Well can we at least make it look easy?

For the model as given here, there are two parameters Pc and Pt – but the focus of interest will be on some parameter representing a treatment effect

– Andrew chose Pt – Pc.

But sticking for a while with Pt and Pc – the prior is a surface over Pt and Pc as is the data model (likelihood)

In particular, the prior is a flat surface (independent uniforms)

and the likelihood is Pt^1 (1 – Pt)^29 * Pc^3 (1 – Pc)^7 (the * is from independence)

(If I reversed the treatment and control groups – I should be blinded to that anyways)