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Full-Text Articles in Probability
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Graduate Theses and Dissertations
Markov chain Monte Carlo (MCMC) is a simulation technique that produces a Markov chain designed to converge to a stationary distribution. In Bayesian statistics, MCMC is used to obtain samples from a posterior distribution for inference. To ensure the accuracy of estimates using MCMC samples, the convergence to the stationary distribution of an MCMC algorithm has to be checked. As computation time is a resource, optimizing the efficiency of an MCMC algorithm in terms of effective sample size (ESS) per time unit is an important goal for statisticians. In this paper, we use simulation studies to demonstrate how the Gibbs …
Effect Of Predictor Dependence On Variable Selection For Linear And Log-Linear Regression, Apu Chandra Das
Effect Of Predictor Dependence On Variable Selection For Linear And Log-Linear Regression, Apu Chandra Das
Graduate Theses and Dissertations
We propose a Bayesian approach to the Dirichlet-Multinomial (DM) regression model, which uses horseshoe, Laplace, and horseshoe plus priors for shrinkage and selection. The Dirichlet-Multinomial model can be used to find the significant association between a set of available covariates and taxa for a microbiome sample. We incorporate the covariates in a log-linear regression framework. We design a simulation study to make a comparison among the performance of the three shrinkage priors in terms of estimation accuracy and the ability to detect true signals. Our results have clearly separated the performance of the three priors and indicated that the horseshoe …