Journal
STATISTICS AND COMPUTING
Volume 18, Issue 4, Pages 421-433Publisher
SPRINGER
DOI: 10.1007/s11222-008-9051-5
Keywords
Adaptive rejection Metropolis sampling; Bayesian inference; Markov chain Monte Carlo; Non-conjugate distribution; State-space model
Funding
- Royal Society of New Zealand
- University of Auckland Research Committee
- NSERC
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Different strategies have been proposed to improve mixing and convergence properties of Markov Chain Monte Carlo algorithms. These are mainly concerned with customizing the proposal density in the Metropolis-Hastings algorithm to the specific target density and require a detailed exploratory analysis of the stationary distribution and/or some preliminary experiments to determine an efficient proposal. Various Metropolis-Hastings algorithms have been suggested that make use of previously sampled states in defining an adaptive proposal density. Here we propose a general class of adaptive Metropolis-Hastings algorithms based on Metropolis-Hastings-within-Gibbs sampling. For the case of a one-dimensional target distribution, we present two novel algorithms using mixtures of triangular and trapezoidal densities. These can also be seen as improved versions of the all-purpose adaptive rejection Metropolis sampling (ARMS) algorithm to sample from non-logconcave univariate densities. Using various different examples, we demonstrate their properties and efficiencies and point out their advantages over ARMS and other adaptive alternatives such as the Normal Kernel Coupler.
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