Twisted particle filters

Whiteley, Nick; Lee, Anthony

doi:10.1214/13-aos1167

Cited by 26 publications

(61 citation statements)

References 34 publications

(51 reference statements)

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“…For example, particle Gibbs with ancestor sampling (Lindsten et al 2014) allows for efficient sampling of state trajectories and could be used in the rejuvenation step in SMC 2 . Recent work by Guarniero et al (2016) combines ideas underpinning the twisted particle filter of Whiteley and Lee (2014) and the APF to give the iterated APF (iAPF). The algorithm approximates an idealised particle filter where observed-data likelihood estimates have zero variance.…”

Section: Use Of Other Particle Filtersmentioning

confidence: 99%

Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

Golightly

Kypraios

2017

Stat Comput

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Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed-data likelihood. There has therefore been considerable attention given to the design of pseudo-marginal Markov chain Monte Carlo algorithms for such models. However, these methods are typically computationally intensive, often require careful tuning and must be restarted from scratch upon receipt of new observations. Sequential Monte Carlo (SMC) methods on the other hand aim to efficiently reuse posterior samples at each time point. Despite their appeal, applying SMC schemes in scenarios with both dynamic states and static parameters is made difficult by the problem of particle degeneracy. A principled approach for overcoming this problem is to move each parameter particle through a Metropolis-Hastings kernel that leaves the target invariant. This rejuvenation step is key to a recently proposed SMC 2 algorithm, which can be seen as the pseudo-marginal analogue of an idealised scheme known as iterated batch importance sampling. Computing the parameter weights in SMC 2 requires running a particle filter over dynamic states to unbiasedly estimate the intractable observed-data likelihood up to the current time point. In this paper, we propose to use an auxiliary particle filter inside the SMC 2 scheme. Our method uses two recently proposed constructs for sampling conditioned jump processes, and we find that the resulting inference schemes typically require fewer state particles than when using a simple bootstrap filter. Using two applications, we compare the performance B Andrew Golightly

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Section: Use Of Other Particle Filtersmentioning

confidence: 99%

Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

Golightly

Kypraios

2017

Stat Comput

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“…[34,15,10]) or potential functions (e.g. [56,9]) to improve estimates. Software has begun to address this complexity in methods, too.…”

Section: Introductionmentioning

confidence: 99%

Automated learning with a probabilistic programming language: Birch

Murray

Schön

2018

Annual Reviews in Control

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This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical workflow and how probabilistic programming languages can help to automate this workflow, especially in the matching of models with inference methods. We focus on two properties of a model that are critical in this matching: its structurethe conditional dependencies between random variablesand its formthe precise mathematical definition of those dependencies. While the structure and form of a probabilistic model are often fixed a priori, it is a curiosity of probabilistic programming that they need not be, and may instead vary according to random choices made during program execution. We introduce a formal description of models expressed as programs, and discuss some of the ways in which probabilistic programming languages can reveal the structure and form of these, in order to tailor inference methods. We demonstrate the ideas with a new probabilistic programming language called Birch, with a multiple object tracking example.

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“…[14] also consider variance comparison, but for linear Gaussian models. Perhaps the most complete approach is in [36], where the fixed N , but asymptotic in n, (the time parameter) properties of second moments of normalizing constant quantities are considered. Rather substantial work is required to compare algorithms using the approach of [36], but several interesting and sometimes known facts are derived.…”

Section: Introductionmentioning

confidence: 99%

“…Perhaps the most complete approach is in [36], where the fixed N , but asymptotic in n, (the time parameter) properties of second moments of normalizing constant quantities are considered. Rather substantial work is required to compare algorithms using the approach of [36], but several interesting and sometimes known facts are derived. In general, however, it is not always trivial to compare SMC algorithms and certainly one important way is by considering specific examples where explicit calculations can be performed.…”

Section: Introductionmentioning

confidence: 99%

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A note on random walks with absorbing barriers and sequential Monte Carlo methods

Moral

Jasra

2018

Stochastic Analysis and Applications

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In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman-Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article, is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.

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Twisted particle filters

Cited by 26 publications

References 34 publications

Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

Automated learning with a probabilistic programming language: Birch

A note on random walks with absorbing barriers and sequential Monte Carlo methods

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