Bayesian estimation and maximum likelihood methods represent two central paradigms in modern statistical inference. Bayesian estimation incorporates prior beliefs through Bayes’ theorem, updating ...

Recently there has been considerable progress on setting good approximate confidence intervals for a single parameter θ in a multi-parameter family. Here we use these frequentist results as a ...

We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First, we characterize the set where the maximum marginal likelihood ...

In the ever-evolving toolkit of statistical analysis techniques, Bayesian statistics has emerged as a popular and powerful methodology for making decisions from data in the applied sciences. Bayesian ...

Whether in everyday life or in the lab, we often want to make inferences about hypotheses. Whether I’m deciding it’s safe to run a yellow light, when I need to leave home in order to make it to my ...

Forbes contributors publish independent expert analyses and insights. Writes about the future of finance and technology, follow for more. Joint probability teaches us to calculate combined outcomes.

The stock market is an ever-changing place. In fact, it’s changing every second of every day as prices go up and down, and new factors impact the trajectory of the market. It’s important for investors ...