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Journal articles on the topic 'Bayes power'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Mugdadi, Abdel-Razzaq, and Min A. "Bayes estimation of the power hazard function." Journal of Interdisciplinary Mathematics 12, no. 5 (October 2009): 675–89. http://dx.doi.org/10.1080/09720502.2009.10700653.

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2

McKenzie, Craig R. M. "Bayes plus environment." Behavioral and Brain Sciences 32, no. 1 (February 2009): 93–94. http://dx.doi.org/10.1017/s0140525x09000399.

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AbstractOaksford & Chater's (O&C's) account of deductive reasoning is parsimonious at a local level (because a rational model is used to explain a wide range of behavior) and at a global level (because their Bayesian approach connects to other areas of research). Their emphasis on environmental structure is especially important, and the power of their approach is seen at both the computational and algorithmic levels.

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3

Calabria, R., and G. Pulcini. "Bayes inference for the modulated power law process." Communications in Statistics - Theory and Methods 26, no. 10 (January 1997): 2421–38. http://dx.doi.org/10.1080/03610929708832057.

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4

Kim, Hyungchul, and Chanan Singh. "Power system probabilistic security assessment using Bayes classifier." Electric Power Systems Research 74, no. 1 (April 2005): 157–65. http://dx.doi.org/10.1016/j.epsr.2004.10.004.

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5

Lerche, Hans Rudolf. "The Shape of Bayes Tests of Power One." Annals of Statistics 14, no. 3 (September 1986): 1030–48. http://dx.doi.org/10.1214/aos/1176350048.

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6

Ghosh, Abhik, and Ayanendranath Basu. "Robust Bayes estimation using the density power divergence." Annals of the Institute of Statistical Mathematics 68, no. 2 (January 1, 2015): 413–37. http://dx.doi.org/10.1007/s10463-014-0499-0.

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7

Brown, Timothy M. "Automated p-mode identification using Bayes' theorem." Symposium - International Astronomical Union 123 (1988): 491–94. http://dx.doi.org/10.1017/s0074180900158590.

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The task of interpreting p-mode spectra is complicated by the presence of a very large number of oscillation modes, each of which may appear (because of aliasing) in the power spectra corresponding to several values of l and m. Identifying peaks in a power spectrum with particular modes in an interactive fashion thus quickly becomes impractical. Here I describe an automated method for doing this identification. The method is based on an application of Bayes' theorem, which provides a simple way to use prior knowledge about the oscillation spectrum. The method takes as input the observed power spectra, and a model of the amplitudes and frequencies one expects to see.

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Liu, Yang, Majid Khan, Syed Masroor Anwar, Zahid Rasheed, and Navid Feroze. "Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution." Mathematical Problems in Engineering 2022 (June 24, 2022): 1–12. http://dx.doi.org/10.1155/2022/5509684.

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The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the Bayes estimates of two-parameter power function distribution under progressive censoring. Different progressive censoring schemes have been used for the analysis. The Bayes estimates are obtained, using conjugate priors, under five loss functions including square error, precautionary, weighted, LINEX, and DeGroot loss function. The Gibbs sampling algorithm and Tierney and Kadane’s Approximation are used for the Bayes estimates of model parameters, reliability function, and stress-strength reliability. The comparison of the Bayes estimates is considered through the root mean squared errors. One real-life dataset is analyzed to illustrate the applications of proposed estimates. The results from the simulation study and real data analysis suggest that the Bayes estimation was more efficient for the progressive censoring schemes with all the withdrawals at the time of first failure.

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9

Sugasawa, S. "Robust empirical Bayes small area estimation with density power divergence." Biometrika 107, no. 2 (January 29, 2020): 467–80. http://dx.doi.org/10.1093/biomet/asz075.

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Summary A two-stage normal hierarchical model called the Fay–Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.

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10

Gravestock, Isaac, and Leonhard Held. "Adaptive power priors with empirical Bayes for clinical trials." Pharmaceutical Statistics 16, no. 5 (June 2, 2017): 349–60. http://dx.doi.org/10.1002/pst.1814.

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11

Pak, Abbas, Arjun Kumar Gupta, and Nayereh Bagheri Khoolenjani. "On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution." Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 251–67. http://dx.doi.org/10.15446/rce.v41n2.69621.

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In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided.

