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).

However, anyone who purchases insurance should always choose the cup predicted by Bayes' Rule.

This is a natural class of decision rules to consider that includes both Bayes' Rule and the conservative and representative heuristics.

Information cascades are defined as patterns of decisions that are both consistent with Bayes' rule and inconsistent with private information.

Decisions that are consistent with private information but inconsistent with Bayes' rule are labeled * mistakes.

The third column shows the number of decisions that are consistent with private information but inconsistent with Bayes' rule (* mistakes).

In particular, a central claim of this Article is that the appropriate application of Bayes' rule as laid out in equation (7) can lead courts and litigants to focus more explicitly on two variables that have to date been omitted from the adversarial process: a, the probability that nonsources in the database will have an alibi, and p, the prior probability that the source is in the database.

But no one promised that applying Bayes' rule would be costless.

This is consistent with Bayes' rule and also makes the supervisor's mixing at her information set rational.

5, as in case 1, so the supervisor's mixing is again rational, given beliefs consistent with Bayes' rule, yielding a sequential equilibrium.

Another strand of the literature looks at central bankers that learn using Bayes' rule.

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.

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

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

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.