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 ...

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 ...

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 ...

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 ...

We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial ...

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, ...

The FDA’s new draft guidance on Bayesian methodology signals a shift toward more flexible, data-driven clinical trial designs, enabling sponsors to use prior data and adaptive approaches to improve ...

Scientists have confirmed that human brains are naturally wired to perform advanced calculations, much like a high-powered computer, to make sense of the world through a process known as Bayesian ...