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A Distributed Block-Split Gibbs Sampler with Hypergraph Structure for High-Dimensional Inverse Problems

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2024年第3期33卷 814-832页

作者： Thouvenin, Pierre-Antoine Repetti, Audrey Chainais, Pierre Univ Lille CNRS Cent Lille UMR 9189CRIStAL Lille France Heriot Watt Univ Sch Math & Comp Sci Edinburgh Scotland Heriot Watt Univ Sch Engn & Phys Sci Edinburgh Scotland

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

关键词： Bayesian inference Block-coordinate algorithm Distributed architecture High dimensional imaging inverse problems mcmc algorithm

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An mcmc algorithm for Parameter Estimation in Signals with Hidden Intermittent Instability

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SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 2014年第1期2卷 647-669页

作者： Chen, Nan Giannakis, Dimitrios Herbei, Radu Majda, Andrew J. NYU Dept Math 550 1St Ave New York NY 10012 USA NYU Courant Inst Math Sci Ctr Atmosphere Ocean Sci New York NY 10012 USA Ohio State Univ Dept Stat Columbus OH 43210 USA

Prediction of extreme events is a highly important and challenging problem in science, engineering, finance, and many other areas. The observed extreme events in these areas are often associated with complex nonlinear dynamics with intermittent instability. However, due to lack of resolution or incomplete knowledge of the dynamics of nature, these instabilities are typically hidden. To describe nature with hidden instability, a stochastic parameterized model is used as the low-order reduced model. Bayesian inference incorporating data augmentation, regarding the missing path of the hidden processes as the augmented variables, is adopted in a Markov chain Monte Carlo (mcmc) algorithm to estimate the parameters in this reduced model from the partially observed signal. Howerver, direct application of this algorithm leads to an extremely low acceptance rate of the missing path. To overcome this shortcoming, an efficient mcmc algorithm which includes a pre-estimation of hidden processes is developed. This algorithm greatly increases the acceptance rate and provides the low-order reduced model with a high skill in capturing the extreme events due to intermittency.

关键词： hidden process intermittency stochastic parameterized model data augmentation mcmc algorithm prediction skill

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A hierarchical Bayesian approach for modeling the evolution of the 7-day moving average of the number of deaths by COVID-19

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JOURNAL OF APPLIED STATISTICS 2023年第10期50卷 2194-2208页

作者： Saraiva, E. F. Sauer, L. Pereira, C. A. B. Univ Fed Mato Grosso do Sul Inst Matemat Campo Grande MS Brazil Univ Fed Mato Grosso do Sul Escola Adm & Negocios Campo Grande MS Brazil Univ Sao Paulo Inst Matemat & Estat Sao Paulo Brazil

In this paper, we propose a hierarchical Bayesian approach for modeling the evolution of the 7-day moving average for the number of deaths due to COVID-19 in a country, state or city. The proposed approach is based on a Gaussian process regression model. The main advantage of this model is that it assumes that a nonlinear function f used for modeling the observed data is an unknown random parameter in opposite to usual approaches that set up f as being a known mathematical function. This assumption allows the development of a Bayesian approach with a Gaussian process prior over f. In order to estimate the parameters of interest, we develop an mcmc algorithm based on the Metropolis-within-Gibbs sampling algorithm. We also present a procedure for making predictions. The proposed method is illustrated in a case study, in which, we model the 7-day moving average for the number of deaths recorded in the state of Sao Paulo, Brazil. Results obtained show that the proposed method is very effective in modeling and predicting the values of the 7-day moving average.

关键词： COVID-19 Bayesian approach Gaussian process predictions mcmc algorithm

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Quantile regression in random effects meta-analysis model

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STATISTICAL METHODS AND APPLICATIONS 2023年第2期32卷 469-492页

作者： Dai, Xiaowen Jin, Libin Shi, Lei Shanghai Lixin Univ Accounting & Finance Sch Stat & Math Shanghai 201209 Peoples R China Shanghai Lixin Univ Accounting & Finance Interdisciplinary Res Inst Data Sci Shanghai 201209 Peoples R China Yunnan Univ Finance & Econ Sch Stat & Math Kunming 650221 Yunnan Peoples R China

