You're sitting in the doctor's office waiting for the result of a test. The test will tell you whether you have a disease you really don't want to have. As you wait, it seems as if the whole world is ...

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 ...

Learn how prior probability informs economic theory and decision-making in Bayesian statistics. Understand its role before collecting new data.

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 ...

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 ...

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 ...

How likely you think something is to happen depends on what you already believe about the circumstances. That is the simple concept behind Bayes' rule, an approach to calculating probabilities, first ...