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So the thing about an
expected value of information,

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it's an expected value.

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That is, we're always
dealing in expectations here

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in the world of uncertainty.

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So you may have the
information that

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says that it's really
good, and it turns out

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that it's not so good.

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So you're not something
that is absolutely sure,

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but it's an expected value.

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So now let me talk
about the way one would

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do this in a full analysis.

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And I think it's
important as a baseline--

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thank you for the word--

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it's a baseline for
how we think about it.

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So the calculations are complex.

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First of all, any test, you can
have many different results.

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For example, a prototype plan
might work very well, well,

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so-so, poorly, fail.

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So you don't get
necessarily a yes/no answer,

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you get a range of answers.

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Now, these answers don't
prove what will happen.

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Why is that?

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I've run it.

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I've got a result,
it works well.

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Do I know that it's going
to work well, or don't I?

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Well, the test results will
not prove what happens.

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They are samples, just like
if I go through a test for TB,

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or contemporaneously, if I
go through a test for COVID

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and I have a negative result,
it doesn't necessarily

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mean that I'm negative.

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It might be there's
a false negative,

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or contrarily, that
it's a false positive.

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They thought they saw
something, but it's not there.

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So what the new
information does is not

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tell you what was happening.

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You knew this already,
but I'm emphasizing it.

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But it says, OK, you
thought it was like this.

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You got some new information.

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It made you think that
it might be different.

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So each piece of
new information,

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whether it performs well, very
well, poorly, so-so, and so on,

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updates the prior estimates.

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The technical way to do
that is using something

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called Bayes' theorem.

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Now, this is not a
particularly simple topic

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we get to because if I
have, say, five results,

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as I listed before, and
each test result implies

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a different value
of the project,

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each with a
different probability

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that five test
results will give you

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five different updates
for your system

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and each will have a
different set of probabilities

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that you updated from the
priors to the posteriors,

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and you have five
different solutions.

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So the calculation
of this process

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that is the expected value
of sample information

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is complicated.

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So first of all,
what's Bayes' theorem?

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I imagine that many of
you, if not most of you who

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have already dealt with this,
maybe you had in a course,

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that had to pass quizzes
on it, and so forth.

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But just as a recall, let me
remind everybody or introduce

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the others to what it is.

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The formula is very
simple, but I'm

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arguing for you this is
what I'm talking about

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because if it comes up is it's
impractical use for a system

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designed on a regular basis.

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But let me tell you what
it is and you'll see what--

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I hope you'll see
what I'm coming to.

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So the probability, the
posterior probability

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of something, A, say, that
the product will sell well,

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after the observation,
B, basically

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called A, probability
of A given B. That

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is, I had a prior
probability, maybe 50%

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it was going to sell well.

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I took my tractor
to the state fair.

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They gushed over it.

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It made me think, oh,
it will probably--

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it's more than a
50/50 chance, it

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will maybe a 70/30
chance it will sell well.

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So my posterior probability,
my revised probability

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is a simple formula.

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It is equal to the
probability you

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had in the beginning
times a factor.

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Now, all the devil
is in the details.

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The factor is the probability
that B is correlated with A,

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that those kinds of
responses actually

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lead to the market
results divided

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by the probability of B,
the prior probability of B.

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Now, the issue is that although
the formula is really simple,

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it's your probability
times a factor,

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and I can state the factor
is, that the elements are

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unavailable in practice.

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That is, if you're
thinking about how

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well the folks at the
state fair are responding

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to my new tractor and
how does that correlate

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with the actual sales,
well, that's something

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you don't have data on.

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And what's the probability of B?

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Well, you could
think that you might

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imagine some ways of doing
this, but you don't now.

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If you're doing a repetitive
test and have been doing this,

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say, agricultural sampling
or test fields, or you

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have lots of data
and so forth, you

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can get these conditional
probabilities,

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as they're called, and
you can run the analysis.

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But in general, you
won't have them,

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so that although the
formula is really simple,

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from the point of view of
system design and management,

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they are really not available.

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But I want to show you how
the thing works so that you

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can appreciate what's
going on and why

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there's another approach.

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