3.1 Bayesian approach
In the Bayesian approach we assign costs to our decisions; in particular we introduce positive numbers
, 
, where 
is the cost incurred by choosing hypothesis 
when hypothesis
is true. We define the conditional risk 
of a decision rule 
for each hypothesis as
where 
is the probability distribution of the data when hypothesis 
is true. Next we assign
probabilities 
and 
to the occurrences of hypothesis 
and 
, respectively. These
probabilities are called a priori probabilities or priors. We define the Bayes risk as the overall average cost
incurred by the decision rule 
:
Finally we define the Bayes rule as the rule that minimizes the Bayes risk 
.
