Discover how credibility theory helps actuaries use historical data to estimate risks and set insurance premiums; learn how ...

Mathematicians rely on numbers, but finding words to explain different levels of certainty has stymied everyone from the ...

Probable cause is important in two aspects of criminal law: Police must have probable cause before they search a person or ...

A team of international physicists has brought Bayes’ centuries-old probability rule into the quantum world. By applying the “principle of minimum change” — updating beliefs as little as possible ...

Their discovery was published on August 28, 2025, in Physical Review Letters and examines how beliefs are updated in the quantum world, where normal physics rules no longer apply The research was ...

Predicting how complex stochastic systems respond to small external perturbations is central in physics, climate science, and engineering. We combine the generalized fluctuation–dissipation theorem ...

Abstract: We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of ...

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.

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...