Prediction with the dynamic Bayesian gamma mixture model

Consider the problem of predicting in real time the next value of a random quantity x greater than or equal to 0 from past observations, We present a flexible solution to this problem, a dynamic Bayesian model which represents the p.d. of x by a mixture of gamma distributions Sigma(i) c(i)G(x/a(i), b(i)). Whenever a new observation on z becomes available, the model updates its estimates of the parameters a(i), b(i), and c(i). It also contains a monitoring mechanism that allows it to react quickly to major changes in the behavior of the input and to adjust itself when its predictions become unsatisfactory. Numerous examples are given; they illustrate the difference between static and dynamic models, and show that the mixture form is flexible enough to represent adequately a variety of inputs, even if their distributions are very different from the gamma.