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 ...

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 ...

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 main focus of this short course will be the Bayesian aspect of it. That means this is a slightly more advanced course requiring some knowledge of basic probability, regression methods, and the R ...

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 ...