abstract:
Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the important estimation techniques for engineering and science, especially in the mobile communications and signal processing applications. The majority of computational complexity incurred in LSE and MLR arises from a Hermitian matrix inversion. In practice, the Yule-Walker equations are not valid, and hence the Levinson-Durbin algorithm cannot be employed for general LSE and MLR problems. Therefore, the most efficient Hermitian matrix inversion method is based on the Cholesky factorization. In this paper, we derive a new dyadic recursion algorithm for sequential rank-adaptive Hermitian matrix inversions. In addition, we provide the theoretical computational complexity analyses to compare our new dyadic recursion scheme and the conventional Cholesky factorization. We can design a variable model-order LSE (MLR) using this proposed dyadic recursion approach thereupon. Through our complexity analyses and the Monte Carlo simulations, we show that our new dyadic recursion algorithm is more efficient than the conventional Cholesky factorization for the sequential rank-adaptive LSE (MLR) and the associated variable model-order LSE (MLR) can seek the trade-off between the targeted estimation performance and the required computational complexity. Our proposed new scheme can benefit future portable and mobile signal processing or communications devices.
13
Jung, Jihyeok, Chan-Oi Song, Deok-Joo Lee, and Kiho Yoon. "Optimal Mechanism in a Dynamic Stochastic Knapsack Environment." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 9 (March 24, 2024): 9807–14. http://dx.doi.org/10.1609/aaai.v38i9.28840.
Abstract:
This study introduces an optimal mechanism in a dynamic stochastic knapsack environment. The model features a single seller who has a fixed quantity of a perfectly divisible item. Impatient buyers with a piece-wise linear utility function arrive randomly and they report the two-dimensional private information: marginal value and demanded quantity. We derive a revenue-maximizing dynamic mechanism in a finite discrete time framework that satisfies incentive compatibility, individual rationality, and feasibility conditions. This is achieved by characterizing buyers' utility and utilizing the Bellman equation. Moreover, we establish the essential penalty scheme for incentive compatibility, as well as the allocation and payment policies. Lastly, we propose algorithms to approximate the optimal policy, based on the Monte Carlo simulation-based regression method and reinforcement learning.
14
Zhang, Yichi, Yangyao Ding, and Panagiotis D. Christofides. "Integrating Feedback Control and Run-to-Run Control in Multi-Wafer Thermal Atomic Layer Deposition of Thin Films." Processes 8, no. 1 (December 21, 2019): 18. http://dx.doi.org/10.3390/pr8010018.
Abstract:
There is currently a lack of understanding of the deposition profile in a batch atomic layer deposition (ALD) process. Also, no on-line control scheme has been proposed to resolve the prevalent disturbances. Motivated by this, we develop a computational fluid dynamics (CFD) model and an integrated online run-to-run and feedback control scheme. Specifically, we analyze a furnace reactor for a SiO2 thin-film ALD with BTBAS and ozone as precursors. Initially, a high-fidelity 2D axisymmetric multiscale CFD model is developed using ANSYS Fluent for the gas-phase characterization and the surface thin-film deposition, based on a kinetic Monte-Carlo (kMC) model database. To deal with the disturbance during reactor operation, a proportional integral (PI) control scheme is adopted, which manipulates the inlet precursor concentration to drive the precursor partial pressure to the set-point, ensuring the complete substrate coverage. Additionally, the CFD model is utilized to investigate a wide range of operating conditions, and a regression model is developed to describe the relationship between the half-cycle time and the feed flow rate. A run-to-run (R2R) control scheme using an exponentially weighted moving average (EWMA) strategy is developed to regulate the half-cycle time for the furnace ALD process between batches.
15
Wang, Tianhao, Quanyi Yu, Xianli Yu, Le Gao, and Huanyu Zhao. "Radiated Susceptibility Analysis of Multiconductor Transmission Lines Based on Polynomial Chaos." Applied Computational Electromagnetics Society 35, no. 12 (February 15, 2021): 1556–66. http://dx.doi.org/10.47037/2020.aces.j.351215.
Abstract:
To address the uncertainties of the radiated susceptibility of multiconductor transmission lines (MTLs), a surrogate model of the MTLs radiated susceptibility is established based on generalized polynomial chaos (gPC), and the gPC is made sparser by combining the adaptive hyperbolic truncation (AHT) scheme and the least angle regression (LAR) method. The uncertainties of the radiated susceptibility of transmission lines are calculated using the adaptive-sparse polynomial chaos (AS-PC) scheme. The parameters related to the incident field, such as elevation angle theta, azimuth angle psi, polarization angle eta, and field amplitude E, are inevitably random. Therefore, these four variables are taken as random input variables, and each of them is subject to different variable distributions. The MTLs model with infinite ground as the reference conductor is adopted, different impedances are used and the AS-PC scheme is combined with transmission line theory to calculate the average, standard deviation and probability distribution of the radiated susceptibility of MTLs. Sobol global sensitivity analysis based on variance decomposition is adopted to calculate the influence of random input variables on the MTLs radiated susceptibility model. The calculation results are compared with the results of the Monte Carlo (MC) method, proving that the proposed method is correct and feasible.
16
Gomes, Véronique, Ricardo Rendall, Marco Seabra Reis, Ana Mendes-Ferreira, and Pedro Melo-Pinto. "Determination of Sugar, pH, and Anthocyanin Contents in Port Wine Grape Berries through Hyperspectral Imaging: An Extensive Comparison of Linear and Non-Linear Predictive Methods." Applied Sciences 11, no. 21 (November 3, 2021): 10319. http://dx.doi.org/10.3390/app112110319.
Abstract:
This paper presents an extended comparison study between 16 different linear and non-linear regression methods to predict the sugar, pH, and anthocyanin contents of grapes through hyperspectral imaging (HIS). Despite the numerous studies on this subject that can be found in the literature, they often rely on the application of one or a very limited set of predictive methods. The literature on multivariate regression methods is quite extensive, so the analytical domain explored is too narrow to guarantee that the best solution has been found. Therefore, we developed an integrated linear and non-linear predictive analytics comparison framework (L&NL-PAC), fully integrated with five preprocessing techniques and five different classes of regression methods, for an effective and robust comparison of all alternatives through a robust Monte Carlo double cross-validation stratified data splitting scheme. L&NLPAC allowed for the identification of the most promising preprocessing approaches, best regression methods, and wavelengths most contributing to explaining the variability of each enological parameter for the target dataset, providing important insights for the development of precision viticulture technology, based on the HSI of grape. Overall, the results suggest that the combination of the Savitzky−Golay first derivative and ridge regression can be a good choice for the prediction of the three enological parameters.
