Exercise 3.3 - Posterior predictive for Beta-Binomial model

Answers

Straightforward algebra (recall (2.61)) gives:

\begin{align} Bb (1 | α_{1}^{'}, α_{0}^{'}, 1) = & \frac{B (α_{1}^{'} + 1, α_{0}^{'})}{B (α_{1}^{'}, α_{0}^{'})} \\ = & \frac{Γ (α_{0}^{'} + α_{1}^{'})}{Γ (α_{0}^{'} + α_{1}^{'} + 1)} \frac{Γ (α_{1}^{'} + 1)}{Γ (α_{1}^{'})} \\ = & \frac{α_{1}^{'}}{α_{1}^{'} + α_{0}^{'}} . \end{align}

The hint provided in the textbook is incorrect by mistaking

Γ (a) = (a - 1) \cdot Γ (a - 1)

for

Γ (a) = a \cdot Γ (a - 1) .

solour_lfq

2021-03-24 13:42