Encounters With Risk PPP
(Perception,Policy and Practice)
During a Career in Operations Research
Stephen Pollock
University of Michigan
1
Oct 3, 2007
A PERSONAL VIEW OF RISK PPP
• MY EXPERIENCES WITH RISK PPP WHILE DOING O.R.
• CLEARLY A BIASED PERSPECTIVE
• A NUMBER OF ANECDOTAL EXAMPLES THAT MIGHT
SERVE TO FORESHADOW OR TIE TOGETHER THE
DIVERSE ISSUES OF THIS WORKSHOP
2
Oct 3, 2007
O.R./I.E/ ENGINEERING?
• OPERATIONAL PROBLEM SOLVING
• MOSTLY MATHEMATICAL MODELS
• ALSO A WAY OF THINKING:
– WATER GLASS
– GUILLOTINE
– FORK
• UNCERTAINTY ALWAYS PRESENT
3
Oct 3, 2007
TYPICAL DECISION ANALYSTS VIEW
d3
p1
d1
d2
d4
DECISION
1-p1
p2
1- p2
CONSEQUENCE x1
CONSEQUENCE x2
CONSEQUENCE x3
CONSEQUENCE x4
CHANCE
4
Oct 3, 2007
MORE GENERIC VIEW
d
f(x|d)
CONSEQUENCE
x
DECISION
CHANCE
5
Oct 3, 2007
MORE GENERAL VIEW
d
DECISION
d’(d,x)
f(x|d)
CHANCE*
*”UNCERTAINTY”
DECISION
f(y|d’,x)
CHANCE
CONSEQUENCE (X,Y)
6
Oct 3, 2007
WHERE DOES RISK POLICY AND PERCEPTION FIT
THIS SCHEMA?
d
DECISION
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
7
Oct 3, 2007
WHERE DOES RISK POLICY AND PERCEPTION FIT
THIS SCHEMA?
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
8
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
RISK HAS TWO NECESSARY ASPECTS:
• UNCERTAINTY -- WHAT WILL HAPPEN?
• CONSEQUENCES -- WHY DOES ONE CARE?
CONFOUNDING THESE ARE
• CONCEPTION (WHAT ONE THINKS THE “RISK”
ASPECTS ARE)
• PERCEPTION (HOW ONE “SEES” THE RISK ASPECTS)
• CODIFICATION (HOW ONE “TALKS” ABOUT -- OR
SHOULD TALK ABOUT -- RISK ASPECTS)
9
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
THE POLICY COMPONENT
(DECISION/MITIGATION) -- WHAT
SHOULD ONE DO?
THIS ALSO INVOLVES A MIXTURE OF
• CONCEPTION (WHERE DO POSSIBLE
DECISIONS/OPTIONS/POLICIES COME FROM?)
• PERCEPTION (HOW ONE “SEES” OPTIONS)
• CODIFICATION (HOW TO DESCRIBE OPTIONS)
10
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
??
FINALLY (AND PERHAPS MOST
IMPORTANT):
PRACTICE (WHAT ACTUALLY GETS
DONE)
11
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
TO THE “PERSON IN THE STREET”,
ARE THE FOLLOWING “RISKY”?
•BUNGEE JUMPING
•NOT BUCKLING UP
•BUCKLING UP
•PICKING UP A $20 BILL FROM THE STREET
•INOCULATING A CHILD AGAINST MEASLES
•NOT INOCULATING A CHILD AGAINST MEASLES
•LIVING
“EVERYDAY” ANSWERS SHOW ALL SORTS OF
COGNITIVE BIASES, BUT NEGATIVE FRAMING
SEEMS TO BE PERVASIVE
Oct 3, 2007
12
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
SOME “EVERYDAY”* CONCEPTION,
PERCEPTION, AND CODIFICATION OF RISK:
*NY TIMES, NEW YORKER, NPR, ETC.
13
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Souffle (NPR 7/23)
David Denby’s review of “A Fine Romance”: (referring to
romantic film comedies)
“ …with a married couple, romance is like “…a duel with
slingshots at close quarters –- exciting but a little risky”
(New Yorker 7/23)
14
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
“The Black Swan” popular book dealing with “The role of
the unexpected” in financial trading (NYT B.R. 7/29)
”What is “unexpected”?