17
Ibrahim, Joseph G., Sungduk Kim, Ming-Hui Chen, Arvind K. Shah, and Jianxin Lin. "Bayesian multivariate skew meta-regression models for individual patient data." Statistical Methods in Medical Research 28, no. 10-11 (October 12, 2018): 3415–36. http://dx.doi.org/10.1177/0962280218801147.
Abstract:
We examine a class of multivariate meta-regression models in the presence of individual patient data. The methodology is well motivated from several studies of cholesterol-lowering drugs where the goal is to jointly analyze the multivariate outcomes, low density lipoprotein cholesterol, high density lipoprotein cholesterol, and triglycerides. These three continuous outcome measures are correlated and shed much light on a subject's lipid status. One of the main goals in lipid research is the joint analysis of these three outcome measures in a meta-regression setting. Since these outcome measures are not typically multivariate normal, one must consider classes of distributions that allow for skewness in one or more of the outcomes. In this paper, we consider a new general class of multivariate skew distributions for multivariate meta-regression and examine their theoretical properties. Using these distributions, we construct a Bayesian model for the meta-data and develop an efficient Markov chain Monte Carlo computational scheme for carrying out the computations. In addition, we develop a multivariate L measure for model comparison, Bayesian residuals for model assessment, and a Bayesian procedure for detecting outlying trials. The proposed multivariate L measure, Bayesian residuals, and Bayesian outlying trial detection procedure are particularly suitable and computationally attractive in the multivariate meta-regression setting. A detailed case study demonstrating the usefulness of the proposed methodology is carried out in an individual patient data multivariate meta-regression setting using 26 pivotal Merck clinical trials that compare statins (cholesterol-lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline.
18
Shahzad, Usman, Ishfaq Ahmad, Ibrahim Mufrah Almanjahie, and Amer Ibrahim Al-Omari. "Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme." PLOS ONE 17, no. 10 (October 24, 2022): e0276514. http://dx.doi.org/10.1371/journal.pone.0276514.
Abstract:
Ranked set sampling (RSS) has created a broad interest among researchers and it is still a unique research topic. It has at long last begun to find its way into practical applications beyond its initial horticultural based birth in the fundamental paper by McIntyre in the nineteenth century. One of the extensions of RSS is median ranked set sampling (MRSS). MRSS is a sampling procedure normally utilized when measuring the variable of interest is troublesome or expensive, whereas it might be easy to rank the units using an inexpensive sorting criterion. Several researchers introduced ratio, regression, exponential, and difference type estimators for mean estimation under the MRSS design. In this paper, we propose three new mean estimators under the MRSS scheme. Our idea is based on three-fold utilization of supplementary information. Specifically, we utilize the ranks and second raw moments of the supplementary information and the original values of the supplementary variable. The appropriateness of the proposed group of estimators is demonstrated in light of both real and artificial data sets based on the Monte-Carlo simulation. Additionally, the performance comparison is also conducted regarding the reviewed families of estimators. The results are empowered and the predominant execution of the proposed group of estimators is seen throughout the paper.
19
Liu, Manhua, Yangyang Wang, Yueping Jiang, Haitao Liu, Jingjing Chen, and Shao Liu. "Quantitation of Oxcarbazepine Clinically in Plasma Using Surfaced-Enhanced Raman Spectroscopy (SERS) Coupled with Chemometrics." Applied Spectroscopy 73, no. 7 (May 21, 2019): 801–9. http://dx.doi.org/10.1177/0003702819845389.
Abstract:
Nondestructive, sensitive, near-real-time quantitative analysis approaches are gaining popularity and attention, especially in clinical diagnosis and detection. There is a need to propose an alternative scheme using surface-enhanced Raman spectroscopy (SERS) assisted by chemometrics to improve some defects existing using other analytical instruments to meet clinical demands. In this study, clinical drug oxcarbazepine (OXC) in human blood plasma has been quantified and detected using this method. Partial least squares regression (PLSR) modeling was employed to assess the relationship between full SERS spectral data and OXC concentration. The calibration set's correlation coefficient of the model is > 0.9, the result suggests that this method is favorable and feasible. Furthermore, other multivariate calibration algorithms like Monte Carlo cross-validation (MCCV) sample set partitioning based on joint XY distances (SPXY), adaptive iteratively reweighted penalized least squares (AIR–PLS), moving window partial least squares regression (MWPLS), and leave-one-out cross-validation were used to handle these spectral data to obtain an accurate predictive model. The results achieved in this study provide a possibility and availability for us to apply SERS in combination with chemometrics to diagnosis detection.
20
Virtanen, Arja, Veli Kairisto, and Esa Uusipaikka. "Regression-based reference limits: determination of sufficient sample size." Clinical Chemistry 44, no. 11 (November 1, 1998): 2353–58. http://dx.doi.org/10.1093/clinchem/44.11.2353.
Abstract:
Abstract Regression analysis is the method of choice for the production of covariate-dependent reference limits. There are currently no recommendations on what sample size should be used when regression-based reference limits and confidence intervals are calculated. In this study we used Monte Carlo simulation to study a reference sample group of 374 age-dependent hemoglobin values. From this sample, 5000 random subsamples, with replacement, were constructed with 10–220 observations per sample. Regression analysis was used to estimate age-dependent 95% reference intervals for hemoglobin concentrations and erythrocyte counts. The maximum difference between mean values of the root mean square error and original values for hemoglobin was 0.05 g/L when the sample size was ≥60. The parameter estimators and width of reference intervals changed negligibly from the values calculated from the original sample regardless of what sample size was used. SDs and CVs for these factors changed rapidly up to a sample size of 30; after that changes were smaller. The largest and smallest absolute differences in root mean square error and width of reference interval between sample values and values calculated from the original sample were also evaluated. As expected, differences were largest in small sample sizes, and as sample size increased differences decreased. To obtain appropriate reference limits and confidence intervals, we propose the following scheme: (a) check whether the assumptions of regression analysis can be fulfilled with/without transformation of data; (b) check that the value of v, which describes how the covariate value is situated in relation to both the mean value and the spread of the covariate values, does not exceed 0.1 at minimum and maximum covariate positions; and (c) if steps 1 and 2 can be accepted, the reference limits with confidence intervals can be produced by regression analysis, and the minimum acceptable sample size will be ∼70.
21
Liang, Xitong, Samuel Livingstone, and Jim Griffin. "Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models." Entropy 25, no. 9 (September 8, 2023): 1310. http://dx.doi.org/10.3390/e25091310.
Abstract:
Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add–delete–swap proposal.
22
Gao, Yuanyuan, Na Liu, Peng Liu, and Chengnuo Wang. "Prediction of stamping parameters for imitation π-shaped lithium battery shells by building variable weight and threshold pelican-BP neural networks." Advances in Mechanical Engineering 14, no. 9 (September 2022): 168781322211122. http://dx.doi.org/10.1177/16878132221112203.
