Prediction with the dynamic Bayesian gamma mixture model

Consider the problem of predicting in real time the next value of a random quantity x⩾0 from past observations. We present a flexible solution to this problem, a dynamic Bayesian model which represents the probability distribution of x by a mixture of gamma distributions Σ_ic_iG(z|a_i, b_i). Whenever a new observation on x 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, which 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