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12

Calabria, R., M. Guida, and G. Pulcini. "Bayes estimation of prediction intervals for a power law process." Communications in Statistics - Theory and Methods 19, no. 8 (January 1990): 3023–35. http://dx.doi.org/10.1080/03610929008830362.

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13

Quatto, Piero, Nicolò Margaritella, Isa Costantini, Francesca Baglio, Massimo Garegnani, Raffaello Nemni, and Luigi Pugnetti. "Brain networks construction using Bayes FDR and average power function." Statistical Methods in Medical Research 29, no. 3 (May 14, 2019): 866–78. http://dx.doi.org/10.1177/0962280219844288.

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Brain functional connectivity is a widely investigated topic in neuroscience. In recent years, the study of brain connectivity has been largely aided by graph theory. The link between time series recorded at multiple locations in the brain and the construction of a graph is usually an adjacency matrix. The latter converts a measure of the connectivity between two time series, typically a correlation coefficient, into a binary choice on whether the two brain locations are functionally connected or not. As a result, the choice of a threshold τ over the correlation coefficient is key. In the present work, we propose a multiple testing approach to the choice of τ that uses the Bayes false discovery rate and a new estimator of the statistical power called average power function to balance the two types of statistical error. We show that the proposed average power function estimator behaves well both in case of independence and weak dependence of the tests and it is reliable under several simulated dependence conditions. Moreover, we propose a robust method for the choice of τ using the 5% and 95% percentiles of the average power function and False Discovery Rate bootstrap distributions, respectively, to improve stability. We applied our approach to functional magnetic resonance imaging and high density electroencephalogram data.

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14

De Santis, Fulvio. "Alternative Bayes factors: Sample size determination and discriminatory power assessment." TEST 16, no. 3 (April 4, 2007): 504–22. http://dx.doi.org/10.1007/s11749-006-0017-7.

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Barros, Wysterlânya K. P., Matheus T. Barbosa, Leonardo A. Dias, and Marcelo A. C. Fernandes. "Fully Parallel Proposal of Naive Bayes on FPGA." Electronics 11, no. 16 (August 17, 2022): 2565. http://dx.doi.org/10.3390/electronics11162565.

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This work proposes a fully parallel hardware architecture of the Naive Bayes classifier to obtain high-speed processing and low energy consumption. The details of the proposed architecture are described throughout this work. Besides, a fixed-point implementation on a Stratix V Field Programmable Gate Array (FPGA) is presented and evaluated regarding the hardware area occupation, processing time (throughput), and dynamic power consumption. In addition, a comparative design analysis was carried out with state-of-the-art works, showing that the proposed implementation achieved a speedup of up to 104× and power savings of up to 107×-times while also reducing the hardware occupancy by up to 102×-times fewer logic cells.

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Liu, Benmei, and Partha Lahiri. "Adaptive Hierarchical Bayes Estimation of Small Area Proportions." Calcutta Statistical Association Bulletin 69, no. 2 (September 26, 2017): 150–64. http://dx.doi.org/10.1177/0008068317722293.

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Unit-level logistic regression models with mixed effects have been used for estimating small area proportions in the literature. Normality is commonly assumed for the random effects. Nonetheless, real data often show significant departures from normality assumptions of the random effects. To reduce the risk of model misspecification, we propose an adaptive hierarchical Bayes estimation approach in which the distribution of the random effect is chosen adaptively from the exponential power class of probability distributions. The richness of the exponential power class ensures the robustness of our hierarchical Bayes approach against departure from normality. We demonstrate the robustness of our proposed model using both simulated and real data. The results suggest that the proposed model works reasonably well to incorporate potential kurtosis of the random effects distribution.

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17

Puviarasi, R., and D. Dhanasekaran. "An integrated bayes soft switching interleaved and sliding window PWM for DC-DC boost converter." International Journal of Engineering & Technology 7, no. 3.6 (July 4, 2018): 249. http://dx.doi.org/10.14419/ijet.v7i3.6.14982.

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In order to develop the efficient dc-dc boost converter in high output power application, an Integrated Bayes Interleaved and Sliding Window (IBI-SW) based PWM framework is proposed. Initially, the integration of interleaving and PWM improves the power factor correction in very high output power applications (photovoltaic panels) and near optimal voltage and current losses. Multiple phase shifts with soft switched Bayes interleaving technique maximizes the power generated in photovoltaic panels and the optimization of power conversion is achieved with sliding window based PWM that performs Maximum Power Point Tracking (MPPT) algorithm on the PV cells connected to the converter. The proposed dc-dc boost converter is efficiently tested on various load conditions for measuring the scalability of IBI-SW framework in multiple high power demanded application. When compared with traditional model, the simulation result of proposed IBI-SW based PWM framework demonstrates that the dc-dc converter improves the power generated in photovoltaic panels accurately and rapidly.

