Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo

  title={Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo},
  author={Jere Koskela and Paul A. Jenkins and A. M. Johansen and Dario Span{\`o}},
  journal={arXiv: Statistics Theory},
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit in… Expand

Figures from this paper

An invitation to sequential Monte Carlo samplers
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. Expand
Smoothing With Couplings of Conditional Particle Filters
This work combines a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing, and establishes the validity of the proposed estimators under mild assumptions. Expand
Fast and numerically stable particle-based online additive smoothing: the AdaSmooth algorithm
Abstract: We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in theExpand
Inferring medication adherence from time-varying health measures
Medication adherence is a problem of widespread concern in clinical care. Poor adherence is a particular problem for patients with chronic diseases requiring long-term medication because poorExpand
Simple conditions for convergence of sequential Monte Carlo genealogies with applications
This work presents simple conditions under which the limiting process, as the number of particles grows, is a time-rescaled Kingman coalescent, and establishes these conditions for standard sequential Monte Carlo with a broad class of low-variance resampling schemes. Expand
Advanced Topics and Open Problems


Genealogical particle analysis of rare events
In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through aExpand
Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models
A path-valued interacting particle systems model for the genealogical structure of genetic algorithms is presented. We connect the historical process and the distribution of the whole ancestral treeExpand
Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
The term sequential Monte Carlo methods or, equivalently, particle filters, refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence ofExpand
Weak convergence to the coalescent in neutral population models
For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certainExpand
Convergence of Sequential Monte Carlo Methods
This paper presents a general sequential Monte Carlo (SMC) method which includes most of the important features present in current SMC methods and generalizes and encompasses many recent algorithms. Expand
The Convergence to Equilibrium of Neutral Genetic Models
This article is concerned with the long-time behavior of neutral genetic population models with fixed population size. We design an explicit, finite, exact, genealogical tree based representation ofExpand
On the stability of interacting processes with applications to filtering and genetic algorithms
Abstract The stability properties of a class of interacting measure valued processes arising in nonlinear filtering and genetic algorithm theory is discussed. Simple sufficient conditions are givenExpand
Particle Markov chain Monte Carlo methods
Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of MarkovExpand
Variance estimation in the particle filter
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resamplingExpand
The n-coalescent is a continuous-time Markov chain on a finite set of states, which describes the family relationships among a sample of n members drawn from a large haploid population. ItsExpand