Optimal Scaling of Random Walk Metropolis Algorithms with Non-Gaussian Proposals
- 169 Downloads
The asymptotic optimal scaling of random walk Metropolis (RWM) algorithms with Gaussian proposal distributions is well understood for certain specific classes of target distributions. These asymptotic results easily extend to any light tailed proposal distribution with finite fourth moment. However, heavy tailed proposal distributions such as the Cauchy distribution are known to have a number of desirable properties, and in many situations are preferable to light tailed proposal distributions. Therefore we consider the question of scaling for Cauchy distributed proposals for a wide range of independent and identically distributed (iid) product densities. The results are somewhat surprising as to when and when not Cauchy distributed proposals are preferable to Gaussian proposal distributions. This provides motivation for finding proposal distributions which improve on both Gaussian and Cauchy proposals, both for finite dimensional target distributions and asymptotically as the dimension of the target density, d → ∞. Throughout we seek the scaling of the proposal distribution which maximizes the expected squared jumping distance (ESJD).
KeywordsMCMC Cauchy distribution Spherical distributions Heavy tailed distributions Random walk metropolis Optimal scaling
AMS 2000 Subject ClassificationsPrimary 60F05; Secondary 65C05
Unable to display preview. Download preview PDF.
- Sherlock C (2006) Methodology for inference on the Markov modulated Poisson process and theory for optimal scaling of the random walk Metropolis. PhD Thesis, Lancaster UniversityGoogle Scholar