Bayes' rule, which is routinely used to update beliefs based on new evidence, arises from a
principle of minimal change. This principle states that updated beliefs must be consistent …

Updating a probability distribution in the light of new evidence is a very basic operation in
Bayesian probability theory. It is also known as state revision or simply as conditioning. This …

The Petz map has been established as a quantum version of the Bayes' rule. It unifies the
conceptual belief update rule of a quantum state observed after a forward quantum process …

In many situations, learning from the results of measurements can be regarded as updating
one's probability distributions over certain variables. According to Bayesians, this updating …

We address the problem of reconstructing quantum theory from the perspective of an agent
who makes bets about the outcomes of possible experiments. We build a general Bayesian …

The probabilities a Bayesian agent assigns to a set of events typically change with time, for
instance when the agent updates them in the light of new data. In this paper we address the …

The mathematical principles of quantum theory provide a general foundation for assigning
probabilities to events. This paper examines the application of these principles to the …

Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical
probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the …

In approaches to quantum theory in which the quantum state is regarded as a representation
of knowledge, information, or belief, two agents can assign different states to the same …

The inference of a hidden variable's historical value, based on observations before and after
the fact, is a controversial subject in quantum mechanics. Here I address the controversy by …