arXiv subjects

Alexander Y. Shestopaloff

Publications and source records attributed to Alexander Y. Shestopaloff.

22 records · Page 2Linked to original sources

arXiv2016

Sampling latent states for high-dimensional non-linear state space models with the embedded HMM method

We propose a new scheme for selecting pool states for the embedded Hidden Markov Model (HMM) Markov Chain Monte Carlo (MCMC) method. This new scheme allows the embedded HMM method to be used for efficient sampling in state space models where the state can be high-dimensional. Previously, embedded HMM methods were only applied to models with a one-dimensional state space. We demonstrate that using our proposed pool state selection scheme, an embedded HMM sampler can have similar performance to a well-tuned sampler that uses a combination of Particle Gibbs with Backward Sampling (PGBS) and Metropolis updates. The scaling to higher dimensions is made possible by selecting pool states locally near the current value of the state sequence. The proposed pool state selection scheme also allows each iteration of the embedded HMM sampler to take time linear in the number of the pool states, as opposed to quadratic as in the original embedded HMM sampler. We also consider a model with a multimodal posterior, and show how a technique we term "mirroring" can be used to efficiently move between the modes.

stat.CO↗

arXiv2014

Efficient Bayesian inference for stochastic volatility models with ensemble MCMC methods

In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter.

stat.CO↗

arXiv2014

On Bayesian inference for the M/G/1 queue with efficient MCMC sampling

We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates together with three novel "shift" and "scale" updates. We show that our novel updates improve the speed of sampling considerably, by factors of about 60 to about 180 on a variety of simulated data sets.

stat.CO↗

arXiv2013

MCMC for non-linear state space models using ensembles of latent sequences

Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble technique of Neal (2010) and the embedded HMM technique of Neal (2003), we introduce a new Markov Chain Monte Carlo method for non-linear state space models. The key idea is to perform parameter updates conditional on an enormously large ensemble of latent sequences, as opposed to a single sequence, as with existing methods. We look at the performance of this ensemble method when doing Bayesian inference in the Ricker model of population dynamics. We show that for this problem, the ensemble method is vastly more efficient than a simple Metropolis method, as well as 1.9 to 12.0 times more efficient than a single-sequence embedded HMM method, when all methods are tuned appropriately. We also introduce a way of speeding up the ensemble method by performing partial backward passes to discard poor proposals at low computational cost, resulting in a final efficiency gain of 3.4 to 20.4 times over the single-sequence method.

stat.CO↗