Confidence About Possible Explanations

We revise the notion of confidence with which we estimate the parameters of a given distribution law in terms of their compatibility with the sample we have observed. This is a recent perspective that allows us to get a more intuitive feeling of the crucial concept of the confidence interval in parametric inference together with quick tools for exactly computing them even in conditions far from the common Gaussian framework where standard methods fail. The key artifact consists of working with a representation of the compatible parameters in terms of random variables without priors. This leads to new estimators that meet the most demanding requirements of the modern statistical inference in terms of learning algorithms. We support our methods with: a consistent theoretical framework, general-purpose estimation procedures, and a set of paradigmatic benchmarks.