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 ...

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 ...

We consider Bayesian inferences on a type of multivariate median and the multivariate quantile functionals of a joint distribution using a Dirichlet process prior. Unlike univariate quantiles, the ...

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 ...

This course introduces the theoretical, philosophical, and mathematical foundations of Bayesian Statistical inference. Students will learn to apply this foundational knowledge to real-world data ...

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 ...