MICHAEL K PITT

Department of Statistics, University of Oxford, OX1 3TG and
Nuffield College, Oxford, OX1 1NF, UK

AND

NEIL SHEPHARD

Nuffield College, Oxford, OX1 1NF, UK

JOINT AND ANTITHETIC MCMC FOR NON-GAUSSIAN MEASUREMENTS WITH APPLICATIONS TO
STOCHASTIC VOLATILITY



In this paper we examine methods for improving the efficiency of sampling
the posterior distribution of the parameters of a non-Gaussian measurement
models by simultaneously drawing the parameters and the states. We suggest
that this is an effective strategy for reducing autocorrelation for MCMC\
methods. We also investigate the effect of attempting to induce negative
correlation in the Metropolis chain by the use of antithetic variables. This
is less successful in our experiments. The stochastic volatility model is
considered as a motivating example throughout.

KEYWORDS: Antithetic variables; Blocking; Kalman filter; Metropolis
sampling; Non-Gaussian measurement models; Simulation smoother; Stochastic
volatility.