  Density tempering (also called density annealing) is a sequential Monte Carlo
approach to Bayesian inference for general state models; it 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. Our paper proposes efficient Markov
moves for generating the parameters and states for each stage of particle based
density tempering. This allows the proposed SMC methods to increase (scale up)
the number of parameters and states that can be handled. Most of the current
literature uses 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 is very inefficient when the states or parameters are
high dimensional. We also build on the work of Dufays (2016) and make data
tempering more robust to outliers and structural changes for models with
intractable likelihoods by adding batch tempering at each stage. 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 both many parameters and many latent
states.
