ISE 562; Dr. to ISE 562!
Decision Analysis
ISE 562; Dr. Smith
• How do you make decisions? – Flip a coin?
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– Procedure?
• Pick the cheapest option?
• Select the alternative you wish or hope would be the
• Look for published reviews?
• Maximize positive impacts?
• Minimize negative impacts?
• Combination of good and bad?
• Pick the choice that others will like?
– What if all the alternatives are bad? • ’s approach?
ISE 562; Dr. do you make decisions?
How do you know if you made the right choice for you? (1min)
What about recommending a choice for your organization?
“We are all slaves to to a matrix of uncertainty.” (Dr S)
Decisions occur within a matrix of uncertainty. Often we cannot know the full truth of the data, the outcomes, or the consequences.
Choosing to understand and quantify uncertainty will get us closer to the truth…
ISE 562; Dr. Smith
• Introductions •You
• Syllabus
• See Blackboard for:
• Announcements, scores • Content: lecture notes
ISE 562; Dr. Smith
• Syllabus
–Importance of this course
–Course Description
–Suggestions for success
–Course Prerequisites
–Course Goal
–Course Requirements and Grading –Office Hours
–Academic Integrity
–Disability Accomodation –Emergency preparedness
ISE 562; Dr. of this course: • Making choices
– Individual and time-staged decisions
– Decisions involving one criterion or multiple criteria
– Decisions made by a group or multiple groups of
decision makers • Value
– Defining metrics to quantify the value of alternatives • Decision biases
– All the things that can go wrong (and how to spot and prepare for them)
ISE 562; Dr. Description
Chapter 1,2, Probability Review Chapter 3, Discrete Bayes Methods
Chapter 4, Continuous Bayes Methods
Chapter 5, Decision Theory, Introduction to Utility Functions
Chapter 6, Value of Information Multiattribute decision analysis Group decision making
Decision biases
Basic concepts, definitions of probability
Decision making distributions for discrete random variables
Decision making distributions for continuous random variables
Structuring decision problems
EVPI, EVSI
Multiple decision variables
Group decision rules
Psychological and behavioral decision issues; framing
What is meant by “decision analysis approach?”
ISE 562; Dr. analysis:
•Application of a framework that identifies an optimal preferred choice which includes a set of alternatives, measurable criteria for the alternatives, and payoffs for the consequences (fixed or uncertain).
This course is about decision making procedures which are not unlike recipes:
ISE 562; Dr. for Success:
• Read over the reading assignments before the corresponding lecture.
• Attempt the homework on your own before asking for help.
• Make an honest attempt to understand the material before uttering the words, “I don’t get this.“
• If having difficulty, see TA or me—we are here to help you.
• Don’t wait until the last minute for anything!
ISE 562; Dr. :
•A course in probability and statistics
•Working knowledge of algebra; some calculus
Course Goal:
• Enable the student to formulate, collect, analyze, frame, and interpret decision making information for selecting the “best” alternative action.
ISE 562; Dr. : Winkler, .,
An Introduction to Bayesian Inference and Decision, Second Edition,
Probabilistic Publishing, Inc., Gainesville, Florida, 2003.
(Note: exams will be open book)
ISE 562; Dr. requirements:
Requirement
3 Homework assignments @ 10 points
Midterm Exam Project*
Final Exam
Course Total
*Miniprojectrequirementsoutlined inearly Total 30
ISE 562; Dr. /Office Hours:
Dr S: After class, by zoom appt, or email.
Office: GER ISE hoteling area
Email: for general communications
TA-Tuesday lec: TA-Wednesday lec: Office hours: TBD
Homework submissions to:
Tuesday class use Wednesday class use
ISE 562; Dr. Submissions:
1.You will be randomly paired with another student partner for each homework to submit the assignment jointly.
2.Submit one file for both of you by the due date.
3.Can be pdf’s, camera phone pics of handwritten text (multiple
pages in ONE file), MS Word, or Excel files.
4.Make sure assignment number and your names are in the file
name and in the file. For example:
• Hw1_lastname1-firstname1_ lastname2-firstname2.xlsx, docx, pdf
5.Put your names inside the file in case you forget 4. 6.Email the assignment to
(Tuesday section) or (Wednesday sections) with the assignment number in the subject line:
Hw1_lastname1-firstname1_ lastname2-firstname2.***[pdf, xlsx, etc.]
