Particle filters for partially observed diffusions

By Paul Fearnhead, Omiros Papaspiliopoulos, Gareth O. Roberts. 2007

171 citations recorded by the source corpus.

Summary. We introduce a novel particle filter scheme for a class of partially observed multivariate diffusions. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson process whose intensity is a known function of the diffusion (Cox process). Unlike currently available methods, our particle filters do not require approximations of the transition and/or the observation density by using time discretizations. Instead, they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density. We introduce the generalized Poisson estimator, which generalizes the Poisson estimator of Beskos and co‐workers. A central limit theorem is given for our particle filter scheme.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/251881487a5a747b27886bb75ed5f534cc15da32

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Citations in the corpus

Particle gibbs with ancestor sampling (2014, background): “This includes many models for which the transition is implicitly given by a simulator (Gander and Stephens, 2007; Fearnhead et al., 2008; Golightly and Wilkinson, 2008; Murray et al., 2013) or degenerate models where the transition density does not even exist (Ristic et al.”
Contribution to the discussion of \Sequential Quasi-Monte-Carlo Sampling" { Gerber, Chopin (2014, unknown): “Fearnhead et al. (2008); Pollock (2013); Pollock et al.”
SMC2: an efficient algorithm for sequential analysis of state space models (2011, background): “Filtering for dynamic models with intractable densities for which unbiased estimators can be computed was discussed in Fearnhead et al. (2008).”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “As a result, SV models, with volatility following a stochastic differential equation (SDE), have been introduced and used for realistic solutions to problems, such as option pricing and hedging (see, e.g. Hull & White, 1987).”
Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) (2006, background): “We have independently been investigating how the EA and related ideas can be applied to particle filters, and in Fearnhead et al. (2005) we have developed a general framework for unbiased particle filters.”
Stochastic Gradient Markov Chain Monte Carlo (2019, methodology): “The slower rate comes from needing to control the bias as well as the variance, and is similar to rates seen for other Monte Carlo problems where there are biases that need to be controlled (e.g. Section 3.3 of Fearnhead et al. , 2008).”
Smoothing algorithms for state–space models (2010, methodology): “Hence, it is possible to obtain an unbiased estimate of the weights given by (46) appearing in the generalised two-filter smoothing algorithm where r (x t k , x t k+1 ) is the realisation of a random variable with mean a(x t k , x t k+1 ); see Fearnhead et al. (2008a) for details.”
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi (2013, methodology): “Weighting with an unbiased estimate of that marginal likelihood gives a valid SMC algorithm as in the random-weight particle filter (Fearnhead et al. 2008; Fearnhead, Papaspiliopoulos, Roberts, and Stuart 2010), and is more specifically called SMC2 (Chopin et al.”
Sequential Monte Carlo with Highly Informative Observations (2014, unknown): “, [19, 20, 44]).”
Geostatistical inference under preferential sampling (2010, methodology): “It may be possible to adapt recent Monte Carlo methods for estimating likelihoods for diffusions (Beskos et al. , 2006; Fearnhead et al. , 2008) to estimating the likelihood (or the score) of the models that are considered in this paper unbiasedly.”