3,138 research outputs found
Sequential Monte Carlo Methods for System Identification
One of the key challenges in identifying nonlinear and possibly non-Gaussian
state space models (SSMs) is the intractability of estimating the system state.
Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced
more than two decades ago), provide numerical solutions to the nonlinear state
estimation problems arising in SSMs. When combined with additional
identification techniques, these algorithms provide solid solutions to the
nonlinear system identification problem. We describe two general strategies for
creating such combinations and discuss why SMC is a natural tool for
implementing these strategies.Comment: In proceedings of the 17th IFAC Symposium on System Identification
(SYSID). Added cover pag
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
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-
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
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