{13 craps in a row}
{this particular person dies within the next five years}
{this levee fails}
{a levee fails}
15
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Louis Menan’s review of Caplan’s “The Myth of the
Rational Voter: Why Democracies Choose Bad
Politics” (New Yorker 7/19)
“You can’t use futures markets for assessing
probabilities like you can for guessing the number of
jellybeans in a bowl, or odds in sports gambling.”
16
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Louis Menan’s (continued): “People exaggerate the
risk of loss; they like the status quo and tend to
regard it as a norm; they overreact to sensational but
unrepresentative information (shark attack
phenomenon) … Most people, even if you explained
…the economically rational choice … would be
reluctant to make it, because … in particular, they
want to protect themselves from the downside of
change. They would rather feel good about
themselves than to maximize ... profit.”
17
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Levitt and Dubner’s article “The Jane Fonda Effect”
“... in 1916 … the legendary economist Frank Knight made a
distinction between two key factors in decision making: risk
and uncertainty. The cardinal difference, he declared, is that
risk — however great — can be measured, whereas uncertainty
cannot.” (NYT Magazine 9/16)
18
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Levitt and Dubner’s* article “The Jane Fonda Effect”
“… Has fear of a [nuclear] meltdown subsided, or has it merely
been replaced by the fear of global warming? …. in 1916 … the
legendary economist Frank Knight made a distinction between
two key factors in decision making: risk and uncertainty. The
cardinal difference, he declared, is that risk — however great
— can be measured, whereas uncertainty cannot.” (NYT
Magazine 9/16)
* Authors of “Freakonomics”
19
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
“EVERYDAY” CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK AND POLICY
HELMET WEARING BY NHL PLAYERS (1979-80
SEASON REQUIREMENT)
20
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
HOW MUCH TIME TO CARRY A GARBAGE CAN FROM A
BACK YARD TO THE CURB?
WHICH CUTTER HEADS WERE THE DEFECTIVE ONES?
WILL A SUB PASS BY DURING AN ASWEX?
21
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
CONCEPTION, PERCEPTION AND
CODIFICATION OF UNCERTAINTY
ELLSBERG PARADOX
BAG A HAS 500 RED BALLS AND 500 GREEN BALLS
BAG B HAS 1000 RED AND GREEN BALLS
YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF
IT IS RED.
WHICH BAG DO YOU PREFER?
MOST PEOPLE PREFER A
22
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
CONCEPTION, PERCEPTION AND
CODIFICATION OF UNCERTAINTY
ELLSBERG PARADOX DEMONSTRATES MANY
PEOPLE’S PREFERENCE FOR
“CRISP” PROBABILITIES VS. “AMBIGUOUS” ONES
23
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
CONCEPTION, PERCEPTION AND
CODIFICATION OF UNCERTAINTY
ELLSBERG PARADOX -- PREFERENCE FOR “CRISP”
PROBABILITIES VS. “AMBIGUOUS” ONES
BAG A HAS 450 RED BALLS AND 550 GREEN BALLS
BAG B HAS 1000 RED AND GREEN BALLS
YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF
IT IS RED.
NOW WHICH BAG DO YOU PREFER?
24
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
CONCEPTION, PERCEPTION AND
CODIFICATION OF UNCERTAINTY
ELLSBERG PARADOX -- PREFERENCE (?) FOR “CRISP”
PROBABILITIES VS. “AMBIGUOUS” ONES
BAG A HAS 200 RED BALLS AND 800 GREEN BALLS
BAG B HAS 1000 RED AND GREEN BALLS
YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF
IT IS RED.
NOW WHICH BAG DO YOU PREFER?