ISE 562; Dr. Smith •Academic Integrity
•Disability accommodation •Emergency preparedness
ISE 562; Dr. Smith
• Tuesday Schedule
Date Tuesday Aug 23 Tuesday Aug 30
Tuesday Sep 6 Tuesday Sep 13 Tuesday Sep 20 Tuesday Sep 27 Tuesday Oct 4 Tuesday Oct 11 Tuesday Oct 18 Tuesday Oct 25 Tuesday Nov 1 Tuesday Nov 8
Tuesday Nov 15
Tuesday Nov 22 Tuesday Nov 29 Thursday Dec 8
Introduction, Review
Discrete Bayes Methods
Continuous Bayes Methods
Decision making criteria and Utility
Utility concepts
The Decision Problem, Midterm review
Value of Perfect Information
Value of Sample Information
Multiattribute Decision Models
Multiattribute Decision Analysis; project requirements
Group Decision Making within stakeholder groups; measuring agreement
Group Decision Making across stakeholder groups; Decision biases 1
Decision Biases 2
Last Class; Improving decision making Final Exam 2-4pm
Readings Assignments/Notes Chapter 1, 2
Chapter 3 4.1- 4.9 5.1 – 5.8 5.9-5.10 5.9 – 5.10
6.1 – 6.2 6.3 Notes Notes Notes
HW3, Projects Due
ISE 562; Dr. Smith
• Wednesday Schedule
Date Wed. Aug 24 Wed. Aug 31
Wed. Sep 7 Wed. Sep 14 Wed. Sep 21 Wed. Sep 28 Wed. Oct 5 Wed. Oct 12 Wed. Oct 19 Wed. Oct 26 Wed. Nov 2 Wed. Nov 9
Wed. Nov 16
Wed. Nov 23 Wed. Nov 30 Mon. Dec 12
Introduction, Review
Discrete Bayes Methods
Continuous Bayes Methods
Decision making criteria and Utility
Utility concepts
The Decision Problem, Midterm review
Value of Perfect Information
Value of Sample Information
Multiattribute Decision Models
Multiattribute Decision Analysis; project requirements
Group Decision Making within stakeholder groups; measuring agreement
Group Decision Making across stakeholder groups; Decision biases 1
Thanksgiving Holiday—No Class
Last Class: Decision Biases 2; Improving decision making Final Exam 2-4pm
Readings Assignments/Notes Chapter 1, 2
Chapter 3 4.1- 4.9 5.1 – 5.8 5.9-5.10 5.9 – 5.10
6.1 – 6.2 6.3 Notes Notes Notes
HW3, Projects due
ISE 562; Dr. Smith
Probability and Statistics Review Part I
Decision Analysis
ISE 562; Dr. Smith
3 branches in probability and statistics
• Descriptive (mean, variance, range,…)
• Inferential (samples, populations, tests of hypothesis)
• Statistical decision theory
Definitions:
Event: outcome of a random experiment Sample space: set of all possible events
Probability: a real number mapping the event, E, to a real number P(E) where:
i. ii. iii.
0≤P(E) ≤ 1
If S=sample space, then P(S)=1
For 2 mutually exclusive events E1, E2, P(E1 E2) = P(E1) + P(E2)
ISE 562; Dr. rules
• If E1 and E2 not mutually exclusive, then
P(E1 U E2)=P(E1)+P(E2) — P(E1 E2)
• P(E) = 1 – P(not E)
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ISE 562; Dr. probabilities
• P(E) = nE / NS (relative frequency or “classical” approach)
• Requires known sample space
• Assumes repeatable and stable under “identical”
conditions However,
• There are many situations where an event is complex or may have never occurred or occurred only once; the sample space is not countable.
• For these situations we can resort to subjective probability
• P(E) = degree of belief that event will occur
• Problem becomes how to measure it
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ISE 562; Dr. Probability Methods
• 8/21/2022
Direct assessment probability of E is 20%
If odds are a to b that event E occurs, then P(E)= a/(a+b)
• If odds of a defendant conviction are 4 to 1 in favor of (E=) conviction, then P(conviction)=4/(4+1)= 0.80
If the probability of rain is 0.10, then odds in favor of rain are 100(.10) to 100(.90) or 10 to 90 =10/90=1/9 or 1 to 9 in favor of rain (or 9 to 1 against rain).
If the probability of rain is 0.50, then we get 50/50=1/1 or 1 to 1 odds (also called “even” or equal odds).
Or, if P(E) = p, then odds in favor of E are a/b where a=100p to b=100(1-p)
ISE 562; Dr. Probability Methods
Lotteries. Also called a p-lottery (probability-lottery) Uncertain (probabilistic outcome) with two or more consequences
Are used to estimate subjective probabilities.
Circle denotes a “chance” node—an uncertain outcome
Consequence 2
Consequence 1 P(Outcome 1)
1 – P(Outcome 1)
ISE 562; Dr. Probability Methods
Lotteries: we face lottery choices all the time; simplest is two outcomes. For example, getting a job:
No Job 1 Salary zero
The choice also depends on the probability of an offer:
Salary X P(offer)
1 – P(offer)
No Job 1 Salary zero
ISE 562; Dr. Probability Methods
• Lottery assessment of probabilities
– Suppose we want to estimate the P(rain). We offer the decision maker a choice…
P=0.50 $100 Rain $100
1-P=0.50 $0 No rain $0
If the DM chooses A then P(rain) < 0.50; if B chosen then P(rain)>0.50 Suppose the DM chooses A; now we offer…
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ISE 562; Dr. Probability Methods • Lotteries
– Suppose we want to estimate the P(rain). We offer the decision maker a choice…
P=0.25 $100 Rain $100
1-P=0.75 $0 No rain $0
If the DM chooses A then P(rain) < 0.25; if B chosen then 0.25
• Substitutabillity: If you are indifferent between two payoffs
X and Y (X~Y), then X can be substituted for Y as the payoff in a lottery without changing your preferences with regard to those lotteries.
