On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation

On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation

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Article ID: iaor201112549
Volume: 38
Issue: 2
Start Page Number: 342
End Page Number: 358
Publication Date: Jun 2011
Journal: Scandinavian Journal of Statistics
Authors:
Keywords: statistics: empirical, probability, markov processes, stochastic processes, statistics: distributions, simulation, simulation: analysis, decision, programming: markov decision
Abstract:

Use of auxiliary variables for generating proposal variables within a Metropolis–Hastings setting has been suggested in many different settings. This has in particular been of interest for simulation from complex distributions such as multimodal distributions or in transdimensional approaches. For many of these approaches, the acceptance probabilities that are used turn up somewhat magic and different proofs for their validity have been given in each case. In this article, we will present a general framework for construction of acceptance probabilities in auxiliary variable proposal generation. In addition to showing the similarities between many of the proposed algorithms in the literature, the framework also demonstrates that there is a great flexibility in how to construct acceptance probabilities. With this flexibility, alternative acceptance probabilities are suggested. Some numerical experiments are also reported.

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