Theoretical And Algorithmic Developments In Markov Chain Monte Carlo

Theoretical And Algorithmic Developments In Markov Chain Monte Carlo

Bibliographic Details
Main Author: Paul, Rajib
Language:English
Published: The Ohio State University / OhioLINK 2008
Subjects:
Statistics
glacial dynamics
batch-mean methods
ergodicity
functional CLT
diffusion
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1218184168
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu12181841682021-08-03T05:54:20Z Theoretical And Algorithmic Developments In Markov Chain Monte Carlo Paul, Rajib Statistics glacial dynamics batch-mean methods ergodicity functional CLT diffusion <p>This PhD thesis is concerned with three problems: (1) "Bayesian Change PointAnalysis for Mechanistic Modeling," (3) "Assessing Convergence and Mixing of MarkovChain Monte Carlo via Stratification," and (2) "Bayesian Analysis via DiffusionMonte Carlo."</p><p>In Bayesian parametric change point modeling, the primary challenges are detectionof the number and locations of change points and obtaining the posteriordistribution of other unknown parameters involved in the model. Chapter 2 suggestsapproaches for dealing with the computational burden arising in change point modelsthat involving mechanistic reasoning as well as random explanatory variables. Wepresent an example invovling flow velocities of ice sheets in the Lambert Glacial Basinof east Antarctica. We pay special attention to the development of reasonable priorsthat can reflect a variety of prior information.</p><p>In Chapter 3 we apply the notion of post-stratification to develop assessment toolsfor MCMC analysis. These tools are based on comparison of variances of two naturalestimators. Based on the estimates of these variances we propose a test statistic whichhelps in checking convergence and mixing of MCMC. Our method is illustrated using aBayesian change-point model for ice flow velocity in East Antarctica, a logistic regressionmodel, a latent variable model for Arsenic concentration in public water systemsin Arizona, and a regime-switching model for Pacific sea surface temperatures.</p><p>Markov chain algorithms using langevin-type diffusion sometimes offer potentiallyuseful methods in cases for which other MCMC methods are challenging. The keyidea is to develop a stochastic process whose stationary distribution is the targetposterior using diffusions represented as solutions to stochastic differential equations(SDE). The main challenge is to solve the required SDE's. Naive discretizationslike the Euler method can lead to lack of ergodicity. Hence, more sophisticateddiscretizations or Metropolis-Hastings correction steps are prescribed. Chapter 4 ofmy dissertation research deals with development of diffusion based algorithms forposterior distributions arising from non-conjugate Gaussian models with non-linearmean and variance functions.</p> 2008-09-11 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1218184168 http://rave.ohiolink.edu/etdc/view?acc_num=osu1218184168 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Statistics
glacial dynamics
batch-mean methods
ergodicity
functional CLT
diffusion
spellingShingle Statistics
glacial dynamics
batch-mean methods
ergodicity
functional CLT
diffusion
Paul, Rajib
Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
author Paul, Rajib
author_facet Paul, Rajib
author_sort Paul, Rajib
title Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
title_short Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
title_full Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
title_fullStr Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
title_full_unstemmed Theoretical And Algorithmic Developments In Markov Chain Monte Carlo
title_sort theoretical and algorithmic developments in markov chain monte carlo
publisher The Ohio State University / OhioLINK
publishDate 2008
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1218184168
work_keys_str_mv AT paulrajib theoreticalandalgorithmicdevelopmentsinmarkovchainmontecarlo
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