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18

Meshram, Sameer, Shital Dongre, and Triveni Fole. "Disease Prediction System using naïve bayes." International Journal for Research in Applied Science and Engineering Technology 10, no. 12 (December 31, 2022): 1492–96. http://dx.doi.org/10.22214/ijraset.2022.48002.

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Abstract: Accurate and on-time analysis of any health-re- lated problem is vital for the prevention and treatment of the illness. The standard way of diagnosis might not be suf-ficient. Developing a diagnosis system with machine learn- ing (ML) algorithms for prediction of any disease can helpina very more accurate diagnosis than the traditional method.The proposed model is an Disease Prediction System with the help of machine learning algorithm Naive Bayes which takes the symptoms as the input and it gives the output as predicted disease. It results in saving time and also makes it easy to induce a warning about your health before it’s too late. By using this model anyone can get the result as pre- dicted disease by simply given the symptoms as input. The accuracy of this model is more than existing models.

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19

Bagchi, S. B., and P. Sarkar. "Bayes Interval Estimation for the Shape Parameter of the Power Distribution." IEEE Transactions on Reliability 35, no. 4 (1986): 396–98. http://dx.doi.org/10.1109/tr.1986.4335481.

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20

Rodrigues, Alexandre, Lucas Martinuzzo, Flavio Miguel Varejao, Vítor E. Silva Souza, and Thiago Oliveira-Santos. "Reducing power companies billing costs via empirical bayes and seasonality remover." Engineering Applications of Artificial Intelligence 81 (May 2019): 387–96. http://dx.doi.org/10.1016/j.engappai.2019.01.007.

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21

Andrews, Isaiah, and Anna Mikusheva. "Optimal Decision Rules for Weak GMM." Econometrica 90, no. 2 (2022): 715–48. http://dx.doi.org/10.3982/ecta18678.

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This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically‐motivated class of priors which give rise to quasi‐Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi‐Bayes approach regardless of model identification status, and we recommend quasi‐Bayes for settings where identification is a concern. We further propose weighted average power‐optimal identification‐robust frequentist tests and confidence sets, and prove a Bernstein‐von Mises‐type result for the quasi‐Bayes posterior under weak identification.

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22

Kim, Gyeongmin, and Jin Hur. "A Short-Term Power Output Forecasting Based on Augmented Naïve Bayes Classifiers for High Wind Power Penetrations." Sustainability 13, no. 22 (November 17, 2021): 12723. http://dx.doi.org/10.3390/su132212723.

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Renewable-power-generating resources can provide unlimited clean energy and emit at most minute amounts of air pollutants and greenhouse gases, whereas fossil fuels are contributing to environmental pollution problems and climate change. The share of global power capacity comprising renewable-power-generating resources is increasing. However, due to the variability and uncertainty of wind resources, predicting the power output of these resources remains a key problem that must be resolved to establish stable power system operation and planning. In this study, we propose an ensemble prediction model for wind-power-generating resources based on augmented naïve Bayes classifiers. To select the principal component that affects the wind power outputs from among various meteorological factors, such as temperature, wind speed, and wind direction, prediction of wind-power-generating resources was performed using multiple linear regression (MLR) and a naïve Bayes classification model based on the selected meteorological factors. We proposed applying the analogue ensemble (AnEn) algorithm and the ensemble learning technique to predict the wind power. To validate this proposed hybrid prediction model, we analyzed empirical data from the wind farm of Jeju Island in South Korea and found that the proposed model has lower error than the single prediction models.

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23

SHRINER, DANIEL. "Mapping multiple quantitative trait loci under Bayes error control." Genetics Research 91, no. 3 (June 2009): 147–59. http://dx.doi.org/10.1017/s001667230900010x.

