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 ...

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 ...

For making probabilistic inferences, a graph is worth a thousand words. A Bayesian network is a graph in which nodes represent entities such as molecules or genes. Nodes that interact are connected by ...

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 ...

A team of international physicists has brought Bayes’ centuries-old probability rule into the quantum world. By applying the “principle of minimum change” — updating beliefs as little as possible ...

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 ...

An international team of physicists has extended Bayes’ rule into the quantum realm, potentially transforming how we handle uncertainty in quantum computing and machine learning. The study is ...