Judea Pearl's book Causality Models ,Reasoning and Inference starts with the Theory of Probability and explores the cause and effect Theories of science models. The Probability Theory combines a Predictive and a diagnostic approach , and we , Pathologists are applying just that everyday in our Professional life.Therefore ,I can tell the practical application of such theories using odds and likelihood ratio parameters. A good theory makes a good practice.The dictates of the approach is that the overall strength of a belief in any Hypothesis, is based on our previous experience /knowledge about it + the observed evidence (data collected and analysed as statistical proof). It is a product of 2 factors .
1 The prior odds .This is the predictive and prospective factor provided by our previous/background knowledge about it.
2. The likelihood ratio which gives the diagnostic or retrospective aspect .This is the evidence by observed data in a particular case/situation.The random variables and our expectations (our mathematical models/predictions) are then compared. In Indian Astronomy this prediction, then observation and correction of mathematically derived and observed data is what is called Beejaganitham. In Pathology , we do this in every case when we diagnose,predict prognosis and then wait for the outcome (The follow up). Thus putting theory into practice is what Causality :Models ,Reasoning and Inference means. And a person's belief comes from these factors. Faith and belief of a scientist (whether it is in God or any other subject) come only from these parameters and their careful study.
A good book for Mathematicians and Nonmathematicians alike.
Dr Suvarna Nalapat