Particle filter
lastmod 2022-07-12created 2016-02-262 edits
A particle filter is a simulation-based estimation technique, also called the sequential Monte Carlo method. Particle filters are used importantly in econometrics.
Particle filters are usually used to estimate Bayesian models. This is the case where the latent variables are related to each other by a Markov chain, similar to a hidden Markov model (HMM), but typically the state space of the unobserved variables is continuous and not restricted enough to allow exact estimation. For example, in a linear dynamical system, the state space of the latent variables is restricted to a Gaussian distribution, so exact estimation can be done efficiently with the Kalman filter alone. In the context of HMMs and related models, filtering determines the distribution of the latent variables at a specific time, given observations only up to that time; particle filters got their name because they use a set of "particles" (samples from a distribution with different weights) to "filter" (in the sense just described) the approximation.
A particle filter is a sequential analogue of the Markov chain Monte Carlo (MCMC) batch method and is sometimes similar to importance sampling. A well-designed particle filter is much faster than MCMC. It is sometimes used instead of the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). Its advantage over the EKF or UKF is that, with enough samples, it approaches the Bayesian optimal estimate and is therefore more accurate than the EKF or UKF. However, problems can arise if the number of samples is not sufficient. Particle filters and Kalman filters can also be combined, by using a kind of Kalman filter to propose the distribution for the particle filter.
See also
- Fragmentation grouping (resolving fragmentation) - Groups multiple fragmented objects and the like into a single object.