Use the two-dimensional version of Jeffreys' rule to determine a prior for the trinomial distribution

(cf. Exercise 15 on Chapter 2).

Exercise 15

Suppose that the vector x = (x, y, z) has a trinomial distribution depending on the index n and the parameter π  = (π , p, σ), where π + p + σ = 1, that is

Show that this distribution is in the two-parameter exponential family.

Transcribed Image Text:

p(x, y, z|π, ρ) απρ (1 -π- ρ).