Abstract:
With the rapid development of artificial neural networks, more sophisticated network models and more accurate prediction results are provided for solving engineering applications. In this paper, the weights and thresholds of the feedforward neural network model were optimized using the pelican algorithm, and the optimal solution was output by simulating the pelican predation scheme and assigned as the new parameters of the neural network. A POA-BP network model was proposed, and its better prediction was demonstrated by comparing the fitting and prediction performance with 13 neural network models such as random forest, support vector machine, and wavelet basis by evaluating metrics such as RMSE, MSE, and MAE. To further improve the prediction accuracy, different hidden layer topologies of POA-BP were compared, and the Monte Carlo method was used to obtain seven design variables for the lithium battery shell size parameters, and parameter regression prediction was performed for the structure after the variable density topology optimization used the isotropic material interpolation model (SIMP) with the moving asymptote method by invoking the MinGW-w64 compiler, and the 1-3-1 neural network was selected model to predict each dimension of the battery shell structure, the final shell weight reduction ratio was 18.12% and the first-order intrinsic frequency was increased by 14.56%.
23
La Rocca, Michele, and Cira Perna. "Opening the Black Box: Bootstrapping Sensitivity Measures in Neural Networks for Interpretable Machine Learning." Stats 5, no. 2 (April 25, 2022): 440–57. http://dx.doi.org/10.3390/stats5020026.
Abstract:
Artificial neural networks are powerful tools for data analysis, particularly in the context of highly nonlinear regression models. However, their utility is critically limited due to the lack of interpretation of the model given its black-box nature. To partially address the problem, the paper focuses on the important problem of feature selection. It proposes and discusses a statistical test procedure for selecting a set of input variables that are relevant to the model while taking into account the multiple testing nature of the problem. The approach is within the general framework of sensitivity analysis and uses the conditional expectation of functions of the partial derivatives of the output with respect to the inputs as a sensitivity measure. The proposed procedure extensively uses the bootstrap to approximate the test statistic distribution under the null while controlling the familywise error rate to correct for data snooping arising from multiple testing. In particular, a pair bootstrap scheme was implemented in order to obtain consistent results when using misspecified statistical models, a typical characteristic of neural networks. Numerical examples and a Monte Carlo simulation were carried out to verify the ability of the proposed test procedure to correctly identify the set of relevant features.
24
La Rocca, Michele, and Cira Perna. "Opening the Black Box: Bootstrapping Sensitivity Measures in Neural Networks for Interpretable Machine Learning." Stats 5, no. 2 (April 25, 2022): 440–57. http://dx.doi.org/10.3390/stats5020026.
Abstract:
Artificial neural networks are powerful tools for data analysis, particularly in the context of highly nonlinear regression models. However, their utility is critically limited due to the lack of interpretation of the model given its black-box nature. To partially address the problem, the paper focuses on the important problem of feature selection. It proposes and discusses a statistical test procedure for selecting a set of input variables that are relevant to the model while taking into account the multiple testing nature of the problem. The approach is within the general framework of sensitivity analysis and uses the conditional expectation of functions of the partial derivatives of the output with respect to the inputs as a sensitivity measure. The proposed procedure extensively uses the bootstrap to approximate the test statistic distribution under the null while controlling the familywise error rate to correct for data snooping arising from multiple testing. In particular, a pair bootstrap scheme was implemented in order to obtain consistent results when using misspecified statistical models, a typical characteristic of neural networks. Numerical examples and a Monte Carlo simulation were carried out to verify the ability of the proposed test procedure to correctly identify the set of relevant features.
25
Faristasari, Selvi, and Adhitya Ronnie Effendie. "Application of Simulated Annealing Method on Tabarru-Fund Valuation using Inflator by Vasicek Model Approach Based on Profit and Loss Sharing Scheme." Indonesian Journal of Mathematics and Applications 1, no. 1 (March 27, 2023): 24–36. http://dx.doi.org/10.21776/ub.ijma.2023.001.01.4.
Abstract:
Currently, the financial services industry is dominated by conventional banks and individuals that apply the system of interest or an excess of loans. In Islam, this excess is referred to as usury, which is prohibited by Islamic law because, in practice, usury makes borrowers poorer as they cannot pay such high-interest installments. Not to mention, late payments are subject to penalties that will continue to accumulate if the borrower is unable to pay the next installment. From these facts, this system is prohibited by Islamic Law because there are harmed parties. Therefore, this research discusses mathematical models in the form of Islamic investment business loans for micro-economic traders by implementing a profit and loss sharing system. Tabarru-fund is a set of funds derived from borrowers’ contributions used to overcome conditions when they experience losses in certain conditions. In this mathematical model, the tabarru-fund acts as the premium that must be paid if the borrower is still profitable after the principal installments have paid off. This sharia model with tabarru funds is obtained by calculating the premium which involves the problem of minimizing the remaining tabarru funds in a certain period. The future value of the trader's profit rate will be projected using the Vasicek Model approach which previously determined the parameter estimation using OLS regression and then the data is generated using Monte Carlo simulation so that the sharia inflator is obtained. This sharia inflator plays a role in the optimization process of minimizing the remaining tabarru-fund which will be solved by the Simulated Annealing (SA) algorithm.
26
Habeck, Christian, Qolamreza Razlighi, and Yaakov Stern. "Predictive utility of task-related functional connectivity vs. voxel activation." PLOS ONE 16, no. 4 (April 8, 2021): e0249947. http://dx.doi.org/10.1371/journal.pone.0249947.
Abstract:
Functional connectivity, both in resting state and task performance, has steadily increased its share of neuroimaging research effort in the last 1.5 decades. In the current study, we investigated the predictive utility regarding behavioral performance and task information for 240 participants, aged 20–77, for both voxel activation and functional connectivity in 12 cognitive tasks, belonging to 4 cognitive reference domains (Episodic Memory, Fluid Reasoning, Perceptual Speed, and Vocabulary). We also added a model only comprising brain-structure information not specifically acquired during performance of a cognitive task. We used a simple brain-behavioral prediction technique based on Principal Component Analysis (PCA) and regression and studied the utility of both modalities in quasi out-of-sample predictions, using split-sample simulations (= 5-fold Monte Carlo cross validation) with 1,000 iterations for which a regression model predicting a cognitive outcome was estimated in a training sample, with a subsequent assessment of prediction success in a non-overlapping test sample. The sample assignments were identical for functional connectivity, voxel activation, and brain structure, enabling apples-to-apples comparisons of predictive utility. All 3 models that were investigated included the demographic covariates age, gender, and years of education. A minimal reference model using simple linear regression with just these 3 covariates was included for comparison as well and was evaluated with the same resampling scheme as described above. Results of the comparison between voxel activation and functional connectivity were mixed and showed some dependency on cognitive outcome; however, mean differences in predictive utility between voxel activation and functional connectivity were rather small in terms of within-modality variability or predictive success. More notably, only in the case of Fluid Reasoning did concurrent functional neuroimaging provided compelling about cognitive performance beyond structural brain imaging or the minimal reference model.
