Simple Monte Carlo integration. Implement inference for Example 4.1. a. Verify the posterior means k shown in Figure 4.1, and add central 50% credible intervals

Simple Monte Carlo integration. Implement inference for Example 4.1.

a. Verify the posterior means πk shown in Figure 4.1, and add central 50%

credible intervals for πk, k = 1, . . . , K.

b. Assume the next patient is treated at dose k5 = 3, and we record no toxicity, y5 = 0. Find the updated posterior means πk = E(πk | D5) and determine the treatment allocation k

? for the next patient.