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Asymptotics of Posteriors for Binary Branching Processes

Part of: Parametric inference Markov processes

Published online by Cambridge University Press:  14 July 2016

Didier Piau
Didier Piau*
Affiliation:
Université Joseph Fourier
*
∗Postal address: Institut Fourier UMR 5582, Université Joseph Fourier Grenoble 1, 100 rue des Maths, BP 74, 38402 Saint Martin d'Hères, France. Email address: didier.piau@ujf-grenoble.fr
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Abstract

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We compute the posterior distributions of the initial population and parameter of binary branching processes in the limit of a large number of generations. We compare this Bayesian procedure with a more naïve one, based on hitting times of some random walks. In both cases, central limit theorems are available, with explicit variances.

Keywords

Branching processBayesian estimationPolymerase chain reaction

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D25: Population dynamics (general) 62F15: Bayesian inference 60J85: Applications of branching processes
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 727 - 742
Copyright
Copyright © Applied Probability Trust 2008 

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