Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 44 / 2 / c

Table of contents
- Solution c

Solution

Integrate the latent variable out to obtain the hospital's marginal likelihood:

p (y_{i} ∣ ψ) = \frac{ψ}{y _{i} !} \int_{0}^{\infty} θ^{y_{i}} e^{- (1 + ψ) θ} d θ = \frac{ψ}{( 1 + ψ ) ^{y_{i} + 1}} .

For

ϕ = (1 + ψ)^{- 1}

this becomes

p (y_{i} ∣ ϕ) = (1 - ϕ) ϕ^{y_{i}}

. It is a geometric distribution on the nonnegative integers, with success probability

1 - ϕ

. The transformation concerns the likelihood, so no Jacobian is inserted here.

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version