Sequential Monte Carlo with transformations

Everitt, Richard G.; Culliford, Richard; Medina-Aguayo, Felipe J.; Wilson, Daniel J.

doi:10.1007/s11222-019-09903-y

Cited by 9 publications

(8 citation statements)

References 42 publications

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“…We cannot expect SMC samplers that rely on MCMC kernels to perform well when these kernels have poor mixing properties. This has motivated the use of other non-equilibrium dynamics [Vaikuntanathan and Jarzynski, 2008, Heng et al, 2015, Bernton et al, 2019a, Everitt et al, 2020. There are some studies on the advantages of interacting particle methods over Markov chains on multimodal targets [Schweizer, 2012b, Paulin et al, 2019.…”

Section: Discussionmentioning

confidence: 99%

An invitation to sequential Monte Carlo samplers

Dai¹,

Heng²,

Jacob³

et al. 2020

Preprint

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Sequential Monte Carlo samplers provide consistent approximations of sequences of probability distributions and of their normalizing constants, via particles obtained with a combination of importance weights and Markov transitions. This article presents this class of methods and a number of recent advances, with the goal of helping statisticians assess the applicability and usefulness of these methods for their purposes. Our presentation emphasizes the role of bridging distributions for computational and statistical purposes. Numerical experiments are provided on simple settings such as multivariate Normals, logistic regression and a basic susceptible-infected-recovered model, illustrating the impact of the dimension, the ability to perform inference sequentially and the estimation of normalizing constants.

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Section: Discussionmentioning

confidence: 99%

An invitation to sequential Monte Carlo samplers

Dai¹,

Heng²,

Jacob³

et al. 2020

Preprint

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“…This reasoning also applies to mixture models and clustering, for which a labelling of components may be introduced in order to avoid identifiability problems with the parameters of interest. We have noted some of these aspects in Everitt et al (2016), where ordering of components leads to the aforementioned intractability of the joint proposal q.…”

Section: Motivationmentioning

confidence: 99%

Revisiting the balance heuristic for estimating normalising constants

Medina-Aguayo,

Everitt

2019

Preprint

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Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in computer graphics. The basic ingredients for computing the estimator are: a set of proposal distributions, indexed by some discrete label, and a predetermined number of draws from each of these proposals. However, if the number of available proposals is much larger than the number of permitted importance points, one needs to select, possibly at random, which of these distributions will be used. The focus of this work lies within the previous context, exploring some improvements and variations of the balance heuristic via a novel extended-space representation of the estimator, leading to straightforward annealing schemes for variance reduction purposes. In addition, we also look at the intractable scenario where the proposal density is only available as a joint function with the discrete label, as may be encountered in problems where an ordering is imposed. For this case, we look at combinations of correlated unbiased estimators which also fit into the extended-space representation and, in turn, will provide other interesting solutions.

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“…The SMCS algorithm is a generalization of the particle filter (Sanjeev Arulampalam et al 2002;Doucet and Johansen 2009) for dynamic state estimation, generating weighted samples from the posterior distribution. Since the SMCS algorithm was proposed in Del Moral et al (2006), considerable improvements and extensions of the method have been proposed, such as Fearnhead and Taylor (2013), Beskos et al (2017), Heng et al (2020), Everitt et al (2020), and more information on the developments of the SMCS methods can be found in the recent reviews (Dai et al 2020;Chopin and Papaspiliopoulos 2020). We also note here that there are other parameter estimation schemes also based on particle filtering, e.g., Gilks and Berzuini (2001), Chopin (2002), and the differences and connections between SMCS and these schemes are discussed in Del Moral et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Ensemble Kalman filter based sequential Monte Carlo sampler for sequential Bayesian inference

Wu¹,

Wen

Green

et al. 2022

Stat Comput

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Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as Markov chain Monte Carlo cannot efficiently address such problems as they do not take advantage of the data’s sequential structure. To this end, sequential methods which seek to update the posterior distribution whenever a new collection of data become available are often used to solve these types of problems. Two popular choices of sequential method are the ensemble Kalman filter (EnKF) and the sequential Monte Carlo sampler (SMCS). While EnKF only computes a Gaussian approximation of the posterior distribution, SMCS can draw samples directly from the posterior. Its performance, however, depends critically upon the kernels that are used. In this work, we present a method that constructs the kernels of SMCS using an EnKF formulation, and we demonstrate the performance of the method with numerical examples.

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Sequential Monte Carlo with transformations

Cited by 9 publications

References 42 publications

An invitation to sequential Monte Carlo samplers

An invitation to sequential Monte Carlo samplers

Revisiting the balance heuristic for estimating normalising constants

Ensemble Kalman filter based sequential Monte Carlo sampler for sequential Bayesian inference

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