Bernoulli

  • Bernoulli
  • Volume 20, Number 4 (2014), 1999-2019.

Optimal filtering and the dual process

Omiros Papaspiliopoulos and Matteo Ruggiero

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Abstract

We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to functions that define changes of measure conjugate to the emission density, the filtering distributions evolve in the family of finite mixtures of such measures and the filter can be computed at a cost that is polynomial in the number of observations. Special cases of our framework include the Kalman filter, and computable filters for the Cox–Ingersoll–Ross process and the one-dimensional Wright–Fisher process, which have been investigated before. The dual we obtain for the Cox–Ingersoll–Ross process appears to be new in the literature.

Article information

Source
Bernoulli, Volume 20, Number 4 (2014), 1999-2019.

Dates
First available in Project Euclid: 19 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1411134451

Digital Object Identifier
doi:10.3150/13-BEJ548

Mathematical Reviews number (MathSciNet)
MR3263096

Zentralblatt MATH identifier
1302.60071

Keywords
Bayesian conjugacy Cox–Ingersoll–Ross process finite mixture models hidden Markov model Kalman filter

Citation

Papaspiliopoulos, Omiros; Ruggiero, Matteo. Optimal filtering and the dual process. Bernoulli 20 (2014), no. 4, 1999--2019. doi:10.3150/13-BEJ548. https://projecteuclid.org/euclid.bj/1411134451


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