From equation 9.9 and by Bayes' theorem, equation 9.1, the estimator may be written as the ratio of integrals
and considering a prior of the form in equation 9.12 and cancelling proportionality constants this may then be written as
Clear from this expression is that the exponents 
of the prior are simply added to 
; from now on they will be ignored and may be replaced at the end of the calculation by substituting 
for within the range of validity of the expression. Thus, defining
the estimator is given by the ratio
When the prior is the sum of terms of the form in equation 9.12, the numerator and denominator both contain respective summations. In each term of each summation though, the respective are simply added to .