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SummaryIn mapping of quantitative trait loci (QTLs), performing hypothesis tests of linkage to a phenotype of interest across an entire genome involves multiple comparisons. Furthermore, linkage among loci induces correlation among tests. Under many multiple comparison frameworks, these problems are exacerbated when mapping multiple QTLs. Traditionally, significance thresholds have been subjectively set to control the probability of detecting at least one false positive outcome, although such thresholds are known to result in excessively low power to detect true positive outcomes. Recently, false discovery rate (FDR)-controlling procedures have been developed that yield more power both by relaxing the stringency of the significance threshold and by retaining more power for a given significance threshold. However, these procedures have been shown to perform poorly for mapping QTLs, principally because they ignore recombination fractions between markers. Here, I describe a procedure that accounts for recombination fractions and extends FDR control to include simultaneous control of the false non-discovery rate, i.e. the overall error rate is controlled. This procedure is developed in the Bayesian framework using a direct posterior probability approach. Data-driven significance thresholds are determined by minimizing the expected loss. The procedure is equivalent to jointly maximizing positive and negative predictive values. In the context of mapping QTLs for experimental crosses, the procedure is applicable to mapping main effects, gene–gene interactions and gene–environment interactions.

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Zhao, Dengfu, Zheng Zhao, Qihong Duan, and Gongnan Xie. "A Poisson-Fault Model for Testing Power Transformers in Service." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/945258.

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This paper presents a method for assessing the instant failure rate of a power transformer under different working conditions. The method can be applied to a dataset of a power transformer under periodic inspections and maintenance. We use a Poisson-fault model to describe failures of a power transformer. When investigating a Bayes estimate of the instant failure rate under the model, we find that complexities of a classical method and a Monte Carlo simulation are unacceptable. Through establishing a new filtered estimate of Poisson process observations, we propose a quick algorithm of the Bayes estimate of the instant failure rate. The proposed algorithm is tested by simulation datasets of a power transformer. For these datasets, the proposed estimators of parameters of the model have better performance than other estimators. The simulation results reveal the suggested algorithms are quickest among three candidates.

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Khalyasmaa, Alexandra I., Stepan A. Dmitriev, and Sergey E. Kokin. "Assessment of Power Transformers Technical State Based on Technical Diagnostics." Applied Mechanics and Materials 492 (January 2014): 218–22. http://dx.doi.org/10.4028/www.scientific.net/amm.492.218.

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This paper deals with power transformers technical state assessment based on technical diagnostics using Bayes method. Present a model for integral power transformers technical state assessment on the three types of technical diagnostics. Determining state of power transformers is based on expert judgment using the membership functions.

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Neumann, P. E. "Three-locus linkage analysis using recombinant inbred strains and Bayes' theorem." Genetics 128, no. 3 (July 1, 1991): 631–38. http://dx.doi.org/10.1093/genetics/128.3.631.

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Abstract Recombinant inbred (RI) strains are useful in linkage analysis and gene mapping. However, the generally small number of strains in an RI strain set limits the power of RI strains in linkage detection. Several methods for increasing the power of RI strains have been used, including summing data across RI strain sets and excluding linkage to genomic regions. In this paper, Bayesian analysis is applied to three-locus linkage data. This method further increases the power of RI strains to detect linkage and gives estimations of the probability of each of the three possible gene orders if the test locus is linked to the pair of marker loci. Several examples are presented, including reconsideration of the position of the proto-oncogene L-myc on the mouse linkage map.

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Aris-Brosou, Stéphane. "Identifying sites under positive selection with uncertain parameter estimates." Genome 49, no. 7 (July 1, 2006): 767–76. http://dx.doi.org/10.1139/g06-038.

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Codon-based substitution models are routinely used to measure selective pressures acting on protein-coding genes. To this effect, the nonsynonymous to synonymous rate ratio (dN/dS = ω) is estimated. The proportion of amino-acid sites potentially under positive selection, as indicated by ω > 1, is inferred by fitting a probability distribution where some sites are permitted to have ω > 1. These sites are then inferred by means of an empirical Bayes or by a Bayes empirical Bayes approach that, respectively, ignores or accounts for sampling errors in maximum-likelihood estimates of the distribution used to infer the proportion of sites with ω > 1. Here, we extend a previous full-Bayes approach to include models with high power and low false-positive rates when inferring sites under positive selection. We propose some heuristics to alleviate the computational burden, and show that (i) full Bayes can be superior to empirical Bayes when analyzing a small data set or small simulated data, (ii) full Bayes has only a small advantage over Bayes empirical Bayes with our small test data, and (iii) Bayesian methods appear relatively insensitive to mild misspecifications of the random process generating adaptive evolution in our simulations, but in practice can prove extremely sensitive to model specification. We suggest that the codon model used to detect amino acids under selection should be carefully selected, for instance using Akaike information criterion (AIC).Key words: codon substitution models, empirical Bayes, Bayes empirical Bayes, full Bayes, ROC curves, AIC.

