given the data { xn }suppose that we use the likelihood ( thn(us with parameter th (us )and wish to compare the following two nested models (amodel where is known and this is incorporated via the prior (th ( ( ps ( - ) ( (bmodel where both mean and variance are unknown with prior (th ( ( ps ( - ) bt ( )- - - / (tshow that the prior (th can be viewed as the limit of the prior (th when and ts henceconclude that ( lim ( tb=ts and use this result to calculate check that the formula for agrees with the savagedickey density ratiog( ( tg( ( where ( tand ( are the posterior and priorrespectivelyunder model