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i.i.d. Given observations r1,...., an N(4, 0?) and using the conjugate prior distribution for u and o?, derive the formula for (ua1,..., xn), the marginal posterior distribution of 4, conditional on the data but marginal over o?. Check your work by comparing your formula to a Monte Carlo estimate of the marginal distribution, using some values of T1,, Xn, lo. Po, Vo, SSo that you choose. Also derive T(õlr1,....), where ở = 1/o? is the precision.

i.i.d. Given observations r1,...., an N(4, 0?) and using the conjugate prior distribution for u and o?, derive the formula for (ua1,..., xn), the marginal posterior distribution of 4, conditional on the data but marginal over o?. Check your work by comparing your formula to a Monte Carlo estimate of the marginal distribution, using some values of T1,, Xn, lo. Po, Vo, SSo that you choose. Also derive T(õlr1,....), where ở = 1/o? is the precision.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Given observations r1,..., In u and o?, derive the formula for #(ur1,.., xn), the marginal posterior distribution of 1, conditional on the data but marginal over o?. Check your work by comparing your formula to a Monte Carlo estimate of the marginal distribution, using some values of T1,.., Xn, lo, Po, Vo, SSo that you choose. Also derive 7(õlx1,....), where ở the precision. i.i.d. N(1, o?) and using the conjugate prior distribution for 1/a is
Transcribed Image Text:Given observations r1,..., In u and o?, derive the formula for #(ur1,.., xn), the marginal posterior distribution of 1, conditional on the data but marginal over o?. Check your work by comparing your formula to a Monte Carlo estimate of the marginal distribution, using some values of T1,.., Xn, lo, Po, Vo, SSo that you choose. Also derive 7(õlx1,....), where ở the precision. i.i.d. N(1, o?) and using the conjugate prior distribution for 1/a is
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