25
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
“CRISP” VS. “AMBIGUOUS” PROBABILITIES
•TEST OF CONCEPT OF TOTAL RE-DESIGN OF A
GLOBAL LOGISTIC CHAIN VIA M.C. SIMULATION
•USED PREVIOUS YEAR’S DEMAND DISTRIBUTION
FOR TO PROVE OUT RE-DESIGN CONCEPT
•MASSIVE CORPORATE PRESSURE AGAINST USING
DISTRIBUTION OVER SIMULATION MODEL’S
PARAMETERS -- SINCE “WE WON’T KNOW WHAT
THEY MIGHT BE”
26
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
“CRISP” VS. “AMBIGUOUS” PROBABILITIES
•ORDER SIZE FOR CRITICAL MATERIAL BASED ON
PROJECTED PRODUCT SALES AND MATERIAL PRICE
•SALES BASED UPON “TARGETS”
•MATERIAL PRICE BASED ON SPECIALIST’S
FORECASTS
•MASSIVE CORPORATE PRESSURE AGAINST USING
DISTRIBUTION OVER EITHER SALES OR PRICES
“THESE ARE EXPERTS, THEY SHOULD KNOW THE
ANSWER”
27
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
CONCEPTION, PERCEPTION AND CODIFICATION
OF UNCERTAINTY
AMBIGUITY EXPRESSED AS PROBABILITY DISTRIBUTIONS
OVER PROBABILITIES (REF: H. KUNREUTHER)
uncertainty in
Probability
uncertainty
in Loss
Probability
{loss > v}
95%
“mean” prob.
5%
v ($)
28
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
WHAT IF ADVERSARIES CHOOSE THE
PROBABILITIES?
29
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
ADVERSARIAL RISK ANALYSIS
FOOTBALL ANALOGY [OFFENSE’S VIEW]
d
OFFENSE
PLAYER
PERSONNEL
d’(x)
f(x|d)
DEFENSIVE
ALIGNMENT
AUDIBLE
PLAY CALL
f(y|x,d’(x))
PLAY
OUTCOME
(y)
30
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF POLICY
WHAT IF THE DECISION MAKER CHOOSES THE
PROBABILITIES?
CONSIDER THE MATHEMATICAL
PROGRAMMING PROBLEM:
min f(x)
s.t.
g(x, z) ≥ 0
31
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION AND
CODIFICATION OF POLICY
“CHANCE CONSTRAINED PROGRAMMING”
min f(x)
s.t.
Prob. { g(x, Z) ≥ 0 } ≥ p
WHERE Z IS NOW A RANDOM VARIABLE
32
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
EXAMPLE: DETERMINE d = BANK’S CASH RESERVES
BANK WANTS TO MINIMIZE d
REGULATORS REQUIRE SMALL PROBABILITY OF RUNNING
OUT OF CASH; Z = DEMAND FOR CASH (A R.V.)
min d
s.t. Prob. { Z ≥ d } ≥ .90
.10
p(z)
z
x = 2M
33
Oct 3, 2007
d
f(x|d)
POLICY
X
CONSEQUENCE
UNCERTAINTY
HOW ABOUT A RANDOMIZED POLICY?
min x
s.t. Prob. {x ≥ Z} ≥ .90
.55
.01
z
x = .6M
Prob. =
.2
x = 2.1M
.8
Prob. { x > Z} = .2(.55) +.8(.99) = .901 (OK)
E(X) = .2(.6M) + .8(2.1M) = 1.93 ( better than 2)
BUT -- WOULD THE REGULATORS APPROVE??
34
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION AND
CODIFICATION OF POLICY
•CAMSHAFT HARDENING
•SEWAGE TREATMENT IN ***
•1979 NHL HELMET REGULATION (REVISITED)
35
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
A US FEDERAL DEPARTMENT REPORT
USES, WITH LITTLE DIFFERENTIATION:
PROBABILITY
LIKELIHOOD
CHANCE
FREQUENCY
RELATIVE PROBABILITY
STOCHASTIC PROBABILITY
36
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
A US FEDERAL DEPARTMENT, IN A PRA
REPORT, USES, AS SYNONYMS:
MEAN
AVERAGE
37
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
ANOTHER US FEDERAL DEPARTMENT
USES, AS SYNONYMS:
DISTRIBUTION FUNCTION
DENSITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY DISTRIBUTION
DISTRIBUTION
38
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF RISK
(computation)
FEDERAL DEPARTMENT REPORT:
RISK = "the probability or frequency of an event
multiplied by the consequences of the event”
39
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
CONCEPTION, PERCEPTION AND
CODIFICATION OF RISK
Society for Risk Analysis (SRA) Glossary
(http://sra.org/resources_glossary.php)
RISK = “The potential for unwanted, adverse
consequences to human life, health, property, or the
environment;
BUT THEN SRA GOES ON TO SAY:
“estimation of risk is usually based on the expected value
of the conditional probability of the event occurring times
the consequence of the event given that it has occurred."
