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The G-Wishart Weighted Proposal algorithm: Efficient Posterior Computation for Gaussian Graphical Models

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2022年第4期31卷 1215-1224页

作者： van den Boom, Willem Beskos, Alexandros De Iorio, Maria Natl Univ Singapore Yong Loo Lin Sch Med Singapore Singapore UCL Dept Stat Sci London England Alan Turing Inst London England ASTAR Singapore Inst Clin Sci Singapore Singapore

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the posterior distribution. However, posterior computation under the conjugate G-Wishart prior distribution on the precision matrix is expensive for general nondecomposable graphs. We therefore propose a new Markov chain Monte Carlo (MCMC) method named the G-Wishart weighted proposal algorithm (WWA). WWA's distinctive features include delayed acceptance MCMC, Gibbs updates for the precision matrix and an informed proposal distribution on the graph space that enables embarrassingly parallel computations. Compared to existing approaches, WWA reduces the frequency of the relatively expensive sampling from the G-Wishart distribution. This results in faster MCMC convergence, improved MCMC mixing and reduced computing time. Numerical studies on simulated and real data show that WWA provides a more efficient tool for posterior inference than competing state-of-the-art MCMC algorithms. Supplemental materials for the article are available online.

关键词： exchange algorithm Hyper Inverse Wishart distribution Locally balanced proposal Reversible jump MCMC Scalable Bayesian computations

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Robust design modeling and optimization for dealing with a non-convex design space

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年 185卷

作者： Ozdemir, Akin Turkoz, Mehmet Ondokuz Mayis Univ Dept Ind Engn Samsun Turkiye William Paterson Univ Dept Mkt Management & Profess Sales Wayne NJ 07470 USA

Classic experimental designs effectively generate experimental design points under standard design spaces such as a circle, a cube, or a sphere. However, for non-convex design spaces, traditional experimental designs are not appropriate due to nonstandard experimental design conditions. No attention has been given to developing an algorithm to generate design points for a non-convex design space in the literature. This paper is three-fold. One, this paper presents a novel exchange algorithm based on an inner approximation approach in order to construct optimal design points where the design space is non-convex. Besides, the proposed algorithm efficiently produces experimental design points for non-convex design space. In addition, it is provided a fair comparison of the proposed algorithm performance. Two, the fitted response functions of the mean, standard deviation, and variance are found using the proposed regression model construction technique where the design space is nonconvex. Three, a selected optimal design concept-based robust design optimization model is developed to find Pareto optimal solution settings of chosen design factors for the non-convex design space. Finally, an Industry 4.0 concept-based numerical example is provided to illustrate how to apply the proposed methodology effectively for the non-convex design space.

关键词： Quality Robust design Inner approximation Non-convex design space Optimal design exchange algorithm

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Flexible Modeling of Hurdle Conway-Maxwell-Poisson Distributions with Application to Mining Injuries

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2024年第3期18卷 34-34页

作者： Yin, Shuang Dey, Dipak K. Valdez, Emiliano A. Gan, Guojun Li, Xiaomeng Univ Connecticut Dept Stat 215 Glenbrook Rd Storrs CT 06269 USA Univ Connecticut Dept Math 341 Mansfield Rd Storrs CT 06269 USA

The Poisson regression is the most popular class of models for count data, but with excessive zeros and unequal dispersion, the ordinary Poisson may be unsuitable to handle the significant presence of zero inflation and dispersion. In this paper, we apply the Hurdle structure with Conway-Maxwell-Poisson (CMP) distribution and integrate use of binary link function as better alternative to Poisson and Negative Binomial. We take a fully Bayesian approach to draw inference from the underlying models to better investigate our inferential methodology, with the Deviance Information Criteria (DIC), Watanabe-Akaike Information Criterion (WAIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) used for model selection. Those criteria incorporate the effective number of parameters to adjust for overfitting, and can be calculated efficiently via likelihood function decomposition. For empirical investigation, we analyze mining injury data from the U.S. Mine Safety and Health Administration (MSHA). The Hurdle regressions are additionally adjusted for exposure, measured by the total employee working time in month;the proposed methodology is of specialty for studying occurrence and severity of the injuries. We tested its competitiveness from a business perspective against other models by estimating the expected injury cost due to adverse predictions.

