limis

Fasiolo M, de Melo F E, Maskell S. Langevin incremental mixture importance sampling[J]. Statistics and Computing, 2016: 1-13.

This paper proposes a novel method through which local information about the target density can be used to construct an efficient importance sampler. The backbone of the proposed method is the Incremental Mixture Importance Sampling (IMIS) algorithm, which builds a mixture importance distribution incrementally.

The efficiency gains brought about by taking into account local information about the target density have been amply demonstrated in the context of MCMC sampling.

The drawback of many particle flow algorithms is that, despite their theoretical elegance, implementing them for general models requires several layes of approximation, whose effect is not easy to quantify.

Incremental Mixture Importance Sampling

The IMIS algorithm is an automatric and non-parametric approach to IS, which is particularly useful for highly non-Gaussian target densities. Let (pi(x)) and (p(x)) be, respectively, the target and the prior densities.

The key idea behind IMIS is that it lets the importance weights determine where new mixture components should be placed.

Langevin Incremental Mixture Importance Sampling

Consider a (d)-dimensional Langevin diffusion, with stationary distribution (pi(x)), which is defined by the stochastic differential equation

(d x_t = frac{dt}{2} nabla log pi (x_t) + db_t)

In the context of importance sampling, an accurate global approximation to (pi(x)) is needed. The IMIS algorithm provides a natural apprach to determining the initial positions.

LIMIS has several advantageous properties.

Conclusions

The LIMIS algorithm provides a simple but flexible iterative framework for concurrently constructing a mixture importance density and performing importance sampling using such a density.