# 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

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#### 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
- Bernoulli
- 2019

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