We first looked at the decision problem at the end of the handout. We decided that there are two actions that we could take: Immediately hire someone to put the machine into the “good” state, or produce one part and if it is “good” continue to make more parts, hoping that the “good” part indicates that the machine is in the “good” state, and if it is bad, hiring the person to fix the machine.

(Click on picture to enlarge).

I’ll mention that last year, the class thought of a third possibility: Never fix the machine, just produce parts. This one wasn’t as good as the best strategy, “produce one part and fix if it is bad.”

In response to a question, I mentioned that any decision problems on the quiz won’t be this involved. The reason is that the class is 50 minutes long, so I’ll design the test so that 10 minutes or less per question should be adequate. We spent over 30 minutes already on this problem by the time the question was asked!

I also pointed out that what I want to know is that you know how to answer each question. I won’t necessarily expect you to do a complete calculation, just indicate how the calculation goes. So, for example, if we had the problem of picking numbered balls out of a hat (and not replacing them), and had picked out #1,2,3, then a typical spreadsheet would look as below:

You should say something about how each of the numbers in the likelihood would be calculated, explain your choice of prior, and explain how the joint, the marginal, and the posterior distributions are calculated. That would be adequate. You don’t need to actually compute every number in the table if it would take too long. On the other hand, some calculations are so simple (for example, Monty Hall type problems, or problems with just two states of nature) that they can easily be calculated in a short time.

See you on Friday!

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