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Gianola, Daniel, and Rohan L. Fernando. "A Multiple-Trait Bayesian Lasso for Genome-Enabled Analysis and Prediction of Complex Traits." Genetics 214, no. 2 (December 26, 2019): 305–31. http://dx.doi.org/10.1534/genetics.119.302934.
Abstract:
A multiple-trait Bayesian LASSO (MBL) for genome-based analysis and prediction of quantitative traits is presented and applied to two real data sets. The data-generating model is a multivariate linear Bayesian regression on possibly a huge number of molecular markers, and with a Gaussian residual distribution posed. Each (one per marker) of the T×1 vectors of regression coefficients (T: number of traits) is assigned the same T−variate Laplace prior distribution, with a null mean vector and unknown scale matrix Σ. The multivariate prior reduces to that of the standard univariate Bayesian LASSO when T=1. The covariance matrix of the residual distribution is assigned a multivariate Jeffreys prior, and Σ is given an inverse-Wishart prior. The unknown quantities in the model are learned using a Markov chain Monte Carlo sampling scheme constructed using a scale-mixture of normal distributions representation. MBL is demonstrated in a bivariate context employing two publicly available data sets using a bivariate genomic best linear unbiased prediction model (GBLUP) for benchmarking results. The first data set is one where wheat grain yields in two different environments are treated as distinct traits. The second data set comes from genotyped Pinus trees, with each individual measured for two traits: rust bin and gall volume. In MBL, the bivariate marker effects are shrunk differentially, i.e., “short” vectors are more strongly shrunk toward the origin than in GBLUP; conversely, “long” vectors are shrunk less. A predictive comparison was carried out as well in wheat, where the comparators of MBL were bivariate GBLUP and bivariate Bayes Cπ—a variable selection procedure. A training-testing layout was used, with 100 random reconstructions of training and testing sets. For the wheat data, all methods produced similar predictions. In Pinus, MBL gave better predictions that either a Bayesian bivariate GBLUP or the single trait Bayesian LASSO. MBL has been implemented in the Julia language package JWAS, and is now available for the scientific community to explore with different traits, species, and environments. It is well known that there is no universally best prediction machine, and MBL represents a new resource in the armamentarium for genome-enabled analysis and prediction of complex traits.
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Prasanna, K., Mudassir Khan, Saeed M. Alshahrani, Ajmeera Kiran, P. Phanindra Kumar Reddy, Mofadal Alymani, and J. Chinna Babu. "Continual Learning Approach for Continuous Data Stream Analysis in Dynamic Environments." Applied Sciences 13, no. 14 (July 8, 2023): 8004. http://dx.doi.org/10.3390/app13148004.
Abstract:
Continuous data stream analysis primarily focuses on the unanticipated changes in the transmission of data distribution over time. Conceptual change is defined as the signal distribution changes over the transmission of continuous data streams. A drift detection scenario is set forth to develop methods and strategies for detecting, interpreting, and adapting to conceptual changes over data streams. Machine learning approaches can produce poor learning outcomes in the conceptual change environment if the sudden change is not addressed. Furthermore, due to developments in concept drift, learning methodologies have been significantly systematic in recent years. The research introduces a novel approach using the fully connected committee machine (FCM) and different activation functions to address conceptual changes in continuous data streams. It explores scenarios of continual learning and investigates the effects of over-learning and weight decay on concept drift. The findings demonstrate the effectiveness of the FCM framework and provide insights into improving machine learning approaches for continuous data stream analysis. We used a layered neural network framework to experiment with different scenarios of continual learning on continuous data streams in the presence of change in the data distribution using a fully connected committee machine (FCM). In this research, we conduct experiments in various scenarios using a layered neural network framework, specifically the fully connected committee machine (FCM), to address conceptual changes in continuous data streams for continual learning under a conceptual change in the data distribution. Sigmoidal and ReLU (Rectified Linear Unit) activation functions are considered for learning regression in layered neural networks. When the layered framework is trained from the input data stream, the regression scheme changes consciously in all scenarios. A fully connected committee machine (FCM) is trained to perform the tasks described in continual learning with M hidden units on dynamically generated inputs. In this method, we run Monte Carlo simulations with the same number of units on both sides, K and M, to define the advancement of intersections between several hidden units and the calculation of generalization error. This is applied to over-learnability as a method of over-forgetting, integrating weight decay, and examining its effects when a concept drift is presented.
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Kalinina, Irina A., and Aleksandr P. Gozhyj. "Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series." Applied Aspects of Information Technology 5, no. 3 (October 25, 2022): 240–55. http://dx.doi.org/10.15276/aait.05.2022.17.
Abstract:
The article describes an approach to modelling and forecasting non-linear non-stationary time series for various purposes using Bayesian structural time series. The concepts of non-linearity and non-stationarity, as well as methods for processing non-linearity’sand non-stationarity in the construction of forecasting models are considered. The features of the Bayesian approach in the processing of nonlinearities and nonstationaryare presented. An approach to the construction of probabilistic-statistical models based on Bayesian structural models of time series has been studied. Parametric and non-parametric methods for forecasting non-linear and non-stationary time series are considered. Parametric methods include methods: classical autoregressive models, neural networks, models of support vector machines, hidden Markov models. Non-parametric methods include methods: state-space models, functional decomposition models, Bayesian non-parametric models. One of the types of non-parametric models isBayesian structural time series. The main features of constructing structural time series are considered. Models of structural time series are presented. The process of learning the Bayesianstructural model of time series is described. Training is performed in four stages: setting the structure of the model and a priori probabilities; applying a Kalman filter to update state estimates based on observed data;application of the “spike-and-slab”method to select variables in a structural model; Bayesian averaging to combine the results to make a prediction. An algorithm for constructing a Bayesian structural time seriesmodel is presented. Various components of the BSTS model are considered andanalysed, with the help of which the structures of alternative predictive models are formed. As an example of the application of Bayesian structural time series, the problem of predicting Amazon stock prices is considered. The base dataset is amzn_share. After loading, the structure and data types were analysed, and missing values were processed. The data are characterized by irregular registration of observations, which leads to a large number of missing values and “masking” possible seasonal fluctuations. This makes the task of forecasting rather difficult. To restore gaps in the amzn_sharetime series, the linear interpolation method was used. Using a set of statistical tests (ADF, KPSS, PP), the series was tested for stationarity. The data set is divided into two parts: training and testing. The fitting of structural models of time series was performed using the Kalman filterand the Monte Carlo method according to the Markov chain scheme. To estimate and simultaneously regularize the regression coefficients, the spike-and-slab method was applied. The quality of predictive models was assessed.
