Quantitative Non-Geometric Convergence Bounds for Independence Samplers

Quantitative Non-Geometric Convergence Bounds for Independence Samplers

Markov chain Monte Carlo (MCMC) algorithms are widely used in statistics, physics, and computer science, to sample from complicated high-dimensional probability distributions. A central question is how quickly the chain converges to the target (stationarity) distribution. In this paper, we consider this question for a particular class of MCMC algorithms, independence samplers (Hastings, 1970; T...

Adaptive independence samplers

Markov chain Monte Carlo (MCMC) is an important computational technique for generating samples from non-standard probability distributions. A major challenge in the design of practical MCMC samplers is to achieve efficient convergence and mixing properties. One way to accelerate convergence and mixing is to adapt the proposal distribution in light of previously sampled points, thus increasing t...

Information bounds for Gibbs samplers

If we wish to eeciently estimate the expectation of an arbitrary function on the basis of the output of a Gibbs sampler, which is better: deterministic or random sweep? In each case we calculate the asymptotic variance of the empirical estimator, the average of the function over the output, and determine the minimal asymptotic variance for estimators that use no information about the underlying...

Independence and convergence in non-additive settings

Geometric Ergodicity of Gibbs Samplers

Due to a demand for reliable methods for exploring intractable probability distributions, the popularity of Markov chain Monte Carlo (MCMC) techniques continues to grow. In any MCMC analysis, the convergence rate of the associated Markov chain is of practical and theoretical importance. A geometrically ergodic chain converges to its target distribution at a geometric rate. In this dissertation,...