In meta-analysis model, due to the appearance of publication bias or outliers, as well as the small sample size, the normal assumption is usually unreliable. Therefore, the exploration of more robust estimation, such quantile regression (QR) method, is extremely important in meta-analysis area. This paper studies the QR estimation method in random-effects meta-analysis model based on the reformulation by asymmetric Laplace distribution (ALD). The maximum likelihood estimation using Monte Carlo Expectation Maximization algorithm and the Bayesian estimation using Markov chain Monte Carlo (mcmc) algorithm are proposed for computation of the QR estimates. The significance tests of regression coefficients are suggested using likelihood ratio statistics. For mcmc algorithm, a simple and efficient Gibbs sampling algorithm is employed based on a location-scale mixture representation of the ALD, and information criterions are considered for choosing the hyper-parameters. Monte Carlo simulations are conducted to study the finite sample performance of the proposed methodology and analysis of two real data sets are presented for illustrations. Our results show that QR estimation methods perform very well, especially in case of non-normal assumption in meta-regression models. The detailed algorithms and software code are available for easy use in applications.

关键词： Random-effects meta-analysis model Quantile regression Asymmetric Laplace distribution MCEM algorithm mcmc algorithm

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Graph-Guided Bayesian Factor Model for Integrative Analysis of Multi-modal Data with Noisy Network Information

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STATISTICS IN BIOSCIENCES 2024年 1-17页

作者： Li, Wenrui Zhang, Qiyiwen Qu, Kewen Long, Qi Univ Connecticut Dept Stat 215 Glenbrook Rd Storrs CT 06269 USA Univ Pittsburgh Dept Med 3550 Terrace St Pittsburgh PA 15261 USA Univ Penn Dept Biostat Epidemiol & Informat 423 Guardian Dr Philadelphia PA 19104 USA

There is a growing body of literature on factor analysis that can capture individual and shared structures in multi-modal data. However, few of these approaches incorporate biological knowledge such as functional genomics and functional metabolomics. Graph-guided statistical learning methods that can incorporate knowledge of underlying networks have been shown to improve predication and classification accuracy, and yield more interpretable results. Moreover, these methods typically use graphs extracted from existing databases or rely on subject matter expertise which are known to be incomplete and may contain false edges. To address this gap, we propose a graph-guided Bayesian factor model that can account for network noise and identify globally shared, partially shared and modality-specific latent factors in multi-modal data. Specifically, we use two sources of network information, including the noisy graph extracted from existing databases and the estimated graph from observed features in the dataset at hand, to inform the model for the true underlying network via a latent scale modeling framework. This model is coupled with the Bayesian factor analysis model with shrinkage priors to encourage feature-wise and modal-wise sparsity, thereby allowing feature selection and identification of factors of each type. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling. We demonstrate the advantages of our method over existing methods in simulations, and through analyses of gene expression and metabolomics datasets for Alzheimer's disease.

关键词： Bayesian shrinkage Factor analysis Latent scale network model mcmc algorithm Noisy graph

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Prediction under an adaptive progressive type-II censoring scheme for Burr Type-XII distribution

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2022年第12期51卷 4029-4041页

作者： Ateya, Saieed F. Amein, M. M. Mohammed, Heba S. Taif Univ Fac Sci Dept Math & Stat At Taif Saudi Arabia Assiut Univ Fac Sci Dept Math Assiut Egypt Al Azhar Univ Fac Sci Dept Math Cairo Egypt New Valley Univ Fac Sci Dept Math El Kharga Egypt Princess Nourah Bint Abdularhman Univ Math Sci Fac Sci Riyadh Saudi Arabia

In this article, Burr type-XII distribution (BXIID) is employed to make one- and two-sample Bayesian prediction schemes for future order statistics and record values in case of adaptive progressive type-II censoring scheme (APTIICS). Real data set are presented as an application. Also, some numerical computations using simulated data from the underlying distribution in case of ATIIPCS are obtained.

关键词： An adaptive progressive type-II censoring scheme one and two sample prediction schemes mcmc algorithm Burr-XII distribution

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mBART: Multidimensional Monotone BART

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BAYESIAN ANALYSIS 2022年第2期17卷 515-544页

作者： Chipman, Hugh A. George, Edward I. McCulloch, Robert E. Shively, Thomas S. Acad Univ Dept Math & Stat Wolfville NS Canada Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA Arizona State Univ Sch Math & Stat Sci Tempe AZ USA Univ Texas Austin Dept Informat Risk & Operat Management Austin TX 78712 USA

