Bayes Inference for a Nonhomogeneous Poisson Process with Power Law Model

Individuals vary in survival chances due to differences in genetics, environmental exposures, and geneenvironment interactions. These chances, as well as the contribution of each factor to mortality, change as individuals get older. In general, human physiological systems are constructed by collecting more than one part to perform either single or multiple functions. In addition, the successive times between failures are not necessarily identically distributed. More generally, they can become smaller (an indication of deterioration). However, if any critical deterioration is detected, then the decision of when to take the intervention, given the costs of diagnosis and therapeutics, is of fundamental importance. At the time of the decision, the degree of future physiological system deterioration, which is likely to be uncertain, is of primary interest for the decision maker. In this paper, a Bayesian decision theoretic approach is developed. A nonhomogeneous Poisson process with a power law failure intensity function is used to describe the behavior of aging physiological systems with chronic disease. Also, a proposed Nonhomogeneous Poisson Process with power low model is applied to make the Bayesian decisionmaking analysis more effective and efficient.