ABSTRACT
This chapter presents Bayesian inferences for processes in continuous time. The Poisson process is a counting process that records many interesting events such as the number of accidents in a given stretch of highway over a selected period, the number of telephone calls at a switchboard, the arrival of customers at a counter, the number of visits to a website, earthquake occurrences in a particular region. The chapter explores that definition of the Poisson process which is followed by a description of the arrival and interarrival times, and then various generalizations are considered such as the nonhomogeneous Poisson processes, which include compound processes and processes that contain covariates. The thinning is a Poisson event that can be one of several types, each occurring with some nonzero probability. Bayesian inferential procedures are presented for continuous-time Markov chains more general than the Poisson process. The goal is to determine relationships between several Poisson processes via their covariates.
