Particle filters
incorporating Interacting Particle Systems, Sequential Monte Carlo and a profusion of other simultaneous-discovery names
July 25, 2014 — March 24, 2023
Bayes
Monte Carlo
particle
probabilistic algorithms
probability
sciml
signal processing
state space models
statistics
swarm
time series
A Monte Carlo algorithm updates a population of samples with a nested update. The easiest entry point is, IMO, to think about random-sample generalisation of state filter models via importance sampling. These are classically considered cousins to the linear Gaussian Kalman filter, applicable to more challenging models at the cost of using Monte Carlo approximations.
This has nothing to do with filters for particulate matter as seen in respirators. These are abstract mathematical particles.
There is too much confusing and unhelpful terminology here, and I am only at the fringe of this field, so I will not attempt to typologize. Let us clear up the main stumbling block though: somehow the theoretical basis field has coalesced under the banner of interacting particle systems, which is an awful unsearchable name that could mean anything, and indeed does in other disciplines. Wikipedia disambiguates this problem with the gritty and also abstruse Mean Field Particle Methods. In practical applications, we talk about particle filters, or sequential Monte Carlo, or bootstrap filters, or iterated importance sampling, and these all denote confusingly similar concepts.
1 Introductions
- Pierre Jacob’s Particle methods for statistics reading list
- The lineage and reasoning are well explained by Cappé, Godsill, and Moulines (2007).
- Chopin and Papaspiliopoulos (2020)
Easy to explain with an example such as this particle filter in scala.
2 Feynman-Kac formulae
See Feynman-Kac.
3 System Identification in
Do not know the parameters governing the system dynamics and need to learn those too? See System identification with particle filters.
4 Relation to Ensemble Kalman filters
Yes.
5 Particle flow
Introduced to me by my colleague Adrian Bishop (Bunch and Godsill 2014; Daum, Huang, and Noushin 2010; Daum and Huang 2010, 2009, 2008, 2013).
6 Non-Gaussian evolution
6.1 Jump process
I am interested in jump-process SMC (to be defined). For those, I should apparently consult Graham and Méléard (1997);Grünbaum (1971);Méléard (1996);Shiga and Tanaka (1985).
6.2 On weird graphs
Christian Andersson Naesseth, Lindsten, and Schön (2014)
7 Rao-Blackwellized particle filter
Particles which represent marginalised densities (Murphy 2012, 23.6).
8 Tooling
Some MCMC toolkits incorporate SMC too.
- particles is a python library for teaching DIY particle filtering, to accompany the book Chopin and Papaspiliopoulos (2020).
- Johansen’s page, with C++ software
- Dirk Eddelbuettel’s lab created RCppSMC for R integration of the Johansen stuff. Documentation is not great — it only consists of black-box toy problems without any hint of how you would construct, e.g. a likelihood function, so I can’t evaluate how easy this would be to use, as opp plain C++.
- most probabilistic programming languages include a particle filter example.
9 References
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