40
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
CODIFICATION OF RISK IN A FORTHCOMING
PROPOSED LEXICON
RISK = The potential for unwanted, adverse consequences.
It is important to distinguish between the term "risk,”
which involves uncertainties, consequences and
conditioning statements, and "expected risk" [q.v.] which
combines these factors using a linear additive operation.
PROBABILITY = One of a set of numerical values between
0 and 1 assigned to a collection of random events (which
are subsets of a sample space) in such a way that the
assigned numbers obey axioms [ …]
41
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
MORE CODIFICATION FROM THE
PROPOSED LEXICON
CONSEQUENCE (OUTCOME) = A description of a
scenario, in terms of measurable factors, that a
decision-maker may consider when assessing
preferences over different scenarios; these factors
are often random variables.
EXPECTED RISK = A summary measure of risk for
an event, scenario, etc., as expressed by the
expected value of any one of the measurable
consequences associated with the risk.
42
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
RISK
CODIFICATION OF UNCERTAINTY IN A
FORTHCOMING PROPOSED LEXICON
•ALEATORY PROBABILITY = A measure of the uncertainty
of an unknown event whose occurrence is governed by
some random physical phenomena that are either: a)
predictable, in principle, with sufficient information (e.g.,
tossing a die); or b) phenomena which are essentially
unpredictable (radioactive decay).
•EPISTEMIC PROBABILITY = A representation of
uncertainty about propositions due to incomplete
knowledge. Such propositions may be about either past or
future events.
Oct 3, 2007
43
(ANECDOTE) “NEWSVENDOR” STADIUM HOTDOG DEMAND
NORMAL SEASON
CONTENDER
44
Oct 3, 2007
(ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS
NORMAL SEASON PROBABILITY = ?
CONTENDER PROB = 1-?
45
Oct 3, 2007
(ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS
OVERALL SALES
46
Oct 3, 2007
(ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS
WHICH PROBS ARE ALEATORY
WHICH ARE EPISTEMIC?
NORMAL SEASON, CONTENDER PROBABILITIES
OR CONDITIONAL DEMAND DISTRIBUTIONS?
47
Oct 3, 2007
(ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS
DIFFERENCE BETWEEN IGNORANCE
AND APATHY?
48
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
WE’RE REALLY TALKING ABOUT
APPROPRIATE PERFORMANCE MEASURES
THIS IS DIFFICULT ENOUGH TO DO IN
DETERMINISTIC O.R. -- THE
UNCERTAINTY ASPECT ONLY MAKES
THINGS MORE “INTERESTING”
49
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
SUBMARINE SEARCH:
MINIMIZE EXPECTED TIME TO DETECT ?
MAXIMIZE PROB. {DETECT TIME ≤ Tcritical} ?
50
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
ALLOCATION OF POLICE PATROLS:
MINIMIZE EXPECTED TIME TO RESPOND ?
MINIMIZE VARIANCE OF RESPONSE TIME ?
51
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
QUALITY CONTROL AND 6-SIGMA
“TAGUCHI” LOSS FUNCTION
ESSENTIALLY QUADRATIC:
DECISION IS d, RANDOM VARIABLE IS X
2
LOSS = CONST. (d - x)
52
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
2
“TAGUCHI” LOSS FUNCTION C(d - x)
x
d
53
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
WITH “TAGUCHI” LOSS FUNCTION
BEST DECISION IS d* = E(X)
WHICH RESULTS IN
MINIMUM EXPECTED LOSS = CONST•VAR(X)
MINIMUM EXPECTED RISK = CONST•S.D.(X)
= CONST•SIGMA
54
Oct 3, 2007
d
POLICY
f(x|d)
X
CONSEQUENCE
UNCERTAINTY
(ANECDOTAL) CONCEPTION, PERCEPTION
AND CODIFICATION OF CONSEQUENCES
MORE REALISTIC MANUFACTURING LOSS FUNCTION
x
d
Oct 3, 2007
55
INTENSITY MODULATED RADIATION
TREATMENT (IMRT)
radiation beam
tumor
critical (healthy) tissue
56
Oct 3, 2007
typical 2-D slice of 3-D image
TUMOR
PAROTID
GLAND
SPINAL CORD
57
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
THE FUNDAMENTAL PROBLEM IN
IMRT
DETERMINE THE NUMBER, ANGLES AND INTENSITIES
OF THE BEAMLETS SO THAT
a) THE TUMOR RECEIVES A SUFFICIENT DOSE, BUT
b) CRITICAL TISSUES (E.G. NORMAL ORGANS) ARE
SPARED HIGH DOSES
58
Oct 3, 2007
CONFLICTING CONSEQUENCES
• want to have:
– at least a “critical dose” of radiation absorbed by the
tumor “target”
– as little radiation as possible absorbed by healthy tissue
• this is a mathematical programming problem, right?
