decission analysis presentation

7/31/2019 Decission Analysis Presentation

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Decisions Analysis Presented By: Afzal WaseemPresented To: Dr. Arnold Yuan


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Decisions AnalysisDecision analysis provides a framework andmethodology for rational decision making when

the outcomes are uncertain


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The GOFERBROKE COMPANY owns a tract of land thatmay contain oil. A consulting geologist has reported tomanagement that she believes there is 1 chance in 4 ofoil. Because of this prospect, another oil company hasoffered to purchase the land for $90,000. However,Goferbroke is considering holding the land in order todrill for oil itself. The cost of drilling is $100,000. If oil is

found, the resulting expected revenue will be $800,000,so the companys expected profit (after deducting thecost of drilling) will be $700,000. A loss of $100,000 (thedrilling cost) will be incurred if the land is dry (no oil)

A PROTOTYPE EXAMPLE


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DECISSION MAKING WITHOUT

EXPERIMENTATION


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1. The Maximin payoff criteriaFor each possible action, find theminimum payoff over all possible statesof nature.Next, find the maximum of theseminimum payoffs.Choose the action whose minimumpayoff Gives this maximum.


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Pessimistic view pointBest guaranteed payoff

The action which provides the best payoff with its worst stateof nature.

Disadvantages

Nature is not a malevolent opponent,This is especially true when the worst possiblePayoff from an action comes from a relatively Unlikelystate of nature

Interested only for a very cautious decision makerDoes not include the effect of prior probabilities it in


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Maximum likelihood criterion: Identify the most likelystate of nature (the one with the largest priorprobability) .For this state of nature, find the action with themaximum payoff. Choose this action.

2. Maximum Likelihood Criterion


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No state of nature is considered other than the most

likely oneIn a problem with many possible states of nature, theprobability of the most likely one may be quite small,so focusing on just this one state of nature is quite

unwarrantedIgnores the extremely attractive payoff of 700 if thecompany drills and finds oil.

Drawbacks



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1. Using the best available estimates of theprobabilities of the respective states of nature(currently the prior probabilities ),

2. Calculate the expected value of the payoff for eachof the possible actions.

3. Choose the action with the maximum expectedpayoff

3. Bayes Decision Rule


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3. Bayes Decision Rule


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3. Bayes Decision Rule ADVANTAGES

It incorporates all the available information1. Payoffs2. Prior Probabilities of states of nature


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It is sometimes argued that these estimates of the

probabilities necessarily are largely subjective and so aretoo shaky to be trusted. There is no accurate way ofpredicting the future, including a future state of nature,even in probability terms

To assess the effect of possible inaccuracies in THE PRIORPROBABILITIES, it often is helpful to conductsensitivityanalysis


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To study the effect if some of the numbers included inthe mathematical model are not correct

1. most questionable are the prior probabilities2. similar approach could be applied to the payoffs

Sensitivity Analysis with BayesDecision Rule


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GOFERBROKES MANAGEMENT true prior probability

1. Oil 0.15 to 0.35

2. Dry 0.85 to 0.65sum of the two prior probabilities must equal 1


Oil = 0.15Dry = 0.85Expected payoff (Selling) = 90Expected Payoff (Drill) = 20

Oil = 0.35Dry = 0.65Expected Payoff (Drill) = 180Expected payoff (Selling) = 90

SELL DRILL

Application of Bayes decision rule twice


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Oil p = 0.15 Expected Payoff (Drill) = 20Dry = 0.85 Expected payoff (Selling) = 90

Oil p = 0.35 Expected Payoff (Drill) = 180Dry = 0.65 Expected payoff (Selling) = 90

0.15 - 0.35


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With more than two lines, there might be more than one

crossover point where the decision shifts from onealternative to another


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DECISION MAKING WITHEXPERIMENTATION

Frequently, additional testing (experimentation) canbe done to improve the preliminary estimates of the

probabilities of the respective states of natureprovided by the prior probabilities. These Improvedestimates are called posterior probabilities

1) how to derive the posterior probabilities !!!2) how to decide whether to conduct

experimentation or not !!!


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DECISION MAKING WITHEXPERIMENTATION

DRY

OIL

Test Results


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how to derive the posteriorprobabilities !!! Bayes theorem

e.g DRY and OIL are 2 number of statese.g 0.25 and 0.75 are the prior probabilities here

Past experience probabilities of findings from

experimentation result as in previous slide


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how to derive the posteriorprobabilities !!!

=0.8 0.75

0.8 0.75 + 0.4 0.25=

6

7

Unfavourable Seismic Surrounding


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how to derive the posteriorprobabilities !!!

=0.2 0.75

0.2 0.75 + 0.6 0.25=

1

2

Favourable Seismic Surrounding


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It shows a nice way of organizing thesecalculations in an intuitive manner.

PROBABILITY TREE DIAGRAM



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Expected Payoff`s


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1. Expected Value of Perfect Information2. Expected Value of Experimentation

how to decide whether to conductexperimentation or not !!!


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The first method assumes ( unrealistically ) that theexperiment will remove all uncertainty about whatthe true state of nature is, and then this methodmakes a very quick calculation of what the resultingimprovement in the expected payoff would be(ignoring the cost of the experiment). This quantity,

called the expected value of perfect information .

Expected Value of PerfectInformation


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Expected Value of PerfectInformation

Since 142.5 far exceeds 30, the cost of experimentation (a seismic survey), itmay be worthwhile to proceed with the seismic survey. To find out for sure,we now go to the second method of evaluating the potential benefit ofexperimentation


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find all the posterior probabilitiesexcluding the cost of the experiment

Expected Value of Experimentation


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Chance fork

Decision Fork

decission analysis presentation

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