7.7 Decision theory and hypothesis testing
7.7.1 Relationship between decision theory and classical hypothesis testing
It is possible to reformulate hypothesis testing in the language of decision theory. If we want to test 
versus 
, we have two actions open to us, namely,
As before, we shall write 
and 
for the prior probabilities of 
and 
and p0 and p1 for their posterior probabilities and
for the Bayes factor. We also need the notation
where 
is the prior density function.
Now let us suppose ...
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