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Barrera, David, Stéphane Crépey, Babacar Diallo, Gersende Fort, Emmanuel Gobet, and Uladzislau Stazhynski. "Stochastic approximation schemes for economic capital and risk margin computations." ESAIM: Proceedings and Surveys 65 (2019): 182–218. http://dx.doi.org/10.1051/proc/201965182.
Abstract:
We consider the problem of the numerical computation of its economic capital by an insurance or a bank, in the form of a value-at-risk or expected shortfall of its loss over a given time horizon. This loss includes the appreciation of the mark-to-model of the liabilities of the firm, which we account for by nested Monte Carlo à la Gordy and Juneja [17] or by regression à la Broadie, Du, and Moallemi [10]. Using a stochastic approximation point of view on value-at-risk and expected shortfall, we establish the convergence of the resulting economic capital simulation schemes, under mild assumptions that only bear on the theoretical limiting problem at hand, as opposed to assumptions on the approximating problems in [17] and [10]. Our economic capital estimates can then be made conditional in a Markov framework and integrated in an outer Monte Carlo simulation to yield the risk margin of the firm, corresponding to a market value margin (MVM) in insurance or to a capital valuation adjustment (KVA) in banking parlance. This is illustrated numerically by a KVA case study implemented on GPUs.
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YEASIN, M., K. N. SINGH, A. LAMA, and B. GURUNG. "Improved weather indices based Bayesian regression model for forecasting crop yield." MAUSAM 72, no. 4 (November 1, 2021): 879–86. http://dx.doi.org/10.54302/mausam.v72i4.3542.
Abstract:
As agriculture is the backbone of the Indian economy, Government needs a reliable forecast of crop yield for planning new schemes. The most extensively used technique for forecasting crop yield is regression analysis. The significance of parameters is one of the major problems of regression analysis. Non-significant parameters lead to absurd forecast values and these forecast values are not reliable. In such cases, models need to be improved. To improve the models, we have incorporated prior knowledge through the Bayesian technique and investigate the superiority of these models under the Bayesian framework. The Bayesian technique is one of the most powerful methodologies in the modern era of statistics. We have discussed different types of prior (informative, non-informative and conjugate priors). The Markov chain Monte Carlo (MCMC) methodology has been briefly discussed for the estimation of parameters under Bayesian framework. To illustrate these models, production data of banana, mango and wheat yield data are taken under consideration. We compared the traditional regression model with the Bayesian regression model and conclusively infer that the models estimated under Bayesian framework provided superior results as compared to the models estimated under the classical approach.
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YEASIN, M., K. N. SINGH, A. LAMA, and B. GURUNG. "Improved weather indices based Bayesian regression model for forecasting crop yield." MAUSAM 72, no. 4 (November 10, 2021): 879–86. http://dx.doi.org/10.54302/mausam.v72i4.670.
Abstract:
As agriculture is the backbone of the Indian economy, Government needs a reliable forecast of crop yield for planning new schemes. The most extensively used technique for forecasting crop yield is regression analysis. The significance of parameters is one of the major problems of regression analysis. Non-significant parameters lead to absurd forecast values and these forecast values are not reliable. In such cases, models need to be improved. To improve the models, we have incorporated prior knowledge through the Bayesian technique and investigate the superiority of these models under the Bayesian framework. The Bayesian technique is one of the most powerful methodologies in the modern era of statistics. We have discussed different types of prior (informative, non-informative and conjugate priors). The Markov chain Monte Carlo (MCMC) methodology has been briefly discussed for the estimation of parameters under Bayesian framework. To illustrate these models, production data of banana, mango and wheat yield data are taken under consideration. We compared the traditional regression model with the Bayesian regression model and conclusively infer that the models estimated under Bayesian framework provided superior results as compared to the models estimated under the classical approach.
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Liu, Qian, Xufang Zhang, and Xianzhen Huang. "A sparse surrogate model for structural reliability analysis based on the generalized polynomial chaos expansion." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 233, no. 3 (October 8, 2018): 487–502. http://dx.doi.org/10.1177/1748006x18804047.
Abstract:
The reliability analysis of a structural system is typically evaluated based on a multivariate model that describes the underlying mechanistic relationship between the system’s input and output random variables. This is the need to develop an effective surrogate model to mimic the input–output relationship as the Monte Carlo simulation–based on the mechanistic model might be computationally intensive. In this regard, the article presents a sparse regression method for structural reliability analysis based on the generalized polynomial chaos expansion. However, results from the global sensitivity analysis have justified that it is unnecessary to contain all polynomial terms in the surrogate model, instead of comprising a rather small number of principle components only. One direct benefit of the sparse approximation allows utilizing a small number of training samples to calibrate the surrogate model, bearing in mind that the required sample size is positively proportional to the number of unknowns in regression analysis. Therefore, by utilizing the standard polynomial chaos basis functions to constitute an explanatory dictionary, an adaptive sparse regression approach characterized by introducing the most significant explanatory variable in each iteration is presented. A statistical approach for detecting and excluding spuriously explanatory polynomials is also introduced to maintain the high sparsity of the meta-modeling result. Combined with a variety of low-discrepancy schemes in generating training samples, structural reliability and global sensitivity analysis of originally true but computationally demanding models are alternatively realized based on the sparse surrogate method in conjunction with the brutal Monte Carlo simulation method. Numerical examples are carried out to demonstrate the applicability of the sparse regression approach to structural reliability problems. Results have shown that the proposed method is an effective, non-intrusive approach to deal with uncertainty analysis of various structural systems.
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Ramnath, Vishal. "Comparison of straight line curve fit approaches for determining parameter variances and covariances." International Journal of Metrology and Quality Engineering 11 (2020): 14. http://dx.doi.org/10.1051/ijmqe/2020011.
Abstract:
Pressure balances are known to have a linear straight line equation of the form y = ax + b that relates the applied pressure x to the effective area y, and recent work has investigated the use of Ordinary Least Squares (OLS), Weighted Least Squares (WLS), and Generalized Least Squares (GLS) regression schemes in order to quantify the expected values of the zero-pressure area A0 = b and distortion coefficient λ = a/b in pressure balance models of the form y = A0(1 + λx). The limitations with conventional OLS, WLS and GLS approaches is that whilst they may be used to quantify the uncertainties u(a) and u(b) and the covariance cov(a, b), it is technically challenging to analytically quantify the covariance term cov(A0, λ) without additional Monte Carlo simulations. In this paper, we revisit an earlier Weighted Total Least Squares with Correlation (WTLSC) algorithm to determine the variances u2(a) and u2(b) along with the covariance cov(a, b), and develop a simple analytical approach to directly infer the corresponding covariance cov(A0, λ) for pressure metrology uncertainty analysis work. Results are compared to OLS, WLS and GLS approaches and indicate that the WTLSC approach may be preferable as it avoids the need for Monte Carlo simulations and additional numerical post-processing to fit and quantify the covariance term, and is thus simpler and more suitable for industrial metrology pressure calibration laboratories. Novel aspects is that a Gnu Octave/Matlab program for easily implementing the WTLSC algorithm to calculate parameter expected values, variances and covariances is also supplied and reported.
