We finished discussing the flu shot problem. I put up the chart as we had it at the end of the last class, and then remarked that I thought we weren’t getting anything useful out of the additional chance node that I had drawn at the upper right. So I redid that part of the chart, with the following result:

We decided to use losses rather than utilities (gains). That is usually a good choice if most of the outcomes are neutral to bad, as we can then represent things with positive numbers which will mean a lesser likelihood of making sign errors. We chose 1,000,000 as the loss for dying. Since many of the probabilities are quite small, this allows us to write our intermediate results using simple integers rather than messy decimal fractiona. We chose 0 for not getting the flu, or recovering from it (not dying). Strictly we should have a small positive loss if one gets sick, but since most illnesses aren’t serious, the number would be quite small and would not significantly affect the outcome. As an illustration, we considered using the number of days sick as a fraction of a lifetime (generously estimated as 100 years), times the loss for dying. So, someone who was sick for 3 days would be sick for 1/100 of a year or 1/1o,ooo of a lifetime. That gives a loss of 100=1,000,000/10,000. So the loss is about 33 per day sick.

We put in a branch for GBS. That caused the liveliest discussion of the day. Dying of GBS is only a 5% chance if you get it, and getting it was estimated with a probability of about 1/1,000,000 (and it may be less, even much less). We estimated a 15% chance of permanent, serious disability, and an 80% chance of recovery after treatment and extensive rehabilitation, which we learned from WikiPedia could be about a year (1/100 of a lifetime), which for that branch gives a loss of 10,000. But how to estimate the loss from permanent disability? Some thought they’d rather die than end up that way, and others felt the opposite. But it’s pretty bad, and the numbers that were suggested ranged from 500,000 to 1,500,000 for the loss. It doesn’t much matter what we put in for the loss if it’s going to be in that range, so we just plugged in 1,000,000. Consulting the tree above, we saw that the decision is clear: Get the flu shot.

We then started looking at the review sheet. We looked at the ants/beetles problem. I remarked that there really are beetles that have this behavior (some thought that I’d just made it up). I think I heard about it from a show I saw that featured the great biologist E. O. Wilson, who has been studying ants all of his life. Anyway this is a “sampling with replacement” scenario, since the number of individuals in the nest is very large. I pointed out that in my mind, for a problem of this sort, on the test, I don’t want you wasting time actually calculating the whole spreadsheet in detail. I know that you can do this with a spreadsheet program, all I want to know is that you know how to set the problem up. So, the spreadsheet, as you could draw it for credit on the test, is shown as I drew it on the board:

Along with the picture, you should have enough text explaining it so that I will know that you know how the problem should be solved.

Monday we will finish our discussion of the study sheet.

In response to a question, I noted that I usually have you answer five questions, each worth 20 points. But I usually have six on the test, so you have a choice, and you are allowed to try all six for extra credit.

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