Antithetic Sampling for Sequential Monte Carlo Methods with Application to
State Space Models
Svetlana Bizjajeva and Jimmy Olsson
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2008
ISSN 14039338

Abstract:

In this paper we cast the idea of antithetic sampling, widely used in standard
Monte Carlo simulation, into the framework of sequential Monte Carlo methods.
A version of the standard auxiliary particle filter (Pitt and Shephard, 1999)
is proposed where the particles are mutated blockwise in such a way that
all particles within each block are, firstly, offspring of a common ancestor
and, secondly, negatively correlated conditionally on this ancestor. By deriving
and examining the weak limit of a central limit theorem describing the
convergence of the algorithm, we conclude that the asymptotic variance of
the produced Monte Carlo estimates can be straightforwardly decreased by
means of antithetic techniques when the particle filter is close to fully
adapted, which involves approximation of the socalled optimal proposal kernel.
As an illustration, we apply the method to optimal filtering in state space
models.



Key words:

antithetic sampling, central limit theorem, optimal filtering, optimal kernel,
particle filter, permuted displacement method, state space models
