4.5 Point null hypotheses for the normal distribution
4.5.1 Calculation of the Bayes’ factor
Suppose 
is a vector of independently 
random variables, and that 
is known. Because of the remarks at the end of the last section, we can work entirely in terms of the sufficient statistic
We have to make some assumption about the density 
of θ under the alternative hypothesis, and clearly one of the most natural things to do is to suppose that this density is normal, say 
. Strictly, this should be regarded as a density on values of θ other than 
, but when probabilities are found by integration of this density, the odd point will make no difference. It will usually seem sensible to take 
as, presumably, ...
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