Consider the loss functions where according as according as Then work out the Bayes test for testing versus and show its relation with the Neyman–Pearson test. For testing (in the N(θ , 1)...

Consider the loss functions

where

according as

according as

Then work out the Bayes test for testing

versus

and show its relation with the Neyman–Pearson test.

For testing

(in the N(θ , 1) setup), let 0(θ) be the folded

distribution over

while

be the folded N(0, τ₁) distribution over (0,∞). Obtain the Bayes test for H₀
versus H₁
and appraise its relation with the Neyman–Pearson test.