14,818 research outputs found
Particle Metropolis-Hastings using gradient and Hessian information
Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in
nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and
particle filtering. The latter is used to estimate the intractable likelihood.
In its original formulation, PMH makes use of a marginal MCMC proposal for the
parameters, typically a Gaussian random walk. However, this can lead to a poor
exploration of the parameter space and an inefficient use of the generated
particles.
We propose a number of alternative versions of PMH that incorporate gradient
and Hessian information about the posterior into the proposal. This information
is more or less obtained as a byproduct of the likelihood estimation. Indeed,
we show how to estimate the required information using a fixed-lag particle
smoother, with a computational cost growing linearly in the number of
particles. We conclude that the proposed methods can: (i) decrease the length
of the burn-in phase, (ii) increase the mixing of the Markov chain at the
stationary phase, and (iii) make the proposal distribution scale invariant
which simplifies tuning.Comment: 27 pages, 5 figures, 2 tables. The final publication is available at
Springer via: http://dx.doi.org/10.1007/s11222-014-9510-
Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces
Nonlinear non-Gaussian state-space models arise in numerous applications in
statistics and signal processing. In this context, one of the most successful
and popular approximation techniques is the Sequential Monte Carlo (SMC)
algorithm, also known as particle filtering. Nevertheless, this method tends to
be inefficient when applied to high dimensional problems. In this paper, we
focus on another class of sequential inference methods, namely the Sequential
Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising
alternative to SMC methods. After providing a unifying framework for the class
of SMCMC approaches, we propose novel efficient strategies based on the
principle of Langevin diffusion and Hamiltonian dynamics in order to cope with
the increasing number of high-dimensional applications. Simulation results show
that the proposed algorithms achieve significantly better performance compared
to existing algorithms
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