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Bayesian analysis of a pure birth process with linear birth rate. (English) Zbl 0704.62028

Bayesian statistics 3, Proc. 3rd Valencia Int. Meet., Altea/Spain 1987, 533-541 (1988).
Summary: [For the entire collection see Zbl 0702.00028.]
Let \(\{\) N(t), \(t\geq 0\}\) be a pure birth process with linear birth rate \(\lambda_ n=n\lambda\), \(n=0,1,...\), where N(t) is the size of a population at time t. Admitting that the process is observed either continuously or at fixed equidistant points during a certain period of time [0,t], the predictive distribution of the population size at \(t+u\), \(u>0\), is obtained. These results are then applied to the study of a simple epidemic model and are compared with those obtained using an estimative method.

MSC:

62F15 Bayesian inference
62M99 Inference from stochastic processes
92D30 Epidemiology
62E15 Exact distribution theory in statistics

Citations:

Zbl 0702.00028