Mylène Bédard

Efficient Sampling Using Metropolis Algorithms: Applications of Optimal Scaling Results

We recently considered the optimal scaling problem of Metropolis algorithms for multidimensional target distributions with non-IID components. The results that were proven have wide applications and the aim of this article is to show how practitioners can take advantage of them. In particular, we use several examples to illustrate the casewhere the asymptotically optimal acceptance rate is the usual 0.234, and also the latest developments where smaller acceptance rates should be adopted for optimal sampling from the target distributions involved. We study the impact of the proposal scaling on the performance of the algorithm, and finally perform simulation studies exploring the efficiency of the algorithm when sampling from some popular statistical models.

Higher Accuracy for Bayesian and Frequentist Interference: Large Sample Theory for Small Sample Likelihood.

Recent likelihood theory produces

Hierarchical models

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Bayes, Reproducibility and the Quest for Truth

-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such

A Dirichlet form approach to MCMC optimal scaling

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Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234

-values is by simulations, and such simulations do verify that the global distribution of the

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

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Scaling analysis of multiple-try MCMC methods

-values is uniform(0, 1), to high accuracy in repeated sampling. The derivation of the

Scaling Analysis of Delayed Rejection MCMC Methods

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On the robustness of optimal scaling for random walk metropolis algorithms

-values, however, asserts a stronger statement, that they have a uniform(0, 1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various