Abstract
In this article we consider the Bayesian statistical analysis of a simple Galton-Watson process. Problems of interest include estimation of the offspring distribution, classification of the process, and prediction. We propose two simple analytic approximations to the posterior marginal distribution of the reproduction mean. This posterior distribution suffices to classify the process. In order to assess the accuracy of these approximations, a comparison is provided with a computationally more expensive approximation obtained via standard Monte Carlo techniques. Similarly, a fully analytic approximation to the predictive distribution of the future size of the population is discussed. Sampling-based and hybrid approximations to this distribution are also considered. Finally, we present some illustrative examples.
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The first author is supported by the Alberto Baillères Chair on Insurance and International Finance of ITAM. This work was partially supported by Sistema Nacional de Investigadores, Mexico.
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Mendoza, M., Gutiérrez-Peña, E. Bayesian conjugate analysis of the Galton-Watson process. Test 9, 149–171 (2000). https://doi.org/10.1007/BF02595856
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DOI: https://doi.org/10.1007/BF02595856
Key Words
- Bayesian inference
- branching process
- Dirichlet distribution
- forecasting
- offspring distribution
- population growth
- reproduction mean