We consider a Wright-Fisher diffusion whose current state cannot be observed directly. Instead, at times < < ..., the observations are such that, given the process , the random variables are independent and the conditional distribution of only depends on . When this conditional distribution has a specific form, we prove that the model , 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.
Mots-clés : stochastic filtering, partial observations, diffusion processes, discrete time observations, hidden Markov models, prior and posterior distributions
@article{PS_2009__13__197_0,
author = {Chaleyat-Maurel, Mireille and Genon-Catalot, Valentine},
title = {Filtering the {Wright-Fisher} diffusion},
journal = {ESAIM: Probability and Statistics},
pages = {197--217},
publisher = {EDP-Sciences},
volume = {13},
year = {2009},
doi = {10.1051/ps:2008006},
mrnumber = {2518546},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2008006/}
}
TY - JOUR AU - Chaleyat-Maurel, Mireille AU - Genon-Catalot, Valentine TI - Filtering the Wright-Fisher diffusion JO - ESAIM: Probability and Statistics PY - 2009 SP - 197 EP - 217 VL - 13 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2008006/ DO - 10.1051/ps:2008006 LA - en ID - PS_2009__13__197_0 ER -
%0 Journal Article %A Chaleyat-Maurel, Mireille %A Genon-Catalot, Valentine %T Filtering the Wright-Fisher diffusion %J ESAIM: Probability and Statistics %D 2009 %P 197-217 %V 13 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2008006/ %R 10.1051/ps:2008006 %G en %F PS_2009__13__197_0
Chaleyat-Maurel, Mireille; Genon-Catalot, Valentine. Filtering the Wright-Fisher diffusion. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 197-217. doi : 10.1051/ps:2008006. http://archive.numdam.org/articles/10.1051/ps:2008006/
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