Bayesian decision-making
J. K. Lindsey · 1996
Abstract Observations of phenomena are always made in conditions where previous theoretical knowledge, or perhaps more informal ideas, about the data generating mechanism are available. As far as possible, these are embodied in the model for the data generating mechanism. The likelihood function contains all of the information in the (new) data for estimation of parameters in this model being entertained and, for this reason, is central to inference procedures. As we have seen in Sections 3.6.4 and 6.4.1, prior empirical information can be incorporated by combining likelihoods. Thus, where possible, any such prior knowledge and information should be used. In a scientific context, only models which are thought to be relevant will be considered, but always with an eye to detecting the unexpected. They are to be ranked by the empirical information from the data, previous and present. However, when decisions, implying actions, must be made, the situation changes and an additional new model, for human behaviour, is required. Prior knowledge relating the models for the data generating mechanism to the decisions, and subsequent actions, will generally be available. If this can be formalized in a precise mathematical way, then it can be combined with the information in the likelihood function to yield a description of the posterior knowledge about the data generating mechanism after obtaining the observations. This model for human behaviour, based on changes in human beliefs, is known as a Bayesian approach.