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Accelerated test system strength models based on Birnbaum-Saunders distribution: a complete Bayesian analysis and comparison

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LIFETIME DATA ANALYSIS 2009年第3期15卷 379-396页

作者： Upadhyay, S. K. Mukherjee, Bhaswati Gupta, Ashutosh Bristol Myers Squibb India Pvt Ltd Dept Global Biometr Sci Mumbai 400018 Maharashtra India Banaras Hindu Univ Dept Stat Varanasi 221005 Uttar Pradesh India Banaras Hindu Univ DST Ctr Interdisciplinary Math Sci Varanasi 221005 Uttar Pradesh India GlaxoSmithKline Pharmaceut Ltd Biomed Data Sci India Bangalore 560052 Karnataka India

Several models for studies related to tensile strength of materials are proposed in the literature where the size or length component has been taken to be an important factor for studying the specimens' failure behaviour. An important model, developed on the basis of cumulative damage approach, is the three-parameter extension of the Birnbaum-Saunders fatigue model that incorporates size of the specimen as an additional variable. This model is a strong competitor of the commonly used Weibull model and stands better than the traditional models, which do not incorporate the size effect. The paper considers two such cumulative damage models, checks their compatibility with a real dataset, compares them with some of the recent toolkits, and finally recommends a model, which appears an appropriate one. Throughout the study is Bayesian based on Markov chain Monte Carlo simulation.

关键词： Birnbaum-Saunders distribution Cumulative damage model Size effect Gibbs sampler metropolis algorithm Hybrid strategy Predictive simulation Partial posterior predictive p-value Bayesian information criterion Deviance information criterion Posterior predictive loss

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Using Randomized Search algorithms to Estimate HMM Learning Parameters

Using Randomized Search Algorithms to Estimate HMM Learning ...

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IEEE International Advance Computing Conference

作者： Nath, Ravindra Jain, Renu CSJM Univ Dept Comp Sci & Engn UIET Kanpur 208024 Uttar Pradesh India Director Krishna Girls Engn Coll Kanpur 20917 Uttar Pradesh India

ISBN: (纸本)9781424429271

Many complex problems like Speech Recognition, Bioinformatics, Climatology, Control and Communication are solved using Hidden Markov Models (HMM). Mostly, optimization problems are modeled as HMM learning problem in which HMM parameters are either maximized or minimized. In general, Baum-Welch Method (BW) is used to solve HMM learning problem giving only local maxima/minima in exponential time. In this paper, we have modeled HMM learning problem as a discrete optimization problem such that randomized search methods can be used to solve the learning problem. We have implemented metropolis algorithm (MA) and Simulated Annealing algorithm (SAA) to solve the discretized HMM learning problem. A comparative study of randomized algorithms with the Baum Welch method to estimate the HMM learning parameters has been made. The metropolis algorithm is found to reach maxima in minimum number of transactions as compared to the Baum-Welch and Simulated Annealing algorithms.

关键词： Simulated Annealing algorithm metropolis algorithm Baum-Welch Hidden Markov Models

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An extension of the metropolis algorithm

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2005年第3期34卷 585-596页

作者： Wu, SS Wells, MT Univ Florida Dept Stat Gainesville FL 32611 USA Cornell Univ Dept Social Stat Ithaca NY USA

The metropolis algorithm and its variants are perhaps the most widely used methods of generating Markov chains with a specified equilibrium distribution. We study an extension of the metropolis algorithm from both a decision theoretic and rate of convergence point of view. The decision theoretic approach was first taken by Peskun (1973) who showed some optimality properties of the classical metropolis sampler. In this article, we propose an extension of the metropolis algorithm which reduces the asymptotic variance and accelerates the convergence rate of its classic from. The principle method used to improve the properties of a sampler is to move mass from the diagonal elements of the Markov chain's transition matrix to the off-diagonal elements. A low dimensional example is given to illustrate that our extended algorithm converges to stationary distribution in the fastest possible order n steps, while the conventional metropolis chain takes at least order n(2) log(n) steps.

