Model Parameter Inference

This chapter contains alternative approaches to model parameter inference. For conjugate pairs of likelihood and prior models, the expressions for the marginal likelihoods of the parameters, given the observations, are analytically available. Thus, a maximum marginal likelihood criterion is used in the inference. The estimators are available in closed form for some parameters, whereas numerical optimisation is recommended for others. Algorithms for model parameter inference are specified. The estimation uncertainty is obtained by the delta method. Alternatively, the inference can be performed in a hierarchical modelling framework. The posterior pdfs for the most influential parameters can be analytically assessed because conjugate prior pdfs are assigned to them. Thus, estimates with credibility regions are available. The running examples are continued.