Journal articles: 'Bivariate Gaussian mixture'

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Frei, Oleksandr, Olav Smeland, Dominic Holland, Alexey Shadrin, Wesley Thompson, Ole Andreassen, and Anders Dale. "BIVARIATE GAUSSIAN MIXTURE MODEL FOR GWAS SUMMARY STATISTICS." European Neuropsychopharmacology 29 (2019): S898—S899. http://dx.doi.org/10.1016/j.euroneuro.2017.08.211.

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Alqahtani, Nada A., and Zakiah I. Kalantan. "Gaussian Mixture Models Based on Principal Components and Applications." Mathematical Problems in Engineering 2020 (July 31, 2020): 1–13. http://dx.doi.org/10.1155/2020/1202307.

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Data scientists use various machine learning algorithms to discover patterns in large data that can lead to actionable insights. In general, high-dimensional data are reduced by obtaining a set of principal components so as to highlight similarities and differences. In this work, we deal with the reduced data using a bivariate mixture model and learning with a bivariate Gaussian mixture model. We discuss a heuristic for detecting important components by choosing the initial values of location parameters using two different techniques: cluster means, k-means and hierarchical clustering, and default values in the “mixtools” R package. The parameters of the model are obtained via an expectation maximization algorithm. The criteria from Bayesian point are evaluated for both techniques, demonstrating that both techniques are efficient with respect to computation capacity. The effectiveness of the discussed techniques is demonstrated through a simulation study and using real data sets from different fields.

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Wójcik, R., Peter A. Troch, H. Stricker, P. Torfs, E. Wood, H. Su, and Z. Su. "Mixtures of Gaussians for Uncertainty Description in Bivariate Latent Heat Flux Proxies." Journal of Hydrometeorology 7, no. 3 (June 1, 2006): 330–45. http://dx.doi.org/10.1175/jhm491.1.

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Abstract This paper proposes a new probabilistic approach for describing uncertainty in the ensembles of latent heat flux proxies. The proxies are obtained from hourly Bowen ratio and satellite-derived measurements, respectively, at several locations in the southern Great Plains region in the United States. The novelty of the presented approach is that the proxies are not considered separately, but as bivariate samples from an underlying probability density function. To describe the latter, the use of Gaussian mixture density models—a class of nonparametric, data-adaptive probability density functions—is proposed. In this way any subjective assumptions (e.g., Gaussianity) on the form of bivariate latent heat flux ensembles are avoided. This makes the estimated mixtures potentially useful in nonlinear interpolation and nonlinear probabilistic data assimilation of noisy latent heat flux measurements. The results in this study show that both of these applications are feasible through regionalization of estimated mixture densities. The regionalization scheme investigated here utilizes land cover and vegetation fraction as discriminatory variables.

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Alotaibi, Refah, Mervat Khalifa, Ehab M. Almetwally, Indranil Ghosh, and Rezk H. "Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model." Journal of Mathematics 2021 (October 16, 2021): 1–20. http://dx.doi.org/10.1155/2021/5200979.

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Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed.

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Al-Mutairi, Dhaifalla K. "Properties of an inverse Gaussian mixture of bivariate exponential distribution and its generalization." Statistics & Probability Letters 33, no. 4 (May 1997): 359–65. http://dx.doi.org/10.1016/s0167-7152(96)00184-8.

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Rabbani, Hossein, Milan Sonka, and Michael D. Abramoff. "Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain." International Journal of Biomedical Imaging 2013 (2013): 1–23. http://dx.doi.org/10.1155/2013/417491.

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In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR.

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Yi, Sang-ri, Ziqi Wang, and Junho Song. "Bivariate Gaussian mixture-based equivalent linearization method for stochastic seismic analysis of nonlinear structures." Earthquake Engineering & Structural Dynamics 47, no. 3 (November 7, 2017): 678–96. http://dx.doi.org/10.1002/eqe.2985.

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Lalpawimawha, Ralte, and Arvind Pandey. "A Mixture Shared Inverse Gaussian Frailty Model under Modified Weibull Baseline Distribution." Austrian Journal of Statistics 49, no. 2 (February 20, 2020): 31–42. http://dx.doi.org/10.17713/ajs.v49i2.914.

