Gibbs sampling of complex-valued distributions

Sampling from Gibbs distributions

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...

Occupancy distributions arising in sampling from Gibbs-Poisson abundance models

Estimating the number n of unseen species from a k−sample displaying only p ≤ k distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a discrete model of iid stochastic species abundances, each with Gibbs-Poisson distribution. A k−sample drawn from the n−species abundances vector is the one obtained while...

Sampling Distributions Sampling Distributions

On particle Gibbs sampling

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...

Herded Gibbs Sampling

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...