  Particle Marginal Metropolis-Hastings (PMMH) is a general approach to
Bayesian inference when the likelihood is intractable, but can be estimated
unbiasedly. Our article develops an efficient PMMH method that scales up better
to higher dimensional state vectors than previous approaches. The improvement
is achieved by the following innovations. First, the trimmed mean of the
unbiased likelihood estimates of the multiple particle filters is used. Second,
a novel block version of PMMH that works with multiple particle filters is
proposed. Third, the article develops an efficient auxiliary disturbance
particle filter, which is necessary when the bootstrap disturbance filter is
inefficient, but the state transition density cannot be expressed in closed
form. Fourth, a novel sorting algorithm, which is as effective as previous
approaches but significantly faster than them, is developed to preserve the
correlation between the logs of the likelihood estimates at the current and
proposed parameter values. The performance of the sampler is investigated
empirically by applying it to non-linear Dynamic Stochastic General Equilibrium
models with relatively high state dimensions and with intractable state
transition densities and to multivariate stochastic volatility in the mean
models. Although our focus is on applying the method to state space models, the
approach will be useful in a wide range of applications
  such as large panel data models and stochastic differential equation models
with mixed effects.