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Frailty models are used in the survival analysis to account for the unobserved heterogeneityin individual risks to disease and death. To analyze the bivariate data on relatedsurvival times (e.g. matched pairs experiments, twin or family data), the shared frailtymodels were suggested. In this manuscript, we propose a new mixture shared inverse Gaussian frailty model based on modified Weibull as baseline distribution. The Bayesian approach of Markov Chain Monte Carlo technique is employed to estimate the parameters involved in the models. In addition, a simulation study is performed to compare the true values of the parameters with the estimated values. A comparison with the existing model was done by using Bayesian comparison techniques. A better model for infectious disease data related to kidney infection is suggested.

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G.V.S., Rajkumar, Srinivasa Rao K., and Srinivasa Rao P. "Image Segmentation and Retrievals based on Finite Doubly Truncated Bivariate Gaussian Mixture Model and KMeans." International Journal of Computer Applications 25, no. 4 (July 31, 2011): 5–13. http://dx.doi.org/10.5120/3022-4087.

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Gournelos, T., V. Kotinas, and S. Poulos. "Fitting a Gaussian mixture model to bivariate distributions of monthly river flows and suspended sediments." Journal of Hydrology 590 (November 2020): 125166. http://dx.doi.org/10.1016/j.jhydrol.2020.125166.

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Camacho, Maximo, María Dolores Gadea, and Ana Gómez-Loscos. "An Automatic Algorithm to Date the Reference Cycle of the Spanish Economy." Mathematics 9, no. 18 (September 12, 2021): 2241. http://dx.doi.org/10.3390/math9182241.

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This paper provides an accurate chronology of the Spanish reference business cycle adapting a multiple change-point model. In that approach, each combination of peaks and troughs dated in a set of economic indicators is assumed to be a realization of a mixture of bivariate Gaussian distributions, whose number of components is estimated from the data. The means of each of these components refer to the dates of the reference turning points. The transitions across the components of the mixture are governed by Markov chain that is restricted to force left-to-right transition dynamic. In the empirical application, seven recessions in the period from February 1970 to February 2020 are identified, which are in high concordance with the timing of the turning point dates established by the Spanish Business Cycle Dating Committee (SBCDC).

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Han, Mengjie, Zhenwu Wang, and Xingxing Zhang. "An Approach to Data Acquisition for Urban Building Energy Modeling Using a Gaussian Mixture Model and Expectation-Maximization Algorithm." Buildings 11, no. 1 (January 16, 2021): 30. http://dx.doi.org/10.3390/buildings11010030.

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In recent years, a building’s energy performance is becoming uncertain because of factors such as climate change, the Covid-19 pandemic, stochastic occupant behavior and inefficient building control systems. Sufficient measurement data is essential to predict and manage a building’s performance levels. Assessing energy performance of buildings at an urban scale requires even larger data samples in order to perform an accurate analysis at an aggregated level. However, data are not only expensive, but it can also be a real challenge for communities to acquire large amounts of real energy data. This is despite the fact that inadequate knowledge of a full population will lead to biased learning and the failure to establish a data pipeline. Thus, this paper proposes a Gaussian mixture model (GMM) with an Expectation-Maximization (EM) algorithm that will produce synthetic building energy data. This method is tested on real datasets. The results show that the parameter estimates from the model are stable and close to the true values. The bivariate model gives better performance in classification accuracy. Synthetic data points generated by the models show a consistent representation of the real data. The approach developed here can be useful for building simulations and optimizations with spatio-temporal mapping.

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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.

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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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Ranger, Jochen, and Anett Wolgast. "Using Response Times as Collateral Information About Latent Traits in Psychological Tests." Methodology 15, no. 4 (October 1, 2019): 185–96. http://dx.doi.org/10.1027/1614-2241/a000181.

