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We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players'…
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem, and of particular interest for Bayesian networks.…
Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers who take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender…
We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual…
The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…
A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurses assignment. Unlike our previous work that used Gas to implement implicit…
The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
Off-Policy Estimation (OPE) methods allow us to learn and evaluate decision-making policies from logged data. This makes them an attractive choice for the offline evaluation of recommender systems, and several recent works have reported…
An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and…
We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves {stochastic mathematical systems} (SMSs), which are stochastic processes that generate pairs of questions and…
Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…
The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule. On the other hand Shafer \cite{Shafer:90} gives a…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
We study a conditional state on a quantum logic using Renyi's approach (or Bayesian principle). This approach helps us to define independence of events and differently from the situation in the classical theory of probability, if an event…