min (radiation to healthy tissue)
s.t. (radiation to tumor)  critical dose
or
max (radiation to tumor)
s.t. (radiation to healthy tissue)  damaging dose
59
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
GRAPHICAL REPRESENTATION OF
CONSEQUENCES: DOSE-VOLUME HISTOGRAM
(“DVH”)
60
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
ADD UNCERTAINTY TO
DVH
61
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
NOTE SIMILARITY TO KUNREUTHER’S
REPRESENTATION
uncertainty in
Probability
uncertainty
in Loss
Probability
{loss > v}
95%
“mean” prob.
5%
v ($)
62
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
REMEMBER PRACTICE? (WHAT ACTUALLY
GETS DONE)
63
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
PRACTICE
CONSEQUENCE
PRACTICE
REMOVING SKUS FROM EOQ POLICIES
FACULTY RETIREMENT OPTIONS
CLASS ACTION SINKING FUND
SIMULATED ANNEALING AND IMRT
“X BAR” CONTROL CHART DESIGN
64
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
PRACTICE
CONSEQUENCE
HERE IS A FINAL CHALLENGE:
DURING THIS WORKSHOP, TRY TO
DISCOVER IMPLIED RESOLUTIONS
(USUALLY VIA ASSUMPTIONS)
TO THE INHERENTLY PROBLEMATIC
NATURE OF RISK
Conception, Perception, Policy, and Practce
65
Oct 3, 2007
CLICK TO HEAR NEXT SPEAKER
66
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
PRACTICE (UNLIKELY DERIVATIVES)
From the New York Times, 2/23/89 -- p. 1(!):
“The underlying rate of inflation is accelerating”
If X(t) = PRICE INDEX, then
INFLATION = X(t)
RATE of INFLATION = X(t)
“ ... is accelerating” ==> [X(t) > 0 ==> X(t) >0
From the NYT 2/4/02
“The increase in Chip Speed is Accelerating …”
[work it out …]
67
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(EVERYDAY) CONCEPTION, PERCEPTION
AND CODIFICATION OF UNCERTAINTY
“CRISP” VS. “AMBIGUOUS” PROBABILITIES
Building a prison in Berlin NH would produce a
revenue increase of $264,000/year (NYT 9/2)
68
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
INTERESTING CONTRAST IN USAGE
INTELLIGENCE COMMUNITY
“ANALYSIS”: GATHER INFORMATION ABOUT OPPONENT’S
INTENTIONS AND CAPABILITIES,
“ASSESSMENT”: USE THIS INFORMATION TO PRESENT A
STATEMENT OF THE CURRENT SITUATION
RISK AND DECISION COMMUNITY
“ASSESSMENT”: OBTAIN INFORMATION ABOUT UNCERTAINTY OF
EVENTS (AND ALSO CONSEQUENCE)
“ANALYSIS”: USE THIS INFORMATION AND COMBINE IT IN SUCH
A WAY THAT ONE CAN MAKE BETTER DECISIONS
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Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION AND
CODIFICATION OF POLICY
“MORAL HAZARD”?: SEEDING HURRICANES
•CONSEQUENCES = WIND SPEED
•SPEED NOW IS 70 MPH
•WITH NO SEEDING, FORECAST: 140 MPH AT LANDFALL
•WITH SEEDING, FORECAST: 100 MPH AT LANDFALL
•