We propose a novel approximate inference framework that approximates a target distribution by amortising the dynamics of a user-selected Markov chain Monte Carlo (MCMC) sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality...

We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the pres...

These notes are intended to provide the reader with knowledge of basic concepts of Markov chain Monte Carlo (MCMC) and hopefully also some intuition about how MCMC works. For more thorough accounts of MCMC the reader is referred to e.g. Gilks et al. (1996), Gamerman (1997), or Robert and Casella (1999). Suppose that we are interested in generating samples from a target probability distribution ...

Adaptive Markov Chain Monte Carlo (MCMC) algorithms attempt to ‘learn’ from the results of past iterations so the Markov chain can converge quicker. Unfortunately, adaptive MCMC algorithms are no longer Markovian, so their convergence is difficult to guarantee. In this paper, we develop new diagnostics to determine whether the adaption is still improving the convergence. We present an algorithm...

We consider the problem of estimating continuous-time autoregressive (CAR) processes from discrete-time noisy observations. This can be done within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Existing methods include the standard random walk Metropolis algorithm. On the other hand, least-squares (LS) algorithms exist where derivatives are approximated by di erences and p...

As the many examples in this book illustrate, Markov chain Monte Carlo (MCMC) methods have revolutionized Bayesian statistical analyses. Rather than using off-the-shelf models and methods, we can use MCMC to fit application specific models that are designed to account for the particular complexities of a problem at hand. These complex multilevel models are becoming more prevalent throughout the...

We present a novel and powerful strategy for estimating and combining classi ers via ROC curves, decision analysis theory and MCMC simulation. This paradigm also allows us to select samples from an MCMC run in a parsimonious and optimal fashion. Each ROC curve, corresponds to a sample (classi er) obtained with a full Bayesian model, which treats the model dimension, model parameters, regularisa...

in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a fourway contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p...