This paper identifies several key properties of a monad that allow us to formulate the basics of conditional probability theory, using states for distributions/measures and predicates for events/probability density functions (pdf’s). The distribution monad for discrete probability and the Giry monad for continuous probability are leading examples. Our categorical description handles discrete an...

It has long been asserted that in univariate location-scale models, when concerned with inference for either the location or scale parameter, the use of the inverse of the scale parameter as a Bayesian prior yields posterior credible sets which have exactly the correct frequentist confidence set interpretation. This claim dates to at least Peers (1965), and has subsequently been noted by variou...

We investigate probability logic with the conditional probability operators. This logic, denoted LCP , allows making statements such as: P sα, CP s(α | β), CP 0(α | β) with the intended meaning “the probability of α is at least s”, “the conditional probability of α given β is at least s”, “the conditional probability of α given β at most 0”. A possible-world approach is proposed to give semanti...