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Nassar, Mazen, Refah Alotaibi, and Ahmed Elshahhat. "Statistical Analysis of Alpha Power Exponential Parameters Using Progressive First-Failure Censoring with Applications." Axioms 11, no. 10 (October 13, 2022): 553. http://dx.doi.org/10.3390/axioms11100553.

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This paper is an endeavor to investigate some estimation problems of the unknown parameters and some reliability measures of the alpha power exponential distribution in the presence of progressive first-failure censored data. In this regard, the classical and Bayesian approaches are considered to acquire the point and interval estimates of the different quantities. The maximum likelihood approach is proposed to obtain the estimates of the unknown parameters, reliability, and hazard rate functions. The approximate confidence intervals are also considered. The Bayes estimates are obtained by considering both symmetric and asymmetric loss functions. The Bayes estimates and the associated highest posterior density credible intervals are given by applying the Monte Carlo Markov Chain technique. Due to the complexity of the given estimators which cannot be compared theoretically, a simulation study is implemented to compare the performance of the different procedures. In addition, diverse optimality criteria are employed to pick the best progressive censoring plans. Two engineering applications are considered to illustrate the applicability of the offered estimators. The numerical outcomes showed that the Bayes estimates based on symmetric or asymmetric loss functions perform better than other estimates in terms of minimum root mean square errors and interval lengths.

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Wan, Xin Wang, and Juan Liang. "Speaker Localization in Reverberant Noisy Environment Using Principal Eigenvector and Classifier." Applied Mechanics and Materials 433-435 (October 2013): 416–19. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.416.

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Sound source localization is essential in many microphone arrays application, ranging from speech enhancement to human-computer interface. The steered response power (SRP) using the phase transform (SRP-PHAT) method has been proved robust, but the algorithm may fail to locate the sound source in highly reverberant noisy environment. The Naive-Bayes localization algorithm based on classification of cross-correlation functions outperforms the SRP-PHAT in highly reverberant noisy environment. This paper proposes the improved Naive-Bayes localization algorithm using principal eigenvector. Simulation results have demonstrated that the proposed algorithm provides higher localization accuracy than the Naive-Bayes algorithm in reverberant noisy environment.

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Revathi, G., K. Nageswara Rao, and G. Sita Ratnam. "Email Spam Detection using Naïve Bayes Algorithm." International Journal for Research in Applied Science and Engineering Technology 10, no. 9 (September 30, 2022): 653–55. http://dx.doi.org/10.22214/ijraset.2022.46654.

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Abstract: Email Spam has become a vital issue currently, with high-speed growth of internet users. Some people are using them for illegal conducts, phishing and fraud. Sending malicious link through spam emails which can harm our system and may also they will seek into our system. The need of email spam detection is to prevent spam messages from lagging into user’s inbox so it’ll improve user experience. This project will identify those spam emails by using machine learning approach. Machine learning is one amongst the applications of Artificial Intelligence that allow systems to read and improve from experience without being specific programmed. This paper will discuss the machine learning algorithm which is Naïve Bayes. It is a probabilistic classifier, which means it predicts on the idea of the probability of an object and it is selected for the email spam detection having best precision and accuracy.

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Jiang, Yuanyuan, and Xingzhong Xu. "A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor." Mathematics 10, no. 10 (May 19, 2022): 1741. http://dx.doi.org/10.3390/math10101741.

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In classical statistics, the primary test statistic is the likelihood ratio. However, for high dimensional data, the likelihood ratio test is no longer effective and sometimes does not work altogether. By replacing the maximum likelihood with the integral of the likelihood, the Bayes factor is obtained. The posterior Bayes factor is the ratio of the integrals of the likelihood function with respect to the posterior. In this paper, we investigate the performance of the posterior Bayes factor in high dimensional hypothesis testing through the problem of testing the equality of two multivariate normal mean vectors. The asymptotic normality of the linear function of the logarithm of the posterior Bayes factor is established. Then we construct a test with an asymptotically nominal significance level. The asymptotic power of the test is also derived. Simulation results and an application example are presented, which show good performance of the test. Hence, taking the posterior Bayes factor as a statistic in high dimensional hypothesis testing is a reasonable methodology.

