 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/28l/b/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 28L / b / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

The

π

-Bayes risk is

r_{π} (δ) = \int R (δ, θ) π (d θ) .

(1)

Conditioning on the observation and applying Tonelli gives

r_{π} (δ) = E_{X} [E {L (δ (X), θ) ∣ X}] .

(2)

Thus choosing, for every observed $x$ , an action minimizing the posterior expected loss minimizes each integrand and hence minimizes the Bayes risk.

 Read the full article

 New to topics? Read the docs here!