[25 Marks] Conjugate Categorical random variable analysis: Consider n iid categorical random variables Yį, (i = 1,...,n)

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25 Marks Conjugate Categorical Random Variable Analysis Consider N Iid Categorical Random Variables Yi I 1 N 1 (45.55 KiB) Viewed 31 times

[25 Marks] Conjugate Categorical random variable analysis: Consider n iid categorical random variables Yį, (i = 1,...,n), each with p.d.f. k P(y | P₁,..., Pk) = = Iptv=n j=1 (1) Suppose that the prior for 0 = : {p₁,…, Pk} is the Dirichlet distribution Dirichlet(a Namely (,..., a(k)). k P(P₁,..., Pk | a¹), (1) (j) α0 -1 a(k)) x ПР j=1 Derive the posterior distribution of 0.