2014/08/19 by Sherlock, Chris
#65C05 #65C40 #Computation (stat.CO) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1408.4344
We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, d→ ∞. We prove that the optimal scaling for a given target varies by less than 20% across a wide range of distributions for the noise in the estimate of the target, and that any scaling that is within 20% of the optimal one will be at least 70% efficient. We demonstrate that this phenomenon occurs even outside the range of distributions for which we rigorously prove it. We then conduct a simulation study on an example with d=10 where importance sampling is used to estimate the target density; we also examine results available from an existing simulations study with d=5 and where a particle filter was used. Our key conclusions are found to hold in these examples also.