On the Stability of Sequential Monte Carlo Methods in High Dimensions

Details On the Stability of Sequential Monte Carlo Methods in High Dimensions On the Stability of Sequential Monte Carlo Methods in High Dimensions

2011-03-21

arxiv.org/abs/1103.3965v2

Statistics

Computation

Scientific paper

We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces an approximation for the target that deteriorates as the dimension $d$ increases, unless the number of Monte Carlo samples $N$ increases at an exponential rate in $d$. We show that this degeneracy can be avoided by introducing a sequence of artificial targets, starting from a `simple' density and moving to the one of interest, using an SMC method to sample from the sequence. Using this class of SMC methods with a fixed number of samples, one can produce an approximation for which the effective sample size (ESS) converges to a random variable $\varepsilon_N$ as $d\rightarrow\infty$ with $1<\varepsilon_{N}

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