Approximate filtering via discrete dual processes - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Stochastic Processes and their Applications Year : 2023

Approximate filtering via discrete dual processes

Abstract

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case of duality between the diffusion and a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox-Ingersoll-Ross and Wright-Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.
Fichier principal
Vignette du fichier
2310.00599.pdf (596.66 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04309185 , version 1 (27-11-2023)

Licence

Attribution

Identifiers

Cite

Guillaume Kon Kam King, Andrea Pandolfi, Marco Piretto, Matteo Ruggiero. Approximate filtering via discrete dual processes. Stochastic Processes and their Applications, In press, 168, pp.104268. ⟨10.1016/j.spa.2023.104268⟩. ⟨hal-04309185⟩
5 View
6 Download

Altmetric

Share

Gmail Facebook X LinkedIn More