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Zhang, Qi, Yihui Zhang, and Yemao Xia. "Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations." Mathematics 12, no. 5 (March 6, 2024): 783. http://dx.doi.org/10.3390/math12050783.
Abstract:
Semi-continuous data are very common in social sciences and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of observed and/or unobserved exogenous factors on semi-continuous data. Our formulation is based on a two-part latent variable model with polytomous responses. We consider two schemes for the penalties of regression coefficients and factor loadings: a Bayesian spike and slab bimodal prior and a Bayesian lasso prior. Within the Bayesian framework, we implement a Markov chain Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model from Part One as a norm-type mixture model. A Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable values of hyperparameters, the spike and slab bimodal method slightly outperforms Bayesian lasso in the current analysis. Finally, a real example related to the Chinese Household Financial Survey is analyzed to illustrate application of the methodology.
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Mandallaz, Daniel, Jochen Breschan, and Andreas Hill. "New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: a design-based Monte Carlo approach with applications to small-area estimation." Canadian Journal of Forest Research 43, no. 11 (November 2013): 1023–31. http://dx.doi.org/10.1139/cjfr-2013-0181.
Abstract:
We consider two-phase sampling schemes where one component of the auxiliary information is known in every point (“wall-to-wall”) and a second component is available only in the large sample of the first phase, whereas the second phase yields a subsample with the terrestrial inventory. This setup is of growing interest in forest inventory thanks to the recent advances in remote sensing, in particular, the availability of LiDAR data. We propose a new two-phase regression estimator for global and local estimation and derive its asymptotic design-based variance. The new estimator performs better than the classical regression estimator. Furthermore, it can be generalized to cluster sampling and two-stage tree sampling within plots. Simulations and a case study with LiDAR data illustrate the theory.
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Nabeel, Moezza, Sajid Ali, Ismail Shah, Mohammed M. A. Almazah, and Fuad S. Al-Duais. "Robust Surveillance Schemes Based on Proportional Hazard Model for Monitoring Reliability Data." Mathematics 11, no. 11 (May 28, 2023): 2480. http://dx.doi.org/10.3390/math11112480.
Abstract:
Product reliability is a crucial component of the industrial production process. Several statistical process control techniques have been successfully employed in industrial manufacturing processes to observe changes in reliability-related quality variables. These methods, however, are only applicable to single-stage processes. In reality, manufacturing processes consist of several stages, and the quality variable of the previous stages influences the quality of the present stage. This interdependence between the stages of a multistage process is an important characteristic that must be taken into account in process monitoring. In addition, sometimes datasets contain outliers and consequently, the analysis produces biased results. This study discusses the issue of monitoring reliability data with outliers. To this end, a proportional hazard model has been assumed to model the relationship between the significant quality variables of a two-stage dependent manufacturing process. Robust regression technique known as the M-estimation has been implemented to lessen the effect of outliers present in the dataset corresponding to reliability-related quality characteristics in the second stage of the process assuming Nadarajah and Haghighi distribution. The three monitoring approaches, namely, one lower-sided cumulative sum and two one-sided exponentially weighted moving average control charts have been designed to effectively monitor the two-stage dependent process. Using Monte Carlo simulations, the efficiency of the suggested monitoring schemes has been examined. Finally, two real-world examples of the proposed control approaches are provided in the study.
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Pooley, C. M., and G. Marion. "Bayesian model evidence as a practical alternative to deviance information criterion." Royal Society Open Science 5, no. 3 (March 2018): 171519. http://dx.doi.org/10.1098/rsos.171519.
Abstract:
While model evidence is considered by Bayesian statisticians as a gold standard for model selection (the ratio in model evidence between two models giving the Bayes factor), its calculation is often viewed as too computationally demanding for many applications. By contrast, the widely used deviance information criterion (DIC), a different measure that balances model accuracy against complexity, is commonly considered a much faster alternative. However, recent advances in computational tools for efficient multi-temperature Markov chain Monte Carlo algorithms, such as steppingstone sampling (SS) and thermodynamic integration schemes, enable efficient calculation of the Bayesian model evidence. This paper compares both the capability (i.e. ability to select the true model) and speed (i.e. CPU time to achieve a given accuracy) of DIC with model evidence calculated using SS. Three important model classes are considered: linear regression models, mixed models and compartmental models widely used in epidemiology. While DIC was found to correctly identify the true model when applied to linear regression models, it led to incorrect model choice in the other two cases. On the other hand, model evidence led to correct model choice in all cases considered. Importantly, and perhaps surprisingly, DIC and model evidence were found to run at similar computational speeds, a result reinforced by analytically derived expressions.
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Butyrkin, A. Ya, V. A. Gelis, and E. B. Kulikova. "Features of application of progressive methods of predictive modeling for solving problems on transport." Herald of the Ural State University of Railway Transport, no. 4 (2021): 68–78. http://dx.doi.org/10.20291/2079-0392-2021-4-68-78.
Abstract:
The paper analyzes the potential of forecasting approaches based on progressive methods of predictive modeling in relation to the transport sector. In the context of peculiarities of Russian and foreign business practices, the possibilities of modern technologies for working with data are considered, schemes and conceptual models formalizing their specifics are formed. Characteristic features of common algorithms and methods are described, the risks and disadvantages of unjustified use of traditional predictive models on the example of simple and multiple regressions are shown. Special attention is paid to the potential of machine learning in solving applied transport problems. The author’s definition of machine learning methods is presented for consideration, characterizing their position in relation to other classes of rational approaches and methods of decision support. The prospects, advantages and challenges of using modern algorithmic implementation of the machine learning concept for forecasting are outlined by the example of analogy using Monte Carlo methods. The results of evaluation of promising models on the example of recurrent neural networks of the architecture of long-term short-term memory such as LSTM for time series forecasting, as well as the problems of introducing such models into the production practice of transport companies, are presented for consideration.
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Silalahi, Divo Dharma, Habshah Midi, Jayanthi Arasan, Mohd Shafie Mustafa, and Jean-Pierre Caliman. "Automated Fitting Process Using Robust Reliable Weighted Average on Near Infrared Spectral Data Analysis." Symmetry 12, no. 12 (December 17, 2020): 2099. http://dx.doi.org/10.3390/sym12122099.
