Related papers: Finite Sample Bounds for Sequential Monte Carlo an…
We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…
In this paper, we provide bounds on the asymptotic variance for a class of sequential Monte Carlo (SMC) samplers designed for approximating multimodal distributions. Such methods combine standard SMC methods and Markov chain Monte Carlo…
We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties…
Statistical inference in evolutionary models with site-dependence is a long-standing challenge in phylogenetics and computational biology. We consider the problem of approximating marginal sequence likelihoods under dependent-site models of…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
In several implementations of Sequential Monte Carlo (SMC) methods it is natural, and important in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In…
We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…
We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…
Sequential Monte Carlo squared (SMC$^2$) methods can be used for parameter inference of intractable likelihood state-space models. These methods replace the likelihood with an unbiased particle filter estimator, similarly to particle Markov…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state space models, but offer an alternative to MCMC in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC…