Sequential Monte Carlo Samplers: Error Bounds and Insensitivity to Initial Conditions

Whiteley, Nick

doi:10.1080/07362994.2012.684323

Cited by 29 publications

(35 citation statements)

References 30 publications

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“…This result is established as d grows with N fixed, whilst the classical results require N to grow. As in [3,30], this establishes that the ergodicity of the Markov kernels used in the algorithm can provide stability of the algorithm, even in high dimensions if the number of artificial densities is scaled appropriately with d.…”

Section: Problems Addressedmentioning

confidence: 58%

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Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions

et al. 2014

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In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d → ∞, while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative L 2 -error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd 2 ).

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Section: Problems Addressedmentioning

confidence: 58%

“…This corresponds to introducing d artificial densities between an initial distribution and the one of interest. The case of fixed d also has been analyzed recently [30].…”

Section: Introductionmentioning

confidence: 99%

Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions

et al. 2014

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“…Simulations demonstrated both the feasability of the SMC method for challenging infinite dimensional inversion, as well as the property of posterior contraction the time parameter. It is of interest to find realistic conditions for which this is not the case (for instance the bounds in [10,11,28] have assumptions which either do not hold or are hard to verify). Secondly, a further algorithmic innovation is to use multi-level Monte Carlo method as in [16], within the SMC context; this is being considered in [6].…”

Section: Discussionmentioning

confidence: 99%

Sequential Monte Carlo methods for Bayesian elliptic inverse problems

et al. 2015

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In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the complexity of the link function between unknown field and measurements can make it difficult to draw inference from the associated posterior. We prove that for this inverse problem a basic SMC method has a Monte Carlo rate of convergence with constants which are independent of the dimension of the discretization of the problem; indeed convergence of the SMC method is established in a function space setting. We also develop an enhancement of the sequential Monte Carlo (SMC) methods for inverse problems which were introduced in [20]; the enhancement is designed to deal with the additional complexity of this elliptic inverse problem. The efficacy of the methodology, and its desirable theoretical properties, are demonstrated on numerical examples in both two and three dimensions.

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“…Relative to static importance sampling, the influence of the choice of this initial distribution is diminished as new information is brought to bear with each additional period of data. The effect of the initial distribution decays exponentially in the number of periods (Whiteley, ).…”

Section: Sequential Monte Carlo Methodsmentioning

confidence: 99%

Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

Blevins

2015

J of Applied Econometrics

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SUMMARYThis paper develops estimators for dynamic microeconomic models with serially correlated unobserved state variables using sequential Monte Carlo methods to estimate the parameters and the distribution of the unobservables. If persistent unobservables are ignored, the estimates can be subject to a dynamic form of sample selection bias. We focus on single-agent dynamic discrete-choice models and dynamic games of incomplete information. We propose a full-solution maximum likelihood procedure and a two-step method and use them to estimate an extended version of the capital replacement model of Rust with the original data and in a Monte Carlo study.

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Sequential Monte Carlo Samplers: Error Bounds and Insensitivity to Initial Conditions

Cited by 29 publications

References 30 publications

Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions

Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions

Sequential Monte Carlo methods for Bayesian elliptic inverse problems

Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

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