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To Bayes or not to Bayes?
In many disciplines (e.g., epidemiology, genetics, medicine, many branches of social science) Bayesian statistics are used instead of Maximum Likelihood (ML, by Ronald Aylmer Fisher). Bayesian statistics gives the inferential probability of the parameter estimates from the posterior distribution, given the data. ML gives the sampling probability of the data given the model, also termed “Null Hypothesis Statistical Testing” (NHST). History shows how sampling probability and inferential probability have been used interchangeably, sometimes with serious consequences. Bayesian statistics has many advantages over NHST e.g., (1) it is logical in its philosophy, and (2) it does not rely on large sample theory. Modern software, both free (e.g., R brms) and commercial ones (e.g., SPSS, Mplus), now include Bayesian algorithms. Examples of logical reasoning, advantages of using the Bayesian estimator, and estimation of posterior probabilities using simulated and real-world data are presented in the talk.
