Probability Models

Abstract

A model is an argument. Models are collections of various premises which we assign to an observable proposition, i.e. an observable. Modelling reverses the probability equation: the proposition of interest or conclusion, i.e. the observable Y, is specified first after which premises X thought probative of the observable are sought or discovered. The ultimate goal is to discover just those premises X which cause or which determine Y. Absent these—and there may be many causes of Y—it is hoped to find X which give Y probabilities close to 0 or 1, given X in its various states. Measures of X’s importance are given. A model’s usefulness depends on what decisions are made with it, and how costly and rewarding those decisions are. Proper scores which help define usefulness are given. Probability models can and do have causative elements. Some probability models are even fully causal or deterministic in the sense given last chapter, but which are treated as probabilistic in practice. Tacit premises are added to the predictions from these models which adds uncertainty. Bayes is not all its cracked up to be. The origin and limitations of parameters and parametric models are given.