关键词： acceleration Markov chain Monte Carlo metropolis algorithm rate of convergence risk domination variance reduction

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Optimal scaling of metropolis algorithms: Heading toward general target distributions

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Canadian Journal of Statistics 2008年第4期36卷 483-503页

作者： Bédard, Mylène Rosenthal, Jeffrey S. Département de Mathématiques et de Statistique Université de Montréal Montréal QC H3C 3J7 C. P. 6128 succursale Centre-ville Canada Department of Statistics University of Toronto Toronto ON M5S 3G3 100 St. George Street Canada

The authors provide an overview of optimal scaling results for the metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high-dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well-known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.

关键词： Acceptance rate Langevin diffusion Marginal process metropolis algorithm Scaling Weak convergence

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Efficient prediction uncertainty approximation in the calibration of environmental simulation models

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WATER RESOURCES RESEARCH 2008年第4期44卷 W04411-1-W04411-1页

作者： Tolson, Bryan A. Shoemaker, Christine A. Univ Waterloo Dept Civil & Environm Engn Waterloo ON N2L 3G1 Canada Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

[ 1] This paper is aimed at improving the efficiency of model uncertainty analyses that are conditioned on measured calibration data. Specifically, the focus is on developing an alternative methodology to the generalized likelihood uncertainty estimation ( GLUE) technique when pseudolikelihood functions are utilized instead of a traditional statistical likelihood function. We demonstrate for multiple calibration case studies that the most common sampling approach utilized in GLUE applications, uniform random sampling, is much too inefficient and can generate misleading estimates of prediction uncertainty. We present how the new dynamically dimensioned search ( DDS) optimization algorithm can be used to independently identify multiple acceptable or behavioral model parameter sets in two ways. DDS could replace random sampling in typical applications of GLUE. More importantly, we present a new, practical, and efficient uncertainty analysis methodology called DDS-approximation of uncertainty ( DDS-AU) that quantifies prediction uncertainty using prediction bounds rather than prediction limits. Results for 13, 14, 26, and 30 parameter calibration problems show that DDS-AU can be hundreds or thousands of times more efficient at finding behavioral parameter sets than GLUE with random sampling. Results for one example show that for the same limited computational effort, DDS-AU prediction bounds can simultaneously be smaller and contain more of the measured data in comparison to GLUE prediction bounds. We also argue and then demonstrate that within the GLUE framework, when behavioral parameter sets are not sampled frequently enough, Latin hypercube sampling does not offer any improvements over simple random sampling.

关键词： WATER-QUALITY MODELS metropolis algorithm BAYESIAN-ESTIMATION GLUE METHODOLOGY EQUIFINALITY CATCHMENT PARAMETER SENSITIVITY OPTIMIZATION INFORMATION

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Feature-Inclusion Stochastic Search for Gaussian Graphical Models

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2008年第4期17卷 790-808页

作者： Scott, James G. Carvalho, Carlos M. Duke Univ Dept Stat Sci Durham NC 27708 USA Univ Chicago Grad Sch Business Chicago IL 60637 USA

We describe a serial algorithm called feature-inclusion stochastic search, or FINCS, that uses online estimates of edge-inclusion probabilities to guide Bayesian model determination in Gaussian graphical models. FINCS is compared to MCMC, to metropolis-based search methods, and to the popular lassos it is found to be superior along a variety of dimensions. leading to better sets of discovered models, greater speed and stability, and reasonable estimates of edge-inclusion probabilities. We illustrate FINCS on an example involving mutual-fund data, where we compare the model-averaged predictive performance of models discovered with FINCS to those discovered by competing methods.

关键词： Bayesian model selection Covariance selection Hyper-inverse Wishart distribution Lasso metropolis algorithm

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Estimating incumbency advantage and its variation, as an example of a before-after study

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2008年第482期103卷 437-446页

作者： Gelman, Andrew Huang, Zaiying Columbia Univ Dept Stat New York NY 10027 USA Columbia Univ Dept Polit Sci New York NY 10027 USA New York Times Co Circulat Dept New York NY USA

Incumbency advantage is one of the most widely studied features in American legislative elections. In this article we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century. Our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. More generally, our multilevel model represents a new method for estimating effects in before-after studies.

