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Decision Analysis 4 (Tree): EVSI - Expected Value of Sample Information - YouTube
Channel: Joshua Emmanuel
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Welcome to this decision tree tutorial
for Expected Value of Sample Information.
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In this tutorial we’ll be constructing
a decision tree with Sample Information.
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We will also be calculating the Expected Value
of Sample information.
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We will be using this Payoff Table
where Payoffs are Profits.
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This is the decision tree for the payoff table.
The expected value for Stocks is calculated
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as 20.2,
for Mutual Funds, it is 18.2,
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and for bonds, it is 20.
The best of the expected values is 20.2
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Therefore, the decision is to invest in Stocks.
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Now suppose there is an economic consultant
that can provide additional information about
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the states of nature (or outcomes). And this
consultant has some success history.
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We now have an additional decision situation.
Should we hire this consultant or not?
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If we don’t hire the consultant,
we will stick to our initial decision to invest
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in stocks.
If we decide to hire the consultant,
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then we will consider two factors:
1. How successful has the consultant’s information
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been in the past?
2. How much does it cost to hire the consultant.
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Here is a reduced version of our decision
situation.
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Now suppose, if we hire the consultant,
he or she could give a positive report
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or a negative report about economic conditions.
These report from additional information is
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often referred to as prediction, forecast,
or result.
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Suppose the probability of the consultant
giving a positive report is 0.44.
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This will mean that the probability of a negative
report is 0.56.
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Since these are probabilities,
we represent them with a chance node
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with positive and negative branches.
Suppose given a positive report,
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the probability of a Growing Economy is 0.59.
And the probability of growth given a negative
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report is 0.25.
This means that the probability of decline
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given positive report
is 1 – 0.59 which is 0.41.
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And the probability of decline given a negative report
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is 1 – 0.25 which is 0.75.
These probabilities are called posterior probabilities,
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we will discuss them in detail in the next
video.
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So if the report is positive, we paste the original tree here
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with the posterior probabilities, 0.59 and 0.41.
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We do the same for negative report
with posterior probabilities 0.25 and 0.75.
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The chance nodes have now been labelled 1 to 5 here for reference purposes, as we calculate
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the expected values:
The Expected Value for node 1 is
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0.59(70) + 0.41(-13) which equals 35.97.
In similar fashion, we calculate the expected
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values for node2, for node 3, and for node 4.
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Now if the report is positive,
the best expected value is 35.97 (from Stocks).
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And if the consultant’s report is negative,
the best expected value is 20 (from Bonds).
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Next we calculate the expected value for node 5
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which is 0.44(35.97) + 0.56(20) which gives 27.0268
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The Expected Value of Sample information estimates
the value of the information supplied by the
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consultant.
Sample information is also known as Imperfect
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Information.
So the Expected Value of Sample information,
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EVSI
is calculated as EV with SI – EV without SI
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EV with SI is the Expected Value with Sample
information.
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That is, best expected payoff if the consultant is hired (without paying the consultant).
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EVwithoutSI is the Expected Value without
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Sample information.
That is, the best expected payoff if the consultant
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is not hired.
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In this case, EV with SI is 27.0268
And EV without SI is 20.2
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Therefore, EVSI is 27.0268 – 20.2 which
gives 6.8268.
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Now let’s see how to use the EVSI to determine
the best decision strategy.
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Suppose the cost to hire the consultant is 7.2
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which is higher than EVSI.
That is, the fee is higher than the value
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added by the consultant.
And so, the decision strategy will be not
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to hire the consultant
As a result, we will stick to our initial
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decision and invest in Stocks.
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On another note, suppose the consultant’s fee is 3.5.
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which is less than EVSI.
Then the strategy will be stated as follows:
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Hire the consultant
If the consultant’s report is positive,
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invest in Stocks.
If the consultant’s report is negative,
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invest in Bonds.
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And that’s how to calculate and use the
EVSI to determine the best decision strategy.
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Please post your comments below.
Thanks for watching.
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Bye for now.
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