TM%20792%20Special%20Topics%20Decision%20Theory%20June%202,%202008%20%20Spring%202008%20Dr.%20Frank%20Joseph%20Matejcik

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TM 792 Special Topics Decision TheoryJune 2,
2008 Spring 2008Dr. Frank Joseph Matejcik
Ch 7 cont. problems Ch 8 Revising by New
Information Ch 9 Biases in Probability Assessment
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Agenda New Assignment

• Tentative Schedule
• Assignment Ch 7 1, 3 Ch 8 3, 8
• Chapters 7 problems, 8, and start of 9 GW
• We will do the survey online
• Decision Analysis for Management Judgment 3rd
  Edition Paul Goodwin George Wright, John Wiley
  EU
• Many slides solutions provided by John Wiley.

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Access Overview

• Instructor Dr. Frank J. Matejcik CM 319
• Work [phone] roughly 10-3 M-F in May
• Cell [phone] Ill try to keep it
  nearby
• Home [phone] Call in June?
• Frank.Matejcik_at_.sdsmt.edu
• Do the book, mostly

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Web Resources

• Class Web site on the HPCnet system
• http//sdmines.sdsmt.edu/sdsmt/directory/courses/2
  008su/tm792M081
• www.wileyeurope.com/go/goodwinwright/
• Streaming video ? http//its.sdsmt.edu/Distance/
  
• The same class session that is on the DVD is on
  the stream in lower quality. http//www.flashget.c
  om/ will allow you to capture the stream more
  readily and review the lecture, anywhere you can
  get your computer to run.

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Tentative Schedule
Chapters Assigned 12-May 1,2,3 e-mail,
contact Discussion Q. 3 page 25 19-May 3,4,5
Ch 3 1, 3bc, 6 Ch 4 5, 10 26-May
Holiday 29-May 5,6,7 Ch 5 3, 8 Ch 6 4, 8
Holiday makeup 02-June 7,8,9 Ch 7 1, 3 Ch 8
3, 8 09-June 9,10 16-June 11,12 23-June
13,14 30-June Overview, Final
Attendance Policy Help me work with you.
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Chapter 7 problem 2

• The managers of a food company are about to
  install a number of automatic vending machines at
  various locations in a major city. A number of
  types of machine are available and the managers
  would like to choose the design which will
  minimize the profit that will be lost because the
  machine is out of order. The following model is
  to be used to represent the lost profit
• Cost of lost profit per month
• (number of breakdowns per month)
• x (time to repair machine after each
  breakdown, in hours)
• x (profit lost per hour)
• One machine that is being considered is the
  Supervend, and the following probability
  distributions have been estimated for this
  machine

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Chapter 7 problem 2

• Number of Repair Average
• breakdowns time profit lost
• per month Prob. (hours) Prob. per hour Prob.
• 0 0.5 1 0.45 10 0.7
• 1 0.3 2 0.55 20 0.3
• 2 0.2
• (a) Use a table of random numbers, or the random
  number button on a calculator, to simulate the
  operation of a machine for 12 months and hence
  estimate a probability distribution for the
  profit that would be lost per month if the
  machine was purchased.
• (b) Explain why the model is likely to be a
  simplification of the real problem
• Excel RAND(), IF

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• Chapter 8
• Revising Judgments
• in the Light of
• New Information

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Bayes theorem Stats book
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Bayes theorem
Prior probability
New information
Posterior probability
Looks more like Bayesian estimation to me.
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The components problem fig. 8.1
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Applying Bayes theorem to the components problem
figure 8.2
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Bayes Procedure

• 1) Construct a tree with branches representing
  all the possible events which can occur and write
  the prior probabilities for these events on the
  branches.
• 2) Extend the tree by attaching to each branch
  a new branch which represents the new information
  which you have obtained. On each branch write the
  conditional probability of obtaining this
  information given the circumstance represented by
  the preceding branch.
• 3) Obtain the joint probabilities by multiplying
  each prior probability by the conditional
  probability which follows it on the tree.
• 4) Sum the joint probabilities.
• 5) Divide the 'appropriate' joint probability by
  the sum of the joint probabilities to obtain the
  posterior probability.

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Vague priors and very reliable information fig.
8.5
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The effect of the reliability of information on
the modification of prior probabilities Fig. 8.6
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The retailers problem with prior probabilities
fig. 8.7a
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Applying Bayes theorem to the retailers problem
fig. 8.7b
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Applying Bayes

theorem to the

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Determining the EVPI fig. 8.8
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Calculating the EVPI table 8.1
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Deciding whether to buy imperfect information
fig. 8.9
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If test indicates virus is present fig. 8.10a
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If test indicates virus is absent fig. 8.10b
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Determining the EVII fig. 8.11
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• Expected profit with imperfect
• information 62 155
• Expected profit without the
• information 57 000
• Expected value of imperfect
• information (EVII) 5 155

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EVII procedure p 233

• (1) Determine the course of action which would be
  chosen using only the prior probabilities and
  record the expected payoff of this course of
  action
• (2) Identify the possible indications which the
  new information can give
• (3) For each indication
• (a) Determine the probability that this
  indication will occur
• (b) Use Bayes' theorem to revise the
  probabilities in the light of this indication
• (c) Determine the best course of action in the
  light of this indication (i.e. using the
  posterior probabilities) and the expected payoff
  of this course of action

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EVII procedure p 233

• (4) Multiply the probability of each indication
  occurring by the expected payoff of the course of
  action which should be taken if that indication
  occurs and sum the resulting products. This will
  give the expected payoff with imperfect
  information
• (5) The expected value of the imperfect
  information is equal to the expected payoff with
  imperfect information (derived in stage 4) less
  the expected payoff of the course of action which
  would be selected using the prior probabilities
  (which was derived in stage 1).

