Optimally combining sampling techniques for Monte Carlo rendering
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Statistics and Computing
On population-based simulation for static inference
Statistics and Computing
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Statistics and Computing
Smooth functional tempering for nonlinear differential equation models
Statistics and Computing
An adaptive sequential Monte Carlo method for approximate Bayesian computation
Statistics and Computing
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Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density 驴(驴). Typically, ST involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say 驴 k (驴)驴 驴(驴) k . In this case, small values of k encourage better mixing, but samples from 驴 are only obtained when the joint chain for (驴,k) reaches k=1. However, the entire chain can be used to estimate expectations under 驴 of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), can disappoint. This is partly because the most immediately obvious implementation is naïve and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that the resulting estimator has a highly desirable property related to the notion of effective sample size. We briefly report on the success of the optimal combination in two modelling scenarios requiring reversible-jump MCMC, where the naïve approach fails.