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Approximate filtering via discrete dual processes

Articolo
Data di Pubblicazione:
2024
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 reversible 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 where the dual is 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.
Tipologia CRIS:
03A-Articolo su Rivista
Elenco autori:
Guillaume Kon Kam King; Andrea Pandolfi; Marco Piretto; Matteo Ruggiero
Autori di Ateneo:
RUGGIERO Matteo
Link alla scheda completa:
https://iris.unito.it/handle/2318/1947332
Pubblicato in:
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Journal
Progetto:
Discrete random structures for Bayesian learning and prediction - Finanziamento dell’Unione Europea – NextGenerationEU – missione 4, componente 2, investimento 1.1.
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Dati Generali

URL

https://www.sciencedirect.com/science/article/pii/S0304414923002405?via=ihub; https://arxiv.org/abs/2310.00599

Aree Di Ricerca

Settori (4)


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