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Ch 8 problem 4

• (4) A mining company is carrying out a survey in
  a region of Western Australia. On the basis of
  preliminary results, the company's senior
  geologist estimates that there is a 60
  probability that a particular mineral will be
  found in quantities that would justify commercial
  investment in the region. Further research is
  then carried out and this suggests that
  commercially viable quantities of the mineral
  will be found. It is estimated that this research
  has a 75 chance of giving a correct indication.
  Revise the senior geologist's prior probability
  in the light of the research results.

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Ch 8 problem 6
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Ch 8 problem 6
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Ch 8 problem 6
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• Chapter 9
• Biases in
• Probability Assessment

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Chapter Outline

• I Introduction
• 15 questions
• II Hueristics Biases
• III The availability heuristic
• A Biases associated with availabilty heuristic
• 1 When ease of recall is not a associated with
  probability
• 2 Ease of imagination is not realted to
  probability
• Q1-Q3
• 3 Illusory correlation

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Chapter Outline

• IV The representativeness heuristic
• A Biases associated with representativeness
  heuristic
• 1 Ignoring base-rate frequencies Q4
• 2 Expecting sequences of events to appear
  random Q5
• 3 Expecting chance to be self-correcting Q6-Q7
• 4 Ignoring regression to the mean Q8
• 5 The conjunction fallacy Q9-Q10
• V The anchoring and adjustment heuristic
• A Biases associated with anchoring and
  adjustment
• 1 Insufficient adjustment Q11
• 2 Overestimating the probability of conjunctive
  events Q12
• 3 Underestimating probabilities for disjunctive
  events Q13
• 3 (sic) Overconfidence Q14

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Chapter Outline

• VI Other judgmental biases
• 1 Believing desirable outcomes are more probable
• 2 Biased assessment of covariation Q15
• VII Is human probability judgment really so poor?
• 1 Subjects in studies may be unrepresentative of
  real decision makers
• 2 Laboratory tasks may be untypical of
  real-world problems
• 3 Tasks may be misunderstood by subjects
• 4 Subjects may be poorly motivated
• 5 Citation bias
• 6 Real-world studies suggest better performance
• 7 People think in frequencies not probabilities

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Heuristics and biases

• People use simple mental strategies or heuristics
  to cope with difficult judgments
• These heuristics are often efficient ways of
  coping with complex problems, but...
• They can also lead to systematically biased
  judgments

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Three common heuristics

1. The availability heuristic Vivid recall more
   likely and vice versa
2. The representativeness heuristic Is Peter a
   salesman?
3. Anchoring and adjustmentBase on know level

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The availability heuristic

• People assess the probability of events
• by how easily these events can be
• brought to mind.
• e.g. how easily they can be recalled or
• imagined

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Biases resulting from the availability heuristic

1. Ease of recall may not be associated with
   probability (Older crime victims)
2. Easily imagined events are not necessarily more
   probable Q1-Q3 (Delays of the project like
   strikes)
3. Illusory correlation (foreign supplier quality)

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The representativeness heuristic

• Used where people have to judge the probability
  that
• an object or person belongs to a particular
  category
• an event originates from a particular process
• The assessed probability is based on the extent
  to which the object, person or event appears to
  be representative of the category or process.

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Biases resulting from the representativeness
heuristic

1. Ignoring base rate frequencies Q4 Engineer,
   salesman judgment
2. Expecting short sequences of events to look
   random Q5 Production miss plan
3. Expecting chance to be self-correcting Q6-Q7 hot,
   cold lottery numbers
4. Ignoring regression to the mean Q8 SI cover
5. The conjunction fallacy Q9-Q10 Linda

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Anchoring and adjustment

• People make estimates by starting from an
  initial value (the anchor) and adjusting from it
  to get their final estimate

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Biases resulting from anchoring and adjustment

1. Insufficient adjustment from the anchor Q11 UN
   membership
2. Overestimating the probability of conjunctive
   events Q12 not multiplying
3. Underestimating the probability of disjunctive
   events Q13 similar to above
4. Overconfidence Q14 too narrow CIs

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Other judgmental biases

• Believing desirable outcomes are more probable
  My life will be better for housing and heart
  attacks.
• Biased assessment of covariation Q15
• table p 263

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Is human judgment really so poor?

1. Subjects taking part in studies may not be
   representative of management decision makers
   undergrads
2. Laboratory tasks may be untypical of real-world
   problems minor context changes important
3. These tasks may often be misunderstood by
   subjects my correlation estimates (continu
   ed)

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Is human judgment really so poor?

• Subjects in studies may be poorly
• motivated (not real)
• 5. Studies showing good performance tend to be
  cited less often (is warning better?)
• 6. Real-world studies suggest better
  performance Experts are good NWS
• 7. People think in terms of frequencies not
  probabilities We are asking unnaturally, Linda
  modified

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Choosing how to develop a subjective probability
assessment figure 9.12
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• Done for the night.