9. Statistical and Physical Models

Statistical models are probability models and physical models are causal or deterministic or mixed causal-deterministic-probability models applied to observable propositions. It is observations which turn probability into statistics. Statistical and physical models are thus verifiable, and all use statistics in their verification. All models should be verified, but most aren’t. Classical modeling emphasizes hypothesis or “significance” testing and estimation. No hypothesis test, Bayesian or frequentist, should ever be used. Death to all p-values or Bayes factors! Hypothesis testing does not prove or show cause; therefore, embedded in every test used to claim cause is a fallacy. If cause is known, probability isn’t needed. Neither should parameter-centric (estimation, etc.) methods be used. Instead, use only probability, make probabilistic predictions of observables given observations and other premises, then verify these predictions. Measures of model goodness and observational relevance are given in a language which requires no sophisticated mathematical training to understand. Speak only in terms of observables and match models to measurement. Hypothesis-testing and parameter estimation are responsible for a pandemic of over-certainty in the sciences. Decisions are not probability, a fact with many consequences.