Summarising Posteriors

Question 1

what is squared error loss?

Answer 1

Posterior mean

Question 2

What is absolute error loss?

Answer 2

posterior median, only computed numerically

Question 3

What is 0-1 loss?

Answer 3

1 if θhat ≠ θ
0 if θhat = θ

(to find, differentiate posterior wrt θ)

Question 4

Give the formula for an interval estimate

Answer 4

∫ p(θ|y) dθ = 1 - α

Question 5

What is the highest posterior density interval?

Answer 5

1-α credible intervals where the probabilities/densities in the interval are higher/larger than the values outside the interval

INTERVAL WITH THE SHORTEST LENGTH