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Rahman, Habibur, M. K. Roy, and Atikur Rahman Baizid. "Bayes Estimation under Conjugate Prior for the Case of Power Function Distribution." American Journal of Mathematics and Statistics 2, no. 3 (May 9, 2012): 44–48. http://dx.doi.org/10.5923/j.ajms.20120203.06.

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Chen, Zhao. "Empirical Bayes Analysis on the Power Law Process with Natural Conjugate Priors." Journal of Data Science 8, no. 1 (July 10, 2021): 139–49. http://dx.doi.org/10.6339/jds.2010.08(1).552.

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Lingham, Rama T., and S. Sivaganesan. "Intrinsic Bayes factor approach to a test for the power law process." Journal of Statistical Planning and Inference 77, no. 2 (March 1999): 195–220. http://dx.doi.org/10.1016/s0378-3758(98)00181-5.

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Lu, Chi-Ken, and Patrick Shafto. "Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning." Entropy 23, no. 11 (October 23, 2021): 1387. http://dx.doi.org/10.3390/e23111387.

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It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

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Li, Naiyi, Yuan Li, Yongming Li, and Yang Liu. "Empirical Bayes Inference for the Parameter of Power Distribution Based on Ranked Set Sampling." Discrete Dynamics in Nature and Society 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/760768.

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37

Mahamdi, Yassine, Ahmed Boubakeur, Abdelouahab Mekhaldi, and Youcef Benmahamed. "Power Transformer Fault Prediction using Naive Bayes and Decision tree based on Dissolved Gas Analysis." ENP Engineering Science Journal 2, no. 1 (July 29, 2022): 1–5. http://dx.doi.org/10.53907/enpesj.v2i1.63.

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Power transformers are the basic elements of the power grid, which is directly related to the reliability of the electrical system. Many techniques were used to prevent power transformer failures, but the Dissolved Gas Analysis (DGA) remains the most effective one. Based on the DGA technique, this paper describes the use of two of the most effective machine learning algorithms: Naive Bayes and Decision Tree for the identification of power transformer’s faults. In our investigation, 9 different input vectors have been developed from widely known DGA techniques. 481 samples have been used and 6 types of faults have been considered. The evaluation result of the implementation of the proposed methods shows an effectiveness of 86.25% in power transformer’s fault recognition.

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Rao, Arun Kumar, and Himanshu Pandey. "BAYESIAN ESTIMATION OF SHAPE PARAMETER OF POWER LOMAX DISTRIBUTION UNDER DIFFERENT LOSS FUNCTION." Journal of Mathematical Sciences & Computational Mathematics 2, no. 2 (January 1, 2021): 227–35. http://dx.doi.org/10.15864/jmscm.2204.

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In this paper, the power Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

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Chang, Tianpeng, Julong Wei, Mang Liang, Bingxing An, Xiaoqiao Wang, Bo Zhu, Lingyang Xu, et al. "A Fast and Powerful Empirical Bayes Method for Genome-Wide Association Studies." Animals 9, no. 6 (May 31, 2019): 305. http://dx.doi.org/10.3390/ani9060305.

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Linear mixed model (LMM) is an efficient method for GWAS. There are numerous forms of LMM-based GWAS methods. However, improving statistical power and computing efficiency have always been the research hotspots of the LMM-based GWAS methods. Here, we proposed a fast empirical Bayes method, which is based on linear mixed models. We call it Fast-EB-LMM in short. The novelty of this method is that it uses a modified kinship matrix accounting for individual relatedness to avoid competition between the locus of interest and its counterpart in the polygene. This property has increased statistical power. We adopted two special algorithms to ease the computational burden: Eigenvalue decomposition and Woodbury matrix identity. Simulation studies showed that Fast-EB-LMM has significantly increased statistical power of marker detection and improved computational efficiency compared with two widely used GWAS methods, EMMA and EB. Real data analyses for two carcass traits in a Chinese Simmental beef cattle population showed that the significant single-nucleotide polymorphisms (SNPs) and candidate genes identified by Fast-EB-LMM are highly consistent with results of previous studies. We therefore believe that the Fast-EB-LMM method is a reliable and efficient method for GWAS.

