Plausible inference and the interpretation of quantitative data

Abstract

The analysis of quantitative data is central to scientific investigation. Probability theory, which is founded on two rules, the sum and product rules, provides the unique, logically consistent method for drawing valid inferences from quantitative data. This primer on the use of probability theory is meant to fulfill a pedagogical purpose. The discussion begins at the foundation of scientific inference by showing how the sum and product rules of probability theory follow from some very basic considerations of logical consistency. The authors then develop general methods of probability theory that are essential to the analysis and interpretation of data. They discuss how to assign probability distributions using the principle of maximum entropy, how to estimate parameters from data, how to handle nuisance parameters whose values are of little interest, and how to determine which of a set of models is most justified by a data set. All these methods are used together in most realistic data analyses. Examples are given throughout to illustrate the basic points.