关键词： Bayesian inference before-after study congressional election Gibbs sampler incumbency advantage metropolis algorithm multilevel model

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Bayesian hierarchical classes analysis

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PSYCHOMETRIKA 2008年第1期73卷 39-64页

作者： Leenen, Iwin Van Mechelen, Iven Gelman, Andrew De Knop, Stijn Univ Complutense Madrid E-28040 Madrid Spain Univ Leuven Louvain Belgium Columbia Univ New York NY 10027 USA

Hierarchical classes models are models for N-way N-mode data that represent the association among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original model, the new probabilistic extension still represents both the association among the two modes and the hierarchical classifications. A fully Bayesian method for fitting the new model is presented and evaluated in a simulation study. Furthermore, we propose tools for model selection and model checking based on Bayes factors and posterior predictive checks. We illustrate the advantages of the new approach with applications in the domain of the psychology of choice and psychiatric diagnosis.

关键词： Bayesian hierarchical classes Markov chain Monte Carlo simulation metropolis algorithm psychiatric diagnosis psychology of choice

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Weak convergence of metropolis algorithms for non-IID target distributions

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ANNALS OF APPLIED PROBABILITY 2007年第4期17卷 1222-1244页

作者： Bedard, Mylene Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England

In this paper, we shall optimize the efficiency of metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the scaling of the proposal distribution as a function of the dimension, which leads to the proof of an asymptotic diffusion theorem. We show that when there does not exist any component with a scaling term significantly smaller than the others, the asymptotically optimal acceptance rate is the well-known 0.234.

关键词： metropolis algorithm weak convergence optimal scaling diffusion Markov chain Monte Carlo

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Neutral network sizes of biological RNA molecules can be computed and are not atypically small

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BMC BIOINFORMATICS 2008年第1期9卷 464-464页

作者： Jorg, Thomas Martin, Olivier C. Wagner, Andreas Univ Zurich Dept Biochem CH-8057 Zurich Switzerland Univ New Mexico Dept Biol Albuquerque NM 87131 USA Swiss Inst Bioinformat CH-1015 Lausanne Switzerland Santa Fe Inst Santa Fe NM 87501 USA Univ Paris 11 Lab Phys Theor & Modeles Stat F-91405 Orsay France Parc Orsay Univ 4 INRIA Inria Saclay Ile de France F-91893 Orsay France Univ Paris 11 UMR0320 Genet Vegetale UMR8120 F-91190 Gif Sur Yvette France

Background: Neutral networks or sets consist of all genotypes with a given phenotype. The size and structure of these sets has a strong influence on a biological system's robustness to mutations, and on its evolvability, the ability to produce phenotypic variation;in the few studied cases of molecular phenotypes, the larger this set, the greater both robustness and evolvability of phenotypes. Unfortunately, any one neutral set contains generally only a tiny fraction of genotype space. Thus, current methods cannot measure neutral set sizes accurately, except in the smallest genotype spaces. Results: Here we introduce a generalized Monte Carlo approach that can measure neutral set sizes in larger spaces. We apply our method to the genotype-to-phenotype mapping of RNA molecules, and show that it can reliably measure neutral set sizes for molecules up to 100 bases. We also study neutral set sizes of RNA structures in a publicly available database of functional, noncoding RNAs up to a length of 50 bases. We find that these neutral sets are larger than the neutral sets in 99.99% of random phenotypes. Software to estimate neutral network sizes is available at http://***/wagner/***. Conclusion: The biological RNA structures we examined are more abundant than random structures. This indicates that their robustness and their ability to produce new phenotypic variants may also be high.

关键词： Sequence Space Biological Structure Neutral Network metropolis algorithm Mutational Robustness

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