Once we have new information, Bayes' rule provides the updated
prior odds are 1:2), then Bayes' rule tells us (via equation (4))
1], the central bank updates beliefs using Bayes' rule.
In this article I assume that the monetary authority makes decisions without fully knowing the effect of monetary policy on the economic environment but learns about it over time using Bayes' rule.
A specific example demonstrates how Bayes' Rule may be used to compute the posterior probability that a given cup was used, as well as how heuristics may lead to a different (or identical) decision.
For example, when a subject draws three orange and three white balls and the prior is 2/3, both Bayes' Rule and the conservative heuristic predict that Cup A will be chosen (see Table 1).
These decisions were consistent with Bayes' rule
and with private information.
As this announcement does not occur on the equilibrium path, this (admittedly strange) belief does not contradict the assumption that on the equilibrium path beliefs are updated by Bayes' rule
b], it is immediate from Bayes' Rule
that the posterior belief associated with [S.
Unless we track the changes in our confidence by using Bayes' rule
to update inductive probabilities, all unrefuted hypotheses remain equally trustworthy and equally testworthy.
But no one promised that applying Bayes' rule
would be costless.
5, as in case 1, so the supervisor's mixing is again rational, given beliefs consistent with Bayes' rule
, yielding a sequential equilibrium.