# Filtering the Wright-Fisher diffusion

Abstract : We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < ..., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent and the conditional distribution of y(ti) only depends on x(ti). When this conditional distribution has a specific form, we prove that the model ((x(ti),y(ti)), i$\ge$1) is a computable filter in the sense that all distributions involved in filtering, prediction and smoothing are exactly computable. These distributions are expressed as finite mixtures of parametric distributions. Thus, the number of statistics to compute at each iteration is finite, but this number may vary along iterations.
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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.197-217. <10.1051/ps:2008006>
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https://hal.archives-ouvertes.fr/hal-00170688
Contributeur : Valentine Genon-Catalot <>
Soumis le : lundi 10 septembre 2007 - 13:38:16
Dernière modification le : mardi 11 octobre 2016 - 14:10:46
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chaleyatgenon07.pdf
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### Citation

Mireille Chaleyat-Maurel, Valentine Genon-Catalot. Filtering the Wright-Fisher diffusion. ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.197-217. <10.1051/ps:2008006>. <hal-00170688>

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