Related papers: Belief Revision in Probability Theory

Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…

Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical…

This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability…

Opinion Dynamics lacks a theoretical basis. In this article, I propose to use a decision-theoretic framework, based on the updating of subjective probabilities, as that basis. We will see we get a basic tool for a better understanding of…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

We study conditioning on null events, or surprises, and behaviorally characterize the Ordered Surprises (OS) representation of beliefs. For feasible events, our Decision Maker (DM) is Bayesian. For null events, our DM considers a hierarchy…

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to…

We argue that the Bayesian paradigm, of a prior which represents the beliefs of the statistician before observing the data, is not feasible in ultra-high-dimensional models. We claim that natural priors that represent the a priori beliefs…

This paper extends the applications of belief-networks to include the revision of belief commitments, i.e., the categorical acceptance of a subset of hypotheses which, together, constitute the most satisfactory explanation of the evidence…

Duda, Hart, and Nilsson have set forth a method for rule-based inference systems to use in updating the probabilities of hypotheses on the basis of multiple items of new evidence. Pednault, Zucker, and Muresan claimed to give conditions…

A Bayesian view of data interpretation suggests that a visualization user should update their existing beliefs about a parameter's value in accordance with the amount of information about the parameter value captured by the new…

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 posterior has to be 0 or 1 as well (this is a…

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…

In this article, I investigate the use of Bayesian updating rules applied to modeling social agents in the case of continuos opinions models. Given another agent statement about the continuous value of a variable $x$, we will see that…

Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable in lack of hints indicating otherwise; yet, a recent line of research spun from the idea of deriving this…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…

Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…