Bayesian estimation of the expected time of first arrival past a truncated time T: the case of NHPP with power law intensity
Non-homogenous Poisson process, \(\{N(t), t > 0\}\) under time-truncated sampling scheme is often used in practice. \(E[S_{N(T)+1}\)], the expected time of arrival of the first event after a truncated time \(T\), is expressed as a function of intensity. A non-informative prior as well as gamma priors for Power Law intensity function are used to obtain Bayes estimates of the expected time.
nhpp power law intensity gamma prior ml estimate bayesian inference monte carlo estimation