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RICHARD DE NEUFVILLE:
So in equation form,

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the expected value
of information

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is this one-line formula.

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It basically says, the
expected value after the test

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is the expected value
without the test.

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So the expected
value after the test

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is you calculate that based upon
your-- fro doing the decision

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tree, your optimal
set of decisions.

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And that's simple.

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Now, the expected
value star, which

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means that it's the
best choice, subscript

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of k, it is the optimal decision
given the test result k.

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So as I suggested before, if
you have five test results,

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you have five different
revisions of the probabilities.

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You have five different
possible answers.

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So there's D, the
best set of decisions,

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is indexed to the number of
test results for example five.

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So each test result
that might be possible

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has a probability of occurring.

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And it also then revises the
probabilities afterwards.

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So there's the pk, the
probability of occurring,

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the probability afterwards
to the posterior

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probabilities of pjk.

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And then the Dk star,
the optimal decisions

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after the test, calculates
using the prior revised

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probabilities.

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Are you confused yet?

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Well, maybe if you've been
through all this before,

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you're not confused.

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And in principle,
it's very simple.

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But as I've shown you, I
hope, through this indexing

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of k and i and j and
D and ij combined

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and so forth, this is a
confusing approach to do.

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And you're not likely to
be able to do it very well.

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So I would like now to-- first
of all, are there any questions

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or comments that you
might have at this point?

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I'm trying to show you--

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give you a feel for, given
that you make a test result

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and you get results, what is
happening, in fact, in terms

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of what should be happening
in terms of your revision

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process of the probabilities.

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All right, so let
me give an example.

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Suppose a company decides
to run a prototype plant,

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and it can anticipate
possible results--

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for example, the operation
is good, medium, or poor.

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For each test result--

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I will change this typo here--

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how would you calculate it?

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So for example, if
you had a poor result,

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it implies that maybe the
system is going to work

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and won't work.

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So the optimal decision
would be not invest,

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so that getting this information
may have significant impacts

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on the decision to be taken.

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So how would you do this?

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How would you analyze
the overall result?

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So you'd estimate
the probability

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of each possible test result--
good, medium, or poor.

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That's hard to do, just
as Robert has suggested.

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How do I know that this thing
that I haven't done before

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is going to lead to good,
medium, or poor results?

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Well, what do I base that
assessment of probability?

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Well, if you've done it 50
times and you have a good track

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record on it, maybe you
have an idea that you could

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get these numbers within reason,
maybe to a first decimal point,

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I mean, like 0.7 or 0.5.

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But that's a pretty
murky thing right there.

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But then you have to calculate
the optimal decision,

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and you would have
to then sum these up

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to get the expected probability
value after the test.

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So it's a complicated thing.

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And ultimately, you would
have to say, all right,

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I'm going to calculate
this value from my best

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design to an estimated value of
my best design after the test.

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And you go through
all this process.

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And here's where Robert
was talking about.

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Somehow they have to come with
a prior probability of the test

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results.

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They have to have the
conditional probability

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of the association of the test
results for the correlation

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with the actual priors.

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And you get to a complicated
situation where--

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I think Robert
described it very well.

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Sometimes they're-- well, I'm
not sure the words he used.

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The point of this first
phase of the presentation

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is that the full analysis
is a complicated process

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with many possible outcomes.

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It involves a lot
of assumptions--

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the probabilities
outcomes of the test.

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So the full analysis cannot be
accurate even if the math is

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correct.

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So bottom line
from this approach

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is I encourage you to be
skeptical of such detailed

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analysis, and you
need some alternative

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to get an assessment of
the value of information.

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That's the point
of this process.

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