Abstract:
With the complexity of Near Infrared (NIR) spectral data, the selection of the optimal number of Partial Least Squares (PLS) components in the fitted Partial Least Squares Regression (PLSR) model is very important. Selecting a small number of PLS components leads to under fitting, whereas selecting a large number of PLS components results in over fitting. Several methods exist in the selection procedure, and each yields a different result. However, so far no one has been able to determine the more superior method. In addition, the current methods are susceptible to the presence of outliers and High Leverage Points (HLP) in a dataset. In this study, a new automated fitting process method on PLSR model is introduced. The method is called the Robust Reliable Weighted Average—PLS (RRWA-PLS), and it is less sensitive to the optimum number of PLS components. The RRWA-PLS uses the weighted average strategy from multiple PLSR models generated by the different complexities of the PLS components. The method assigns robust procedures in the weighing schemes as an improvement to the existing Weighted Average—PLS (WA-PLS) method. The weighing schemes in the proposed method are resistant to outliers and HLP and thus, preserve the contribution of the most relevant variables in the fitted model. The evaluation was done by utilizing artificial data with the Monte Carlo simulation and NIR spectral data of oil palm (Elaeis guineensis Jacq.) fruit mesocarp. Based on the results, the method claims to have shown its superiority in the improvement of the weight and variable selection procedures in the WA-PLS. It is also resistant to the influence of outliers and HLP in the dataset. The RRWA-PLS method provides a promising robust solution for the automated fitting process in the PLSR model as unlike the classical PLS, it does not require the selection of an optimal number of PLS components.
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Naz, Aqdas, Muhammad Javed, Nadeem Javaid, Tanzila Saba, Musaed Alhussein, and Khursheed Aurangzeb. "Short-Term Electric Load and Price Forecasting Using Enhanced Extreme Learning Machine Optimization in Smart Grids." Energies 12, no. 5 (March 5, 2019): 866. http://dx.doi.org/10.3390/en12050866.
Abstract:
A Smart Grid (SG) is a modernized grid to provide efficient, reliable and economic energy to the consumers. Energy is the most important resource in the world. An efficient energy distribution is required as smart devices are increasing dramatically. The forecasting of electricity consumption is supposed to be a major constituent to enhance the performance of SG. Various learning algorithms have been proposed to solve the forecasting problem. The sole purpose of this work is to predict the price and load efficiently. The first technique is Enhanced Logistic Regression (ELR) and the second technique is Enhanced Recurrent Extreme Learning Machine (ERELM). ELR is an enhanced form of Logistic Regression (LR), whereas, ERELM optimizes weights and biases using a Grey Wolf Optimizer (GWO). Classification and Regression Tree (CART), Relief-F and Recursive Feature Elimination (RFE) are used for feature selection and extraction. On the basis of selected features, classification is performed using ELR. Cross validation is done for ERELM using Monte Carlo and K-Fold methods. The simulations are performed on two different datasets. The first dataset, i.e., UMass Electric Dataset is multi-variate while the second dataset, i.e., UCI Dataset is uni-variate. The first proposed model performed better with UMass Electric Dataset than UCI Dataset and the accuracy of second model is better with UCI than UMass. The prediction accuracy is analyzed on the basis of four different performance metrics: Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Mean Square Error (MSE) and Root Mean Square Error (RMSE). The proposed techniques are then compared with four benchmark schemes. The comparison is done to verify the adaptivity of the proposed techniques. The simulation results show that the proposed techniques outperformed benchmark schemes. The proposed techniques efficiently increased the prediction accuracy of load and price. However, the computational time is increased in both scenarios. ELR achieved almost 5% better results than Convolutional Neural Network (CNN) and almost 3% than LR. While, ERELM achieved almost 6% better results than ELM and almost 5% than RELM. However, the computational time is almost 20% increased with ELR and 50% with ERELM. Scalability is also addressed for the proposed techniques using half-yearly and yearly datasets. Simulation results show that ELR gives 5% better results while, ERELM gives 6% better results when used for yearly dataset.
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Kadarmideen, H. N., R. Rekaya, and D. Gianola. "Genetic parameters for clinical mastitis in Holstein-Friesians in the United Kingdom: a Bayesian analysis." Animal Science 73, no. 2 (October 2001): 229–40. http://dx.doi.org/10.1017/s1357729800058203.
Abstract:
AbstractA Bayesian threshold-liability model with Markov chain Monte Carlo techniques was used to infer genetic parameters for clinical mastitis records collected on Holstein-Friesian cows by one of the United Kingdom’s national recording schemes. Four data sets were created to investigate the effect of data sampling methods on genetic parameter estimates for first and multi-lactation cows, separately. The data sets were: (1) cows with complete first lactations only (8671 cows); (2) all cows, with first lactations whether complete or incomplete (10 967 cows); (3) cows with complete multi-lactations (32 948 records); and (4) all cows with multiple lactations whether complete or incomplete (44 268 records). A Gaussian mixed linear model with sire effects was adopted for liability. Explanatory variables included in the model varied for each data set. Analyses were conducted using Gibbs sampling and estimates were on the liability scale. Posterior means of heritability for clinical mastitis were higher for first lactations (0·11 and 0·10 for data sets 1 and 2, respectively) than for multiple lactations (0·09 and 0·07, for data sets 3 and 4, respectively). For multiple lactations, estimates of permanent environmental variance were higher for complete than incomplete lactations. Repeatability was 0·21 and 0·17 for data sets 3 and 4, respectively. This suggests the existence of effects, other than additive genetic effects, on susceptibility to mastitis that are common to all lactations. In first or multi-lactation data sets, heritability was proportionately 0·10 to 0·19 lower for data sets with all records (in which case the models had days in milk as a covariate) than for data with only complete lactation records (models without days in milk as a covariate). This suggests an effect of data sampling on genetic parameter estimates. The regression of liability on days in milk differed from zero, indicating that the probability of mastitis is higher for longer lactations, as expected. Results also indicated that a regression on days in milk should be included in a model for genetic evaluation of sires for mastitis resistance based on records in progress.
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Li, Xiaofei, Yi Wu, Quanxin Zhu, Songbo Hu, and Chuan Qin. "A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations." Advances in Difference Equations 2021, no. 1 (April 16, 2021). http://dx.doi.org/10.1186/s13662-021-03361-5.
Abstract:
AbstractThe purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.
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De Bortoli, Valentin, Alain Durmus, Marcelo Pereyra, and Ana F. Vidal. "Efficient stochastic optimisation by unadjusted Langevin Monte Carlo." Statistics and Computing 31, no. 3 (March 19, 2021). http://dx.doi.org/10.1007/s11222-020-09986-y.
