Bayes' theorem, also called Bayes' rule or Bayesian theorem, is a mathematical formula used to determine the conditional probability of events. The theorem uses the power of statistics and probability ...

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {φi}, one from each data stratum. A class ...

The notion of free energy in inference derives from a mathematical method of inverting a probability distribution. If the brain knows the probability of its sensations (given a “generative model of ...

In many application areas, a primary focus is on assessing evidence in the data refuting the assumption of independence of Y and X conditionally on Z, with Y response variables, X predictors of ...

Chris Wiggins, an associate professor of applied mathematics at Columbia University, offers this explanation. A patient goes to see a doctor. The doctor performs a test with 99 percent ...