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TY - JOUR
T1 - Optimal scaling for the pseudo-marginal random walk Metropolis
T2 - insensitivity to the noise generating mechanism
AU - Sherlock, Christopher
N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-015-9471-6
PY - 2016/9
Y1 - 2016/9
N2 - 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 noise 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 simulation study with d = 5 and where a particle filter was used. Our key conclusions are found to hold in these examples also.
AB - 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 noise 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 simulation study with d = 5 and where a particle filter was used. Our key conclusions are found to hold in these examples also.
KW - Pseudo marginal Markov chain Monte Carlo
KW - Random walk Metropolis
KW - Optimal scaling
KW - Particle MCMC
KW - Robustness
KW - 65C05
KW - 65C40
U2 - 10.1007/s11009-015-9471-6
DO - 10.1007/s11009-015-9471-6
M3 - Journal article
VL - 18
SP - 869
EP - 884
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
SN - 1387-5841
IS - 3
ER -