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, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{N(t), t > 0\}$$</EquationSource> </InlineEquation> under time-truncated sampling scheme is often used in practice. <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$E[S_{N(T)+1}$$</EquationSource> </InlineEquation>], the expected time of arrival of the first event after a truncated time <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$T$$</EquationSource> </InlineEquation>, 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. Copyright Springer-Verlag Berlin Heidelberg 2013