Statistical Inference for Branching Processes
An examination of the difficulties that statistical theory and, in particular, estimation theory can encounter within the area of dependent data. This is achieved through the study of the theory of branching processes starting with the demographic question: what is the probability that a family name becomes extinct? Contains observations on the generation sizes of the Bienaymé-Galton-Watson (BGW) process. Various parameters are estimated and branching process theory is contrasted to a Bayesian approach. Illustrations of branching process theory applications are shown for particular problems.
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What Can Be Done? 1 The Extinction of Family Lines
A Probabilistic Construction
23 other sections not shown
Analysis ancillarity ancillary Application approximate assume asymptotic variance asymptotically normal Bayes become extinct BGW process branching process central limit theorem compute conditional distribution conjugate prior consistent estimator converges a.s. Corollary corresponding efficiency epidemic equation ergodic estimate the offspring Example Exercise explosion set exponential family extinction probability family sizes family tree finite Fisher information follows geometric distribution geometric offspring distribution given Hence Heyde independent integral Keiding large numbers Lemma linear Markov chain martingale maximum likelihood estimator measure Methods mutation nonergodic nonextinction offspring distribution offspring mean offspring variance parameter Poisson distribution Poisson offspring distribution population posterior density power series offspring problem Proof Proposition prove random variables result sample Second Edition sequence series offspring distribution stationary Statistical Inference stochastic process sufficient statistic supercritical Suppose term Theorem 1.1 theory verify write Y„_l yields zero