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Abstract. In psychological tests, the time needed to respond to the items provides collateral information about the latent traits of the test takers. This, however, requires a measurement model that incorporates the response times in addition to the responses. Such a measurement model is usually based on a full specification of the response time distribution. In the present article, we suggest a novel modeling approach that requires fewer assumptions. In the approach, the responses are modeled with a unidimensional two-parameter logistic model. The single response times are summed to the scale-specific total testing time which is then related to the latent trait of the two-parameter logistic model via a smooth adaptive Gaussian mixture (SAGM) model. The approach can be justified against the background of the bivariate generalized linear item response theory modeling framework ( Molenaar, Tuerlinckx, & van der Maas, 2015a ). Its utility is investigated in two simulation studies and an empirical example.

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Bazrkar, Mohammad Hadi, and Xuefeng Chu. "Development of category-based scoring support vector regression (CBS-SVR) for drought prediction." Journal of Hydroinformatics 24, no. 1 (January 1, 2022): 202–22. http://dx.doi.org/10.2166/hydro.2022.104.

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Abstract Using the existing measures for training numerical (non-categorical) prediction models can cause misclassification of droughts. Thus, developing a drought category-based measure is critical. Moreover, the existing fixed drought category thresholds need to be improved. The objective of this research is to develop a category-based scoring support vector regression (CBS-SVR) model based on an improved drought categorization method to overcome misclassification in drought prediction. To derive variable threshold levels for drought categorization, K-means (KM) and Gaussian mixture (GM) clustering are compared with the traditional drought categorization. For drought prediction, CBS-SVR is performed by using the best categorization method. The new drought model was applied to the Red River of the North Basin (RRB) in the USA. In the model training and testing, precipitation, temperature, and actual evapotranspiration were selected as the predictors, and the target variables consisted of multivariate drought indices, as well as bivariate and univariate standardized drought indices. Results indicated that the drought categorization method, variable threshold levels, and the type of drought index were the major factors that influenced the accuracy of drought prediction. The CBS-SVR outperformed the support vector classification and traditional SVR by avoiding overfitting and miscategorization in drought prediction.

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Hannachi, A., and A. G. Turner. "20th century intraseasonal Asian monsoon dynamics viewed from Isomap." Nonlinear Processes in Geophysics 20, no. 5 (October 8, 2013): 725–41. http://dx.doi.org/10.5194/npg-20-725-2013.

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Abstract. The Asian summer monsoon is a high-dimensional and highly nonlinear phenomenon involving considerable moisture transport towards land from the ocean, and is critical for the whole region. We have used daily ECMWF reanalysis (ERA-40) sea-level pressure (SLP) anomalies on the seasonal cycle, over the region 50–145° E, 20° S–35° N, to study the nonlinearity of the Asian monsoon using Isomap. We have focused on the two-dimensional embedding of the SLP anomalies for ease of interpretation. Unlike the unimodality obtained from tests performed in empirical orthogonal function space, the probability density function, within the two-dimensional Isomap space, turns out to be bimodal. But a clustering procedure applied to the SLP data reveals support for three clusters, which are identified using a three-component bivariate Gaussian mixture model. The modes are found to appear similar to active and break phases of the monsoon over South Asia in addition to a third phase, which shows active conditions over the western North Pacific. Using the low-level wind field anomalies, the active phase over South Asia is found to be characterised by a strengthening and an eastward extension of the Somali jet. However during the break phase, the Somali jet is weakened near southern India, while the monsoon trough in northern India also weakens. Interpretation is aided using the APHRODITE gridded land precipitation product for monsoon Asia. The effect of large-scale seasonal mean monsoon and lower boundary forcing, in the form of ENSO, is also investigated and discussed. The outcome here is that ENSO is shown to perturb the intraseasonal regimes, in agreement with conceptual ideas.

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Sikaroudi, Ali Esmaieeli, and Chiwoo Park. "A mixture of linear-linear regression models for a linear-circular regression." Statistical Modelling, November 6, 2019, 1471082X1988184. http://dx.doi.org/10.1177/1471082x19881840.

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We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modelling approach of a wrapped normal distribution that describes angular variables and angular distributions and advances them for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a nonparametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.

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Journal articles on the topic 'Bivariate Gaussian mixture'

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