Convergence of adaptive direction sampling
Journal of Multivariate Analysis
Bayesian forecasting and dynamic models (2nd ed.)
Bayesian forecasting and dynamic models (2nd ed.)
Editorial: Special issue on adaptive Monte Carlo methods
Statistics and Computing
On adaptive Metropolis---Hastings methods
Statistics and Computing
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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.