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Xu, Jiang Jun, and Zhi Jian Xiao. "Research on Reliability Analysis of Plane Power Supplying System Based Bayesian Fusion." Applied Mechanics and Materials 651-653 (September 2014): 822–25. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.822.

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Reliable operation of the aircraft power distribution system is critical to the flight safety of a plane。In this paper,the reliability evaluation model of aircraft power supplying system based on Bayesian fusion is set up。 Calculating reliability indexes by using MATLAB simulation softwaer。Comparing with the traditional Bayes approach,the result shows the method is efficient。

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Murat, Małgorzata, and Dominik Szynal. "On the Bayes estimators of the parameters of inflated modified power series distributions." Discussiones Mathematicae Probability and Statistics 20, no. 2 (2000): 189. http://dx.doi.org/10.7151/dmps.1011.

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Anisimova, Maria, Joseph P. Bielawski, and Ziheng Yang. "Accuracy and Power of Bayes Prediction of Amino Acid Sites Under Positive Selection." Molecular Biology and Evolution 19, no. 6 (June 1, 2002): 950–58. http://dx.doi.org/10.1093/oxfordjournals.molbev.a004152.

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Guida, M., R. Calabria, and G. Pulcini. "Bayes inference for a non-homogeneous Poisson process with power intensity law (reliability)." IEEE Transactions on Reliability 38, no. 5 (1989): 603–9. http://dx.doi.org/10.1109/24.46489.

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Mishra, Kaushal K., and Sujit K. Ghosh. "Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models." Communications in Statistics - Theory and Methods 38, no. 16-17 (August 20, 2009): 2856–71. http://dx.doi.org/10.1080/03610920902947196.

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Martz, Harry F., Paul H. Kvam, and Lee R. Abramson. "Empirical Bayes Estimation of the Reliability of Nuclear-Power-Plant Emergency Diesel Generators." Technometrics 38, no. 1 (February 1996): 11–24. http://dx.doi.org/10.1080/00401706.1996.10484412.

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Ateeq, Kahkashan, Saima Altaf, and Muhammad Aslam. "Modeling and Bayesian Analysis of Time between the Breakdown of Electric Feeders." Modelling and Simulation in Engineering 2022 (May 30, 2022): 1–13. http://dx.doi.org/10.1155/2022/5830945.

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The failure of electric feeders is a common problem in the summer season in Pakistan. In this article, one of the troubling aspects of the electric power system of Pakistan (Multan city) has been studied. The time lapses between the breakdown of electric feeders of the city have been modeled by suggesting an inverse Rayleigh-exponential distribution. The parameters of the distribution are estimated in both the frequentist and Bayesian paradigms. Since the Bayes estimators under informative priors are not attained in the closed form, this paper provides a comparative analysis of the Bayes estimators under Lindley and Tierney–Kadane approximation methods. The simulation study and the real-life data set assessed the validity of the model and the superiority of the Bayes estimators over the maximum likelihood estimators.

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Nam, Seungbeom, and Jin Hur. "Probabilistic Forecasting Model of Solar Power Outputs Based on the Naïve Bayes Classifier and Kriging Models." Energies 11, no. 11 (November 1, 2018): 2982. http://dx.doi.org/10.3390/en11112982.

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Solar power’s variability makes managing power system planning and operation difficult. Facilitating a high level of integration of solar power resources into a grid requires maintaining the fundamental power system so that it is stable when interconnected. Accurate and reliable forecasting helps to maintain the system safely given large-scale solar power resources; this paper therefore proposes a probabilistic forecasting approach to solar resources using the R statistics program, applying a hybrid model that considers spatio-temporal peculiarities. Information on how the weather varies at sites of interest is often unavailable, so we use a spatial modeling procedure called kriging to estimate precise data at the solar power plants. The kriging method implements interpolation with geographical property data. In this paper, we perform day-ahead forecasts of solar power based on the probability in one-hour intervals by using a Naïve Bayes Classifier model, which is a classification algorithm. We augment forecasting by taking into account the overall data distribution and applying the Gaussian probability distribution. To validate the proposed hybrid forecasting model, we perform a comparison of the proposed model with a persistence model using the normalized mean absolute error (NMAE). Furthermore, we use empirical data from South Korea’s meteorological towers (MET) to interpolate weather variables at points of interest.

