# Variance estimation in the particle filter

@article{Lee2015VarianceEI, title={Variance estimation in the particle filter}, author={Anthony Lee and Nick Whiteley}, journal={arXiv: Computation}, year={2015} }

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 resampling operations, it is possible to estimate variances of a number of standard Monte Carlo approximations which particle filters deliver. All our estimators can be computed from a single run of a particle filter with no further simulation. We establish that as the number of particles grows, our estimators are… Expand

#### 31 Citations

Coupling of Particle Filters

- Mathematics
- 2016

Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the… Expand

Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment

- Mathematics, Computer Science
- IEEE Transactions on Signal Processing
- 2017

A novel method for assessing the convergence of particle filters in an online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment, are proposed. Expand

New results on particle filters with adaptive number of particles

- Mathematics
- 2019

In this paper, we present new results on particle filters with adaptive number of particles. First, we analyze a method which is based on generating fictitious observations from an approximated… Expand

Smoothing With Couplings of Conditional Particle Filters

- Computer Science, Mathematics
- 2017

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

Optimal potential functions for the interacting particle system method

- Computer Science
- Monte Carlo Methods Appl.
- 2021

This paper provides the expressions of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method and it proposes recommendations for the practical design of the potential functions. Expand

Optimal input potential functions in the interacting particle system method

- Mathematics
- 2018

The assessment of the probability of a rare event with a naive Monte-Carlo method is computationally intensive, so faster estimation or variance reduction methods are needed. We focus on one of these… Expand

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

- Mathematics, Biology
- 2018

The tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as it is illustrated by characterising the limiting mean and variance of the tree height. Expand

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

- Computer Science, Mathematics
- 2016

This work considers importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution and shows that the IS type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelisation. Expand

Unbiased estimation of log normalizing constants with applications to Bayesian cross-validation

- Mathematics
- 2018

Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number… Expand

Stability and examples of some approximate MCMC algorithms.

- Mathematics
- 2017

Approximate Monte Carlo algorithms are not uncommon these days, their applicability is related to the possibility of controlling the computational cost by introducing some noise or approximation in… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES

Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

- Mathematics
- 2004

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 of… Expand

Recursive Monte Carlo filters: Algorithms and theoretical analysis

- Mathematics
- 2003

Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform the computations in general state space models. We discuss and compare the accept-reject version with the… Expand

Adaptive particle allocation in iterated sequential Monte Carlo via approximating meta-models

- Mathematics, Computer Science
- Stat. Comput.
- 2016

The approximating model approach presented in this article is novel in the context of SMC and offers a computationally attractive procedure for practical analysis of a broad class of time series models. Expand

Stability properties of some particle filters

- Mathematics
- 2013

Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded… Expand

A general theory of particle filters in hidden Markov models and some applications

- Mathematics
- 2013

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although… Expand

Limit theorems for weighted samples with applications to sequential Monte Carlo methods

- Mathematics
- 2008

In the last decade, sequential Monte Carlo methods (SMC) emerged as a key tool in computational statistics [see, e.g., Sequential Monte Carlo Methods in Practice (2001) Springer, New York, Monte… Expand

A Tutorial on Particle Filtering and Smoothing: Fifteen years later

- Mathematics
- 2008

Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very… Expand

Numerically stable online estimation of variance in particle filters

- Mathematics
- 2017

This paper discusses variance estimation in sequential Monte Carlo methods, alternatively termed particle filters. The variance estimator that we propose is a natural modification of that suggested… Expand

Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers

- Mathematics
- 2013

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers [J. R.… Expand

Sequential Monte Carlo samplers

- Mathematics, Physics
- 2002

We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These… Expand