Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method

Shestopaloff, Alexander Y.; Neal, Radford M.

doi:10.1214/17-ba1077

Cited by 10 publications

(27 citation statements)

References 6 publications

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“…The proof proceeds by induction on n by similar arguments as in [7]. At time n = 1, by Minkowski's inequality combined with Lemma 2 as well as (32) and (33), we have…”

Section: Lemma 1 Under Assumptions A1 and B1-b3 For Anymentioning

confidence: 96%

“…Furthermore, the conditional SMC scheme proposed in [1] can also be extended to MCMC-PFs as demonstrated in [33]. As discussed in [14], the resulting 'conditional' MCMC-PF can be used within the particle Gibbs sampler from [3].…”

Section: Generic Mcmc-pf Algorithmmentioning

confidence: 99%

“…with a n := 10 n p=1 T p r p,n β(P p,n ), where the last line follows from Minkowski's inequality combined with Lemma 2, (32), and (33). Since f n ∈ B (E n ), we can replace β(P p,n ) by β (P p,n ) in the derivation above.…”

Section: Lemma 1 Under Assumptions A1 and B1-b3 For Anymentioning

confidence: 99%

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Limit theorems for sequential MCMC methods

2020

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Both sequential Monte Carlo (SMC) methods (a.k.a. ‘particle filters’) and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish an $\mathbb{L}_r$ -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.

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“…The proof proceeds by induction on n by similar arguments as in [7]. At time n = 1, by Minkowski's inequality combined with Lemma 2 as well as (32) and (33), we have…”

Section: Lemma 1 Under Assumptions A1 and B1-b3 For Anymentioning

confidence: 96%

Section: Generic Mcmc-pf Algorithmmentioning

confidence: 99%

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Limit theorems for sequential MCMC methods

2020

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“…(2) This sampling problem is now commonly addressed using an MCMC scheme known as the iterated cSMC sampler (Andrieu et al, 2010) and extensions of it; see, e.g., (Shestopaloff & Neal, 2018). This algorithm relies on a SMC-type proposal mechanism.…”

Section: Introductionmentioning

confidence: 99%

Replica Conditional Sequential Monte Carlo

Shestopaloff,

Doucet

2019

Preprint

Self Cite

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We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such as the iterated conditional Sequential Monte Carlo (cSMC) scheme, which uses a Sequential Monte Carlo (SMC) type proposal within MCMC. A deficiency of standard SMC proposals is that they only use observations up to time t to propose states at time t when an entire observation sequence is available. More sophisticated SMC based on lookahead techniques could be used but they can be difficult to put in practice. We propose here replica cSMC where we build SMC proposals for one replica using information from the entire observation sequence by conditioning on the states of the other replicas. This approach is easily parallelizable and we demonstrate its excellent empirical performance when compared to the standard iterated cSMC scheme at fixed computational complexity.

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“…The advantage of the agent– based approach is that household structure and subject–level covariates may be incorporated into the model (Auranen et al, 2000, Höhle and Jørgensen, 2002, Cauchemez et al, 2004, Neal and Roberts, 2004, O’Neill, 2009). Development of DA methods for SEMs is of continuing interest, and recent works by Pooley et al (2015), Qin and Shelton (2015), and Shestopaloff and Neal (2016) have presented methods that could possibly be applied to epidemic count data. However, their algorithms forgo the flexibility of agent–based DA, and in the case of the latter two papers have not been applied to SEMs.…”

Section: Introductionmentioning

confidence: 99%

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Fintzi

Cui

Wakefield

et al. 2017

Journal of Computational and Graphical Statistics

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Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject–level disease histories. In our MCMC algorithm, we propose each new subject–level path, conditional on the data, using a time–inhomogeneous continuous–time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school.

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Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method

Cited by 10 publications

References 6 publications

Limit theorems for sequential MCMC methods

Limit theorems for sequential MCMC methods

Replica Conditional Sequential Monte Carlo

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

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