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Li, Xin, and Jin Sun. "Genetic Algorithm-Based Multi-Objective Optimization for Statistical Yield Analysis Under Parameter Variations." Journal of Circuits, Systems and Computers 26, no. 01 (October 4, 2016): 1750009. http://dx.doi.org/10.1142/s0218126617500098.

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Due to process scaling, variability in process, voltage, and temperature (PVT) parameters leads to a significant parametric yield loss, and thus impacts the optimization for circuit designs seriously. Previous parametric yield optimization algorithms are limited to optimizing either power yield or timing yield separately, without combining them together for simultaneous optimization. However, neglecting the negative correlation between the performance metrics, such as power and timing measurements, will bring on significant accuracy loss. This paper suggests an efficient multi-objective optimization framework based on Bayes’ theorem, Markov chain method, and an NSGA-II-based genetic algorithm. In the proposed framework, power and timing yields are considered as the optimization objectives to be optimized simultaneously, in order to maintain the negative correlation between power and timing metrics. First, the framework explicitly expresses both leakage current and gate delay in terms of the underlying PVT parameter variations. Then, parametric yields for both metrics are predicted by the computation of cumulative distribution function (CDF) based on Bayes’ theorem and Markov chain method. Finally, a NSGA-II-based genetic algorithm is suggested to solve power–timing optimization problem and generate well-distributed Pareto solutions. Experimental results demonstrate that the proposed multi-objective optimization procedure is able to provide the designer with guaranteed trade-off information between power and timing yields and give them the flexibility in choosing the most appropriate solution(s).

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Boik, Robert J. "Analysis of Repeated Measures Under Second-Stage Sphericity: An Empirical Bayes Approach." Journal of Educational and Behavioral Statistics 22, no. 2 (June 1997): 155–92. http://dx.doi.org/10.3102/10769986022002155.

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The conventional multivariate analysis of repeated measures is applicable in a wide variety of circumstances, in part, because assumptions regarding the pattern of covariances among the repeated measures are not required. If sample sizes are small, however, then the estimators of the covariance parameters lack precision and, as a result, the power of the multivariate analysis is low. If the covariance matrix associated with estimators of orthogonal contrasts is spherical, then the conventional univariate analysis of repeated measures is applicable and has greater power than the multivariate analysis. If sphericity is not satisfied, an adjusted univariate analysis can be conducted, and this adjusted analysis may still be more powerful than the multivariate analysis. As sample size increases, the power advantage of the adjusted univariate test decreases, and, for moderate sample sizes, the multivariate test can be more powerful. This article proposes a hybrid analysis that takes advantage of the strengths of each of the two procedures. The proposed analysis employs an empirical Bayes estimator of the covariance matrix. Existing software for conventional multivariate analyses can, with minor modifications, be used to perform the proposed analysis. The new analysis behaves like the univariate analysis when samples size is small or sphericity is nearly satisfied. When sample size is large or sphericity is strongly violated, then the proposed analysis behaves like the multivariate analysis. Simulation results suggest that the proposed analysis controls test size adequately and can be more powerful than either of the other two analyses under a wide range of non-null conditions.

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Gu, Zi-Wen, Peng Li, Xun Lang, Xin Shen, Min Cao, and Xiao-Hua Yang. "Hierarchical classification method of electricity consumption industries through TNPE and Bayes." Measurement and Control 54, no. 3-4 (March 2021): 346–59. http://dx.doi.org/10.1177/0020294021997494.

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As the multi-daily electricity consumption behaviors have the strong characteristics of dynamicity, nonlinearity and locality caused by temporal manifold structure, the existing methods are difficult to fine-grained and accurately classify it. To solve this problem, this paper proposes a hierarchical classification method based on the temporal extension of the neighborhood preserving embedding algorithm (TNPE) and Bayes. The input data are multi daily-load curves of a single consumer, including power-hour-day three dimensions, which contains the full information of the user’s consumption behaviors not only in hours, but also in days. Firstly, electricity consumption behaviors are divided into routine and non-routine types by k-means clustering algorithm. Secondly, the load feature mapping matrix of different industries is extracted through the TNPE, and each TNPE model can regard as one binary classifier, so the multi-classifier is constructed through multiple TNPE models. Finally, by converting the feature similarity between samples into probabilities, a Bayesian model is established to realize which the power consumption type belongs to. The case results show that this method can effectively recognize the local dynamic features in the temporal load data, and obtain a higher classification accuracy through a smaller number of training samples.

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