Bayes' Rule is often written as p([theta]|y) [varies] p([theta])p(y|[theta]), when treated as a function of [theta] for a fixed y, and p(y|[theta]) is the likelihood L(y|[theta]).

In order to apply Bayesian analysis to fMRI data and make inference to the parameters that we are interested in, like finding the change points in the dataset, we need to set up a probability model for the data and find a prior to apply Bayes' Rule.

7) Applying Bayes' rule, we argue that triers of fact

10) But to apply Bayes' rule, the probability that the database

We do so by setting up density functions from where the ability levels are drawn, and we then compute, using

Bayes' rule, the initial belief of each individual.

Bayes' rule does this narrowing in via the standard multiplication principle of conjunction whereby one can determine the probability of the conjunction of two outcomes algebraically.

I use a theoretical two-period model to study the short-run dynamics of monetary policy when the central bank is uncertain about the economic environment but learns about it over time using

Bayes' rule.

In one frequently cited example, Grether (1980) finds evidence that people give less weight to base rates than

Bayes' Rule requires when solving statistical problems that require them to weigh prior information and sample information.

Information cascades are defined as patterns of decisions that are both consistent with

Bayes' rule and inconsistent with private information.

Beliefs are then always updated by

Bayes' rule after the announcement and very counterintuitive equilibria disappear.

Employing

Bayes' Rule and relationship 2, these probabilities are given by

Probabilism affirms, first, that the degrees of confidence one may reasonably repose in the competing hypotheses of a partition are adequately represented by probabilities, and, second, that probabilities are to be adjuste in light of new data by

Bayes' rule.

In principle, the revision process is mechanical and occurs via

Bayes' Rule.

131) The inescapable logic of

Bayes' rule is that even if there is another suspect with a 30% (prior) chance of being the guilty party, once we have a partial DNA match from Puckett, his chance of being the guilty party rises to a level (98.

Thus, if an employee goes to her for advice, she must use

Bayes' rule to determine the probability that the employee's problem is big or small.