• All of the above methods attempt to infer the subjective probability through the choices (actions) of the decision maker rather than just asking for the probability.
• Goal is to use a behavioral approach to quantify the judgment.
(We’ll come back to subjective probability later in the course) 8/21/2022 29
ISE 562; Dr. and Decision Making Framework
• Define the decision maker’s alternatives
• Define events (outcomes) and associated probabilities
• Identify the decision variable (cost, time, …)
• Identify the payoffs or costs of each alternative for each
• Compute the expected payoff of each alternative
• Select the “best” alternative
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ISE 562; Dr. tables
• Useful for arranging the decision problem for calculation • Combines alternatives, events, probabilities and payoffs
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Alternatives
P(Event 1)
P(Event 2)
Decision A
Payoff for A if event 1 occurs
Payoff for A if event 2 occurs
Decision B
Payoff for B if event 1 occurs
Payoff for B if event 2 occurs
ISE 562; Dr. payoff table for car breakdown (battery light is “on”)
Can drive to get new battery (but may be other problems) Can drive home to get new battery and fix myself
Can go to auto repair shop and pay for solution
What are the alternatives?
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Alternatives
P(Event 1)
P(Event 2)
A. Drive to get new battery
Payoff for A if event 1 occurs
Payoff for A if event 2 occurs
B. Drive home to get new battery and fix if generator failed
Payoff for B if event 1 occurs
Payoff for B if event 2 occurs
C. Go to auto repair shop
ISE 562; Dr. are the uncertain events?
Alternatives
Battery failed
Battery failed & generator failed
Generator failed
P(Event 1)
P(Event 2)
P(Event 3)
A. Drive to get new battery
Payoff for A if event 1 occurs
Payoff for A if event 2 occurs
Payoff for A if event 3 occurs
B. Drive home to get new battery and fix if generator failed
Payoff for B if event 1 occurs
Payoff for B if event 2 occurs
Payoff for B if event 3 occurs
C. Go to auto repair shop
Payoff for C if event 1 occurs
Payoff for C if event 2 occurs
Payoff for C if event 3 occurs
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ISE 562; Dr. are the probabilities of the uncertain events?
Alternatives
Battery failed
Battery failed & generator failed
Generator failed
A. Drive to get new battery
Payoff for A if event 1 occurs
Payoff for A if event 2 occurs
Payoff for A if event 3 occurs
B. Drive home to get new battery and fix if generator failed
Payoff for B if event 1 occurs
Payoff for B if event 2 occurs
Payoff for B if event 3 occurs
C. Go to auto repair shop
Payoff for C if event 1 occurs
Payoff for C if event 2 occurs
Payoff for C if event 3 occurs
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ISE 562; Dr. are the payoffs (costs) for each event?
Alternatives
Battery failed
Battery failed & generator failed
Generator failed
A. Drive to get new battery
B. Drive home to get new battery and fix if generator failed
C. Go to auto repair shop
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ISE 562; Dr. are the expected payoffs (costs) for each alternative?
Optimal decision is the one with minimum expected cost: “Drive home and fix”
8/21/2022 36
Alternatives
Battery failed
Battery failed & generator failed
Generator failed
Expected Cost
Drive to get new battery
Drive home to get new battery and fix if generator failed
Go to auto repair shop
ISE 562; Dr. also use decision tree to organize the order of events
Driveto get battery
Drive home
.60 G $320
Repair shop
home Etc…
$3 .15 B+G $320
B $15 .25 B+G
.15 $185 .60 G $185
Repair shop
= Choice node = Chance node
$90 .15 B+G $430
.60 G $370
ISE 562; Dr. probability: “Event A depends on event B” P(A|B)= joint probability of both A and B divided by the
marginal probability of B or = P(A and B)/P(B)
Example: let A= flight arrives on time; D=departs on time; and P(D)=0.83; P(A)=0.82; P(A and D)=0.78. Find the P(A|D) and P(D|A).
P(A|D)=P(A and D)/P(D)=0.78/0.83=0.94
P(D|A)=P(D and A)/P(A)=0.78/0.82=0.95
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ISE 562; Dr. probabilities are important because events of interest happen because some other event occurred first.
For example:
• The probability of delivering an integrated software app on
time depends on the prior delivery of other key
subcomponents first.
• The probability of a Class 7 nuclear accident depends on
the failure probabilities for the primary and secondary
coolant systems (among others).
• Patient probability of death from Covid-19 given not
vaccinated with vaccine vs. vaccinated.
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