1,197 research outputs found
Particle Gibbs with Ancestor Sampling
Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining
the two main tools used for Monte Carlo statistical inference: sequential Monte
Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC
algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS).
PGAS provides the data analyst with an off-the-shelf class of Markov kernels
that can be used to simulate the typically high-dimensional and highly
autocorrelated state trajectory in a state-space model. The ancestor sampling
procedure enables fast mixing of the PGAS kernel even when using seemingly few
particles in the underlying SMC sampler. This is important as it can
significantly reduce the computational burden that is typically associated with
using SMC. PGAS is conceptually similar to the existing PG with backward
simulation (PGBS) procedure. Instead of using separate forward and backward
sweeps as in PGBS, however, we achieve the same effect in a single forward
sweep. This makes PGAS well suited for addressing inference problems not only
in state-space models, but also in models with more complex dependencies, such
as non-Markovian, Bayesian nonparametric, and general probabilistic graphical
models
An extended space approach for particle Markov chain Monte Carlo methods
In this paper we consider fully Bayesian inference in general state space
models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an
augmented model that takes into account all the variable sampled in a
sequential Monte Carlo algorithm. This paper describes an approach that also
uses sequential Monte Carlo to construct an approximation to the state space,
but generates extra states using MCMC runs at each time point. We construct an
augmented model for our extended space with the marginal distribution of the
sampled states matching the posterior distribution of the state vector. We show
how our method may be combined with particle independent Metropolis-Hastings or
particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis
acceptance probabilities are identical to those obtained in existing
approaches, so there is no extra cost in term of Metropolis-Hastings rejections
when using our approach. The number of MCMC iterates at each time point is
chosen by the used and our augmented model collapses back to the model in
Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show
empirically that our approach works well on applied examples and can outperform
existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version
On Scalable Particle Markov Chain Monte Carlo
Particle Markov Chain Monte Carlo (PMCMC) is a general approach to carry out
Bayesian inference in non-linear and non-Gaussian state space models. Our
article shows how to scale up PMCMC in terms of the number of observations and
parameters by expressing the target density of the PMCMC in terms of the basic
uniform or standard normal random numbers, instead of the particles, used in
the sequential Monte Carlo algorithm. Parameters that can be drawn efficiently
conditional on the particles are generated by particle Gibbs. All the other
parameters are drawn by conditioning on the basic uniform or standard normal
random variables; e.g. parameters that are highly correlated with the states,
or parameters whose generation is expensive when conditioning on the states.
The performance of this hybrid sampler is investigated empirically by applying
it to univariate and multivariate stochastic volatility models having both a
large number of parameters and a large number of latent states and shows that
it is much more efficient than competing PMCMC methods. We also show that the
proposed hybrid sampler is ergodic
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