Bayesian statistics represents a powerful framework for data analysis that centres on Bayes’ theorem, enabling researchers to update existing beliefs with incoming evidence. By combining prior ...

Bayesian inference provides a robust framework for combining prior knowledge with new evidence to update beliefs about uncertain quantities. In the context of statistical inverse problems, this ...

It is well known that standard frequentist inference breaks down in IV regressions with weak instruments. Bayesian inference with diffuse priors suffers from the same problem. We show that the issue ...

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 my practice, I find most people involved with advanced analytics, such as predictive, data science, and ML, are familiar with the name Bayes, and can even reproduce the simple theorem below. Still, ...

Articulate the primary interpretations of probability theory and the role these interpretations play in Bayesian inference Use Bayesian inference to solve real-world statistics and data science ...

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families ...

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and non-random selection. Mortality rates in patient discharge records are widely ...

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 Western Conference standings are a jumbled mess with only five games separating positions No. 4 through No. 10. In the Eastern Conference, things are not as competitive, except at the top where ...