... differently.¹

Those of you who know me will be astonished that it's taken me this long to get to a discussion of Bayesian approaches.

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... forest health.²

There are obviously other reasons why we might want to regulate air quality as well, but we're only going to consider this aspect of the problem.

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... health.³

This example is taken from [1].

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... an effect.⁴

The effect may not be particularly large or important, but it's unlikely that there is no effect. A complete discussion would phrase the question differently and ask whether pollution is having a large enough effect on forest health to make it worth regulating. To keep things simple, we'll ignore that subtlety.

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... health,⁵

For simplicity we'll ignore the possibility that their decision is influenced by other factors, like economic impact.

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... too.⁶

Although we hope that we're less likely to be wrong than they are.

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... compare.⁷

This is a point we'll come back to after Thanksgiving break.

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....⁸

For those of you who've had a little economics (and especially for those of you who haven't), let me remind you that if you're using dollars as your measure, it's not enough to calculate how much something is worth 100 years from now. Investment decisions are generally, and reasonably, based on the amount of money you'd have to invest now at some specified interest rate (the discounting rate) to have the amount you're interested in at the end of that period. To have $1,000,000 100 years from now, I would need $10,051.84 today, assuming a 5% discount rate (the magic of compound interest). Thus, the present value of $1,000,000 in 2100 is $10,051.84 today. We'll return to these ideas in the next couple of lectures.

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... gambling.⁹

Which we are, in some sense.

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... ``worth.''¹⁰

Economists are often accused of trying to put a dollar value on everything, and we'll talk about valuation methods after Thanksgiving break. It's important to realize, however, that dollars are really just a convenient shorthand for economists. What they are usually trying to do is to maximize expected utility.

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... function.¹¹

I put a lot more value in Bach and Mozart now than I did in junior high, for example.

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... water?¹²

Would I be asking this question if the answer were ``Yes''?

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... pollution.¹³

This example is adapted from [3].

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... conservative.¹⁴

Because I've changed their example a bit, what they call a maxi-min choice is the same as the mini-max choice as I've described it here. Sorry for the confusion, but I find it easier to make costs positive than to leave them negative. That's the cause of the difference.

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