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This article develops a general-purpose adaptive sampler that approximatesthe target density by a mixture of multivariate t densities. The adaptivesampler is based on reversible proposal distributions each of which has themixture of multivariate t densities as its invariant density. The reversibleproposals consist of a combination of independent and correlated steps thatallow the sampler to traverse the parameter space efficiently as well asallowing the sampler to keep moving and locally exploring the parameter space.We employ a two-chain approach, in which a trial chain is used to adapt theproposal densities used in the main chain. Convergence of the main chain and astrong law of large numbers are proved under reasonable conditions, and withoutimposing a Diminishing Adaptation condition. The mixtures of multivariate tdensities are fitted by an efficient Variational Approximation algorithm inwhich the number of components is determined automatically. The performance ofthe sampler is evaluated using simulated and real examples. Our autocorrelatedframework is quite general and can handle mixtures other than multivariate t.

Adaptive Metropolis-Hastings Sampling using Reversible Dependent Mixture Proposals