Start a new page clearly marked Question 1 1. [12 marks] Consider a decision problem with parameter space o {@1,02} and

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Start A New Page Clearly Marked Question 1 1 12 Marks Consider A Decision Problem With Parameter Space O 1 02 And 1 (105.61 KiB) Viewed 33 times

Start a new page clearly marked Question 1 1. [12 marks] Consider a decision problem with parameter space o {@1,02} and a set of non-randomized decisions D = = {di, 1 <i< 7} with risk points {R(01, dị), R(02, dị)} as follows: 5 6 7 i 1 R(01, d;) 0 R(02, dị) 5 2 3 1 3 2 4 4 4 1 6 5 3 4 6 3 S a) [1 mark] Find the minimax rule(s) in the set of non-randomized decision rules D. b) [1 mark] Sketch the risk set of all randomized decision rules D generated by the set of non-randomized decision rules D. c) [3 marks] Find the risk point of the minimax rule in D and determine its minimax risk. Compare this risk with the minimax risk found in the set of non-randomized decision rules D. d) [3 marks] Define the minimax rule in the set D in terms of rules in D. e) [3 marks) Find the prior on {01, 62} such that the minimax rule in the set D is also a Bayes rule. Computes it's Bayes risk. f) [1 mark] For a small positive e, illustrate on the risk set the risk points of all rules which are e-Bayes for the prior found in part (e).