Geometric ergodicity of a random-walk Metropolis algorithm for a transformed density

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Geometric ergodicity of a random-walk Metropolis algorithm for a transformed density

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Johnson, Leif

Geyer, Charles J.

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2010-11-22

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Abstract

Curvature conditions on a target density in R^k for the geometric ergodicity of a random-walk Metropolis algorithm have previously been established (Mengersen and Tweedie(1996), Roberts and Tweedie(1996), Jarner and Hansen(2000)). However, the conditions for target densities in R^k that have exponentially light tails, but are not super-exponential are difficult to apply. In this paper I establish a variable transformation to apply to such target densities, that along with a regularity condition on the target density, ensures that a random-walk Metropolis algorithm for the transformed density is geometrically ergodic. Inference can be drawn for the original target density using Markov chain Monte Carlo estimates based on the transformed density. An application to inference on the regression parameter in multinomial logit regression with a conjugate prior is given.

Keywords

Markov chain Monte Carlo

MCMC

Metropolis

random walk

transformed density

geometric ergodicity

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School of Statistics Graduate Student Research

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Technical Report
680

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Johnson, Leif; Geyer, Charles J.. (2010). Geometric ergodicity of a random-walk Metropolis algorithm for a transformed density. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/96959.

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