Input modelling for multimodal data

Multimodal data occurs frequently in discrete-event simulation input analysis, typically arising when an input sample stream comes from different sources. A finite mixture distribution is a simple input model for representing such data, but fitting a mixture distribution is not straightforward as the problem is well-known to be statistically non-standard. Even though much studied, the most common fitting approach, Bayesian reversible jump Markov Chain Monte Carlo (RJMCMC), is not very satisfactory for use in setting up input models. We describe an alternative Bayesian approach, MAPIS, which uses maximum a posteriori estimation with importance sampling, showing it overcomes the main problems encountered with RJMCMC. We demonstrate use of a publicly available implementation of MAPIS, which we have called FineMix, applying it to practical examples coming from finance and manufacturing.