For the discovery of regression relationships between Y and a large set of p potential predictors x(1), ... , x(p), the flexible nonparametric nature of BART (Bayesian Additive Regression Trees) allows for a much richer set of possibilities than restrictive parametric approaches. However, subject matter considerations sometimes warrant a minimal assumption of monotonicity in at least some of the predictors. For such contexts, we introduce mBART, a constrained version of BART that can flexibly incorporate monotonicity in any predesignated subset of predictors using a multivariate basis of monotone trees, while avoiding the further confines of a full parametric form. For such monotone relationships, mBART provides (i) function estimates that are smoother and more interpretable, (ii) better out-of-sample predictive performance, and (iii) less post-data uncertainty. While many key aspects of the unconstrained BART model carry over directly to mBART, the introduction of monotonicity constraints necessitates a fundamental rethinking of how the model is implemented. In particular, the original BART Markov Chain Monte Carlo algorithm relied on a conditional conjugacy that is no longer available in a monotonically constrained space. Various simulated and real examples demonstrate the wide ranging potential of mBART.

关键词： Bayesian nonparametrics ensemble model isotonic regression mcmc algorithm multidimensional nonparametric regression shape constrained inference

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Bayesian variable selection in quantile regression with random effects: an application to Municipal Human Development Index

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JOURNAL OF APPLIED STATISTICS 2022年第13期49卷 3436-3450页

作者： Nascimento, Marcus G. L. Goncalves, Kelly C. M. Univ Fed Rio de Janeiro Dept Metodos Estatist Rio De Janeiro Brazil

According to the Atlas of Human Development in Brazil, the income dimension of Municipal Human Development Index (MHDI-I) is an indicator that shows the population's ability in a municipality to ensure a minimum standard of living to provide their basic needs, such as water, food and shelter. In public policy, one of the research objectives is to identify social and economic variables that are associated with this index. Due to the income inequality, evaluate these associations in quantiles, instead of the mean, could be more interest. Thus, in this paper, we develop a Bayesian variable selection in quantile regression models with hierarchical random effects. In particular, we assume a likelihood function based on the Generalized Asymmetric Laplace distribution, and a spike-and-slab prior is used to perform variable selection. The Generalized Asymmetric Laplace distribution is a more general alternative than the Asymmetric Laplace one, which is a common approach used in quantile regression under the Bayesian paradigm. The performance of the proposed method is evaluated via a comprehensive simulation study, and it is applied to the MHDI-I from municipalities located in the state of Rio de Janeiro.

关键词： Location-scale mixture representation hierarchical models mcmc algorithm

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A Mixed-Membership Model for Social Network Clustering

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Journal of Data Science 2023年第3期21卷 508-522页

作者： Ouyang, Guang Dey, Dipak K. Zhang, Panpan Department of Statistics University of Connecticut Storrs 06269 CT United States Department of Biostatistics Vanderbilt University Medical Center Nashville 37203 TN United States

We propose a simple mixed membership model for social network clustering in this paper. A flexible function is adopted to measure affinities among a set of entities in a social network. The model not only allows each entity in the network to possess more than one membership, but also provides accurate statistical inference about network *** estimate the membership parameters using an mcmc algorithm. We evaluate the performance of the proposed algorithm by applying our model to two empirical social network data, the Zachary club data and the bottlenose dolphin network data. We also conduct some numerical studies based on synthetic networks for further assessing the effectiveness of our algorithm. In the end, some concluding remarks and future work are addressed briefly. © 2023 The Author(s).

关键词： cosine similarity mcmc algorithm mixed membership social network clustering stochastic blockmodels

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Bayesian transformation models with partly interval-censored data

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STATISTICS IN MEDICINE 2022年第7期41卷 1263-1279页

作者： Wang, Chunjie Jiang, Jingjing Song, Xinyuan Changchun Univ Technol Sch Math & Stat Changchun Peoples R China Chinese Univ Hong Kong Dept Stat Hong Kong Peoples R China

In many scientific fields, partly interval-censored data, which consist of exactly observed and interval-censored observations on the failure time of interest, appear frequently. However, methodological developments in the analysis of partly interval-censored data are relatively limited and have mainly focused on additive or proportional hazards models. The general linear transformation model provides a highly flexible modeling framework that includes several familiar survival models as special cases. Despite such nice features, the inference procedure for this class of models has not been developed for partly interval-censored data. We propose a fully Bayesian approach coped with efficient Markov chain Monte Carlo methods to fill this gap. A four-stage data augmentation procedure is introduced to tackle the challenges presented by the complex model and data structure. The proposed method is easy to implement and computationally attractive. The empirical performance of the proposed method is evaluated through two simulation studies, and the model is then applied to a dental health study.

关键词： Bayesian method data augmentation mcmc algorithm partly interval-censored data transformation model

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