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The linear birth‒death process: an inferential retrospective

Part of: Inference from stochastic processes Parametric inference Applications

Published online by Cambridge University Press:  01 February 2019

Simon Tavaré
Simon Tavaré*
Affiliation:
University of Cambridge
*
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK. Email address: simon.tavare@cruk.cam.ac.uk
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Abstract

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In this paper we provide an introduction to statistical inference for the classical linear birth‒death process, focusing on computational aspects of the problem in the setting of discretely observed processes. The basic probabilistic properties are given in Section 2, focusing on computation of the transition functions. This is followed by a brief discussion of simulation methods in Section 3, and of frequentist methods in Section 4. Section 5 is devoted to Bayesian methods, from rejection sampling to Markov chain Monte Carlo and approximate Bayesian computation. In Section 6 we consider the time-inhomogeneous case. The paper ends with a brief discussion in Section 7.

Keywords

Approximate Bayesian computationMarkov chain Monte Carloestimation

MSC classification

Primary: 62M05: Markov processes
Secondary: 62F15: Bayesian inference 62P10: Applications to biology and medical sciences
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 253 - 269
Copyright
Copyright © Applied Probability Trust 2018 

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