We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian...

Bayesian networks and conditional independence is studied via functional dependences. Armstrong’s axioms known from the theory of relational databases is used to reformulate the concept of Bayesian networks into the theory of join-semidistributive lattices. Lattice theory provides us with a richer language to discuss causation than graph theory does.

We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalised to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from t...

Probabilistic graphical models are useful tools for modeling systems governed by probabilistic structure. Bayesian networks are one class of probabilistic graphical model that have proven useful for characterizing both formal systems and for reasoning with those systems. Probabilistic dependencies in Bayesian networks are graphically expressed in terms of directed links from parents to their ch...

the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to enginee...

Kehler and Rohde (2013) proposed a Bayesian theory of pronoun interpretation where the influence of world knowledge emerges as effects on the prior and the influence of information structure as effects on the likelihood: P(referent|pronoun) μ P(pronoun|referent)P(referent). Here we present two experiments on Mandarin Chinese that allow us to test the generality of the theory for a language with...

Given a few assumptions, the probability of a conjunction is raised, and the probability of its negation is lowered, by conditionalising upon one of the conjuncts. This simple result appears to bring Bayesian confirmation theory into tension with the prominent dogmatist view of perceptual justification – a tension often portrayed as a kind of ‘Bayesian objection’ to dogmatism. In a recent paper...