Abstract:
AbstractStochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric empirical Bayesian estimation. Combined with Markov chain Monte Carlo algorithms, these stochastic optimisation methods have been successfully applied to a wide range of problems in science and industry. However, this strategy scales poorly to large problems because of methodological and theoretical difficulties related to using high-dimensional Markov chain Monte Carlo algorithms within a stochastic approximation scheme. This paper proposes to address these difficulties by using unadjusted Langevin algorithms to construct the stochastic approximation. This leads to a highly efficient stochastic optimisation methodology with favourable convergence properties that can be quantified explicitly and easily checked. The proposed methodology is demonstrated with three experiments, including a challenging application to statistical audio analysis and a sparse Bayesian logistic regression with random effects problem.
45
Riebl, Hannes, Nadja Klein, and Thomas Kneib. "Modelling intra-annual tree stem growth with a distributional regression approach for Gaussian process responses." Journal of the Royal Statistical Society Series C: Applied Statistics, March 22, 2023. http://dx.doi.org/10.1093/jrsssc/qlad015.
Abstract:
AbstractHigh-resolution circumference dendrometers measure the irreversible growth and the reversible shrinking and swelling due to the water content of a tree stem. We propose a novel statistical method to decompose these measurements into a permanent and a temporary component, while explaining differences between the trees and years by covariates. Our model embeds Gaussian processes with parametric mean and covariance functions as response structures in a distributional regression framework with structured additive predictors. We discuss different mean and covariance functions, connections with other model classes, Markov chain Monte Carlo inference, and the efficiency of our sampling scheme.
46
Khan, Sajid Ali, Sayyad Khurshid, Tooba Akhtar, and Kashmala Khurshid. "Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme." Qubahan Academic Journal 1, no. 1 (February 15, 2021). http://dx.doi.org/10.48161/qaj.v1n1a22.
Abstract:
In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators.
By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations.
By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.
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Zhu, Yu, Yinhao Wang, Quanyi Yu, Dayong Wu, Yang Zhang, and Tong Zhang. "Uncertainty Quantification and Global Sensitivity Analysis of Radiated Susceptibility in Multiconductor Transmission Lines using Adaptive Sparse Polynomial Chaos Expansions." Applied Computational Electromagnetics Society Journal (ACES), November 23, 2021. http://dx.doi.org/10.13052/2021.aces.j.361004.
Abstract:
This study analyzes the uncertainties of the radiated susceptibility in multiconductor transmission lines (MTLs), and introduces an adaptive sparse polynomial chaos expansion combining hyperbolic truncation scheme with orthogonal matching pursuit method (AS-PCE (OMP)). This method is used as the basis to realize the uncertainty quantification (UQ) of radiated susceptibility and global sensitivity analysis (GSA) of input variables to output variables. GSA considers the influencing factors of the incident field and transmission-line geometric parameters. The global sensitivity indices of each input variable are calculated for varying impedance loads. The accuracy and efficiency of the proposed method are verified compared with the results of the polynomial chaos expansion based least angle regression method and Monte Carlo methods.
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La Rocca, Michele, Marcella Niglio, and Marialuisa Restaino. "Bootstrapping binary GEV regressions for imbalanced datasets." Computational Statistics, February 4, 2023. http://dx.doi.org/10.1007/s00180-023-01330-y.
Abstract:
AbstractThis paper proposes and discusses a bootstrap scheme to make inferences when an imbalance in one of the levels of a binary variable affects both the dependent variable and some of the features. Specifically, the imbalance in the binary dependent variable is managed by adopting an asymmetric link function based on the quantile of the generalized extreme value (GEV) distribution, leading to a class of models called GEV regression. Within this framework, we propose using the fractional-random-weighted (FRW) bootstrap to obtain confidence intervals and implement a multiple testing procedure to identifying the set of relevant features. The main advantages of FRW bootstrap are as follows: (1) all observations belonging to the imbalanced class are always present in every bootstrap resample; (2) the bootstrap can be applied even when the complexity of the link function does not allow to easily compute second-order derivatives for the Hessian; (3) the bootstrap resampling scheme does not change whatever the link function is, and can be applied beyond the GEV link function used in this study. The performance of the FRW bootstrap in GEV regression modelling is evaluated using a detailed Monte Carlo simulation study, where the imbalance is present in the dependent variable and features. An application of the proposed methodology to a real dataset to analyze student churn in an Italian university is also discussed.
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Aßmann, Christian, Jean-Christoph Gaasch, and Doris Stingl. "A Bayesian Approach Towards Missing Covariate Data in Multilevel Latent Regression Models." Psychometrika, November 23, 2022. http://dx.doi.org/10.1007/s11336-022-09888-0.
Abstract:
AbstractThe measurement of latent traits and investigation of relations between these and a potentially large set of explaining variables is typical in psychology, economics, and the social sciences. Corresponding analysis often relies on surveyed data from large-scale studies involving hierarchical structures and missing values in the set of considered covariates. This paper proposes a Bayesian estimation approach based on the device of data augmentation that addresses the handling of missing values in multilevel latent regression models. Population heterogeneity is modeled via multiple groups enriched with random intercepts. Bayesian estimation is implemented in terms of a Markov chain Monte Carlo sampling approach. To handle missing values, the sampling scheme is augmented to incorporate sampling from the full conditional distributions of missing values. We suggest to model the full conditional distributions of missing values in terms of non-parametric classification and regression trees. This offers the possibility to consider information from latent quantities functioning as sufficient statistics. A simulation study reveals that this Bayesian approach provides valid inference and outperforms complete cases analysis and multiple imputation in terms of statistical efficiency and computation time involved. An empirical illustration using data on mathematical competencies demonstrates the usefulness of the suggested approach.
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Washaya, S., B. Masunda, and N. T. Ngongoni. "Impact and adoption of feed technologies at Nharira-Lancashire Dairy Scheme." Journal of Applied Animal Nutrition, March 26, 2024, 1–8. http://dx.doi.org/10.1163/2049257x-20231002.
Abstract:
Abstract The objective of this study was to investigate the impact and adoption of nutrition technologies and their effect on milk production at the Nharira-Lancashire dairy scheme. Sixty households (30 from each scheme) were randomly selected and interviewed by use of a semi-structured questionnaire. Fisher’s exact and Monte Carlo tests were carried out to determine the association between farmer experience and feed technology. Logistic regression was used to rank farmers’ awareness and adoption of feed technologies. The results indicated that farmers have been exposed to at least five new feed technologies and adoption is influenced by education status, sex, age and gender of household head (P < 0.05). Feed technology adoption was in the order: silage 70.83% > sunflower cake 41.66% > legume reinforcement 27.1% > legume trees 16.66% > napier fodder 8.33% > urea treatment 4.17%. Milk yield was affected by month and year (P < 0.05). The impact of adoption was below anticipation, as indicated by lack of economic surpluses. A cost-benefit analysis needs to be carried out for all feed technologies within the study area to streamline viable options.