Flexible and Robust Particle Tempering for State Space Models

Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models which is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a collection of parameters and latent states (which are called particles) through a number of stages, with each stage having its own target distribution. The particles are initially generated from a distribution that is easy to sample from, e.g. the prior; the target at the final stage is the posterior distribution. Tempering is usually carried out either in batch mode, involving all the data at each stage, or sequentially with observations added at each stage, which is called data tempering. Efficient Markov moves for generating the parameters and states for each stage of particle based density tempering are proposed. This allows the proposed SMC methods to increase (scale up) the number of parameters and states that can be handled. Most current methods use a pseudo-marginal Markov move step with the states “integrated out”, and the parameters generated by a random walk proposal; although this strategy is general, it can be very inefficient when the states or parameters are high dimensional. By adding batch tempering at each stage, previous methods are extended to make data tempering more robust to outliers and structural changes for models with intractable likelihoods. The performance of the proposed methods is evaluated using univariate stochastic volatility models with outliers and structural breaks, and high dimensional factor stochastic volatility models having many parameters and many latent states.¹