Exercise 3.5 - Uninformative prior for log-odds ratio

Answers

Since:

ϕ = \log \frac{𝜃}{1 - 𝜃} .

By using change of variables formula:

p (𝜃) = p (ϕ) \cdot | \frac{d ϕ}{d 𝜃} | \propto \frac{1}{𝜃 (1 - 𝜃)},

hence

p (𝜃) = Beta (𝜃 | 0, 0) .

That is to say, we can generate samples subject to a Beta distribution by transforming samples drawn from a uniform distribution. This trick is of significant practical value. Direct sampling from a Beta distribution requires inverting its cumulative probability function, which involves too much computation.

solour_lfq

2021-03-24 13:42

Exercise 3.5 - Uninformative prior for log-odds ratio

Answers

Comments

Add answer