关键词： Conway-Maxwell-Poisson exchange algorithm Hurdle model Likelihood function decomposition WAIC LPML Zero-truncated models

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D-optimal experimental design for production models in nonstandard experiments

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2020年第5期36卷 1537-1552页

作者： Ozdemir, Akin Bayburt Univ Dept Ind Engn TR-69000 Bayburt Turkey

Robust design is an effective Quality by Design method to reduce product variation by selecting levels of design factors. For a number of situations, a nonstandard design region with linearly limited resources is needed to conduct an experiment. In the literature, little attention has been given to the development of robust design models for the nonstandard design region with a combination of linearly limited resources and a limited number of design points. In this paper, a selection scheme of D-optimal experimental design points is proposed to generate design points using the modified exchange algorithm for the nonstandard design region while specifying linearly limited resources and the limited number of design points. The modified exchange algorithm is able to generate global design points with less time complexity than the improved Fedorov algorithm. In addition, robust design models linking a D-optimal experimental design with quality considerations are proposed in order to obtain optimum settings of design factors for the product. Comparative studies are also presented. Finally, a real-life experimental study shows that the proposed models with the desirability function and the sequential quadratic programming technique achieve greater variance reduction than the traditional counterparts.

关键词： D-optimal experimental design exchange algorithm product improvement Quality by Design robust design

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Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model

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BAYESIAN ANALYSIS 2020年第1期15卷 1-27页

作者： Moores, Matthew Nicholls, Geoff K. Pettit, Anthony N. Mengersen, Kerrie Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Univ Wollongong Sch Math & Appl Stat NIASRA Wollongong NSW 2522 Australia Univ Oxford Dept Stat 24-29 St Giles Oxford OX1 3LG England Queensland Univ Technol Australian Res Council Ctr Excellence Math & Stat Frontiers ACEMS Brisbane Qld 4001 Australia Queensland Univ Technol Sch Math Sci Brisbane Qld 4001 Australia

The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There is a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open-source implementation of our algorithm is available in the R package bayesImageS.

关键词： approximate Bayesian computation exchange algorithm hidden Markov random field image analysis indirect inference intractable likelihood

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Optimal Design of Experiments for Hybrid Nonlinear Models, with Applications to Extended Michaelis-Menten Kinetics

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2020年第4期25卷 601-616页

作者： Huang, Yuanzhi Gilmour, Steven G. Mylona, Kalliopi Goos, Peter Newcastle Univ Sch Math Stat & Phys Newcastle Upon Tyne Tyne & Wear England Kings Coll London Dept Math London England Katholieke Univ Leuven Dept Biosyst Leuven Belgium

Biochemical mechanism studies often assume statistical models derived from Michaelis-Menten kinetics, which are used to approximate initial reaction rate data given the concentration level of a single substrate. In experiments dealing with industrial applications, however, there are typically a wide range of kinetic profiles where more than one factor is controlled. We focus on optimal design of such experiments requiring the use of multifactor hybrid nonlinear models, which presents a considerable computational challenge. We examine three different candidate models and search for tailor-made D- or weighted-A-optimal designs that can ensure the efficiency of nonlinear least squares estimation. We also study a compound design criterion for discriminating between two candidate models, which we recommend for design of advanced kinetic studies. Supplementary materials accompanying this paper appear on-line

关键词： Biochemistry Compound criterion D-optimality exchange algorithm Weighted-A-optimality

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On designing experiments for a dynamic response modeled by regression splines

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2020年第2期36卷 251-267页

作者： Pan, Rong Saleh, Moein Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85281 USA PayPal San Jose CA USA

Dynamic response systems are often found in science, engineering, and medical applications, but the discussion on experimental design for such a system is relatively rare in literature. For an experimenter, designing such experiments requires making decisions on (1) when or where to take response measurements along the dynamic variable and (2) how to choose the combination of experimental factors and their levels. The first consideration is unique for such experiments, especially when the measurement cost is high. In this paper, we present a design approach through the mixed-effect linear model, which is based on a hierarchical B-spline function for the dynamic response. We develop several theorems that can assist in finding a statistically efficient sampling plan and propose an algorithm for searching the D-optimal design of a dynamic response system.

关键词： B-splines dynamic system exchange algorithm optimal experimental design

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Order-of-addition experiments: A review and some new thoughts

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QUALITY ENGINEERING 2019年第1期31卷 49-59页

作者： Lin, Dennis K. J. Peng, Jiayu Penn State Univ Dept Stat Thomas Bldg State Coll PA 16802 USA

The study of order-of-addition (OofA) experiments is prevalent in many scientific and industrial areas. The statistical design of experiments (DOE) will considerably improve the efficiency of OofA experiments. Designing and modeling the OofA experiments have increasingly received a great deal of attention. In this article, we review the latest work on the design and model of OofA experiments, and introduce some new thoughts. We believe that this article will motivate fruitful applications in real OofA experiments as well as future developments in the methodology.

关键词： constraints design construction exchange algorithm higher-order optimal designs pairwise-order symmetry

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Fast Model-Fitting of Bayesian Variable Selection Regression Using the Iterative Complex Factorization algorithm

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BAYESIAN ANALYSIS 2019年第2期14卷 573-594页

作者： Zhou, Quan Guan, Yongtao Rice Univ Dept Stat 6100 Main St Houston TX 77005 USA Baylor Coll Med USDA ARS Childrens Nutr Res Ctr Dept Pediat 1100 BatesRoom 2070 Houston TX 77030 USA Baylor Coll Med Dept Mol & Human Genet 1100 BatesRoom 2070 Houston TX 77030 USA Baylor Coll Med Program Quantitat & Computat Biosci Houston TX 77030 USA Duke Univ Sch Med Dept Biostat & Bioinformat Durham NC 27707 USA

Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special class of linear systems, which can increase the speed of the BVSR model-fitting tenfold. The iterative method hinges on the complex factorization of the sum of two matrices and the solution path resides in the complex domain (instead of the real domain). Compared to the Gauss-Seidel method, the complex factorization converges almost instantaneously and its error is several magnitude smaller than that of the Gauss-Seidel method. More importantly, the error is always within the pre-specified precision while the Gauss-Seidel method is not. For large problems with thousands of covariates, the complex factorization is 10-100 times faster than either the Gauss-Seidel method or the direct method via the Cholesky decomposition. In BVSR, one needs to repetitively solve large penalized regression systems whose design matrices only change slightly between adjacent MCMC steps. This slight change in design matrix enables the adaptation of the iterative complex factorization method. The computational innovation will facilitate the wide-spread use of BVSR in reanalyzing genome-wide association datasets.

关键词： Cholesky decomposition exchange algorithm fastBVSR Gauss-Seidel method heritability

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Spatial hidden Markov models and species distributions

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JOURNAL OF APPLIED STATISTICS 2018年第9期45卷 1595-1615页

作者： Spezia, Luigi Friel, Nial Gimona, Alessandro Biomath & Stat Scotland Aberdeen AB15 8QH Scotland Univ Coll Dublin Sch Math Sci Belfield Ireland James Hutton Inst Aberdeen Scotland

A spatial hidden Markov model (SHMM) is introduced to analyse the distribution of a species on an atlas, taking into account that false observations and false non-detections of the species can occur during the survey, blurring the true map of presence and absence of the species. The reconstruction of the true map is tackled as the restoration of a degraded pixel image, where the true map is an autologistic model, hidden behind the observed map, whose normalizing constant is efficiently computed by simulating an auxiliary map. The distribution of the species is explained under the Bayesian paradigm and Markov chain Monte Carlo (MCMC) algorithms are developed. We are interested in the spatial distribution of the bird species Greywing Francolin in the south of Africa. Many climatic and land-use explanatory variables are also available: they are included in the SHMM and a subset of them is selected by the mutation operators within the MCMC algorithm.

关键词： Atlas surveys autologistic model binary images exchange algorithm mutation operators

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