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 ...

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.

"Yes or no: was there once life on Mars?" I can't say. "What about intelligent life?"' That seems most unlikely, but again, I can't really say. The simple yes-or-no framework has no place for shadings ...

It’s estimated that human adults make about 35,000 decisions a day — the percentage of good decisions depends on the adult. These choices can be as banal as deciding to roll or crumple toilet paper or ...

We suggest a new method for integrating volatility information for estimating the value-at-risk and conditional value-at-risk of a portfolio. This new method is developed from the perspective of ...