We address the classic problem of interval estimation of a binomial proportion. The Wald interval p̂ ± zα/2n−1/2(p̂(1 − p̂))1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative inter...

One method for building classification trees is to choose split variables by maximising expected entropy. This can be extended through the application of imprecise probability by replacing instances of expected entropy with the maximum possible expected entropy over credal sets of probability distributions. Such methods may not take full advantage of the opportunities offered by imprecise proba...

The question of how to determine which states and actions are responsible for a certain outcome is known as the credit assignment problem remains central research in reinforcement learning artificial intelligence. Eligibility traces enable efficient recent sequence experienced by agent, but not counterfactual sequences that could also have led current state. In this work, we introduce expected ...

We introduce and study the main properties of a class convex risk measures that refine Expected Shortfall by simultaneously controlling expected losses associated with different portions tail distribution. The corresponding adjusted Shortfalls quantify as minimum amount capital has to be raised injected into financial position X ensure ES p ( ) does not exceed pre-specified threshold g for ever...