The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the space of the auxiliary variables generated by an interacting particle system. This paper makes the following contributions to the theoretical study of this a...

The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an O(1/T ) convergence rate for models with independent variables and for fully connected probabilistic graphical models. Herded Gibbs is shown to outperfo...

The wide applicability of Gibbs sampling has increased the use of more complex and multi-level hierarchical models. To use these models entails dealing with hyperparameters in the deeper levels of a hierarchy. There are three typical methods for dealing with these hyperparameters: specify them, estimate them, or use a 'flat' prior. Each of these strategies has its own associated problems. In th...

Sampling from Gibbs distributions by Eric Joseph Vigoda Doctor of Philosophy in Computer Science University of California at Berkeley Professor Alistair Sinclair, Chair This thesis considers computational questions concerning statistical mechanical models of idealized physical systems. The equilibrium state of the physical system is described by a probability distribution over the allowed con g...