On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

Convergence of Adaptive Markov Chain Monte Carlo Algorithms

In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions (Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not ne...

On the Containment Condition for Adaptive Markov Chain Monte Carlo Algorithms

This paper considers ergodicity properties of certain adaptive Markov chain Monte Carlo (MCMC) algorithms for multidimensional target distributions, in particular Adaptive Metropolis and Adaptive Metropoliswithin-Gibbs. It was previously shown by Roberts and Rosenthal (2007) that Diminishing Adaptation and Containment imply ergodicity of adaptive MCMC. We derive various sufficient conditions to...

Spatial count models on the number of unhealthy days in Tehran

Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models i...

Markov Chain Monte Carlo Algorithms: Theory and Practice

We describe the importance and widespread use of Markov chain Monte Carlo (MCMC) algorithms, with an emphasis on the roles in which theoretical analysis can help with their practical implementation. In particular, we discuss how to achieve rigorous quantitative bounds on convergence to stationarity using the coupling method together with drift and minorisation conditions. We also discuss recent...

On the Convergence of Unconstrained Adaptive Markov Chain Monte Carlo Algorithms