Amaral Turkman, M. A.; Turkman, K. F. 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. Cited in 1 Document MSC: 62F15 Bayesian inference 62M99 Inference from stochastic processes 92D30 Epidemiology 62E15 Exact distribution theory in statistics Keywords:pure birth process; linear birth rate; predictive distribution; population size; epidemic model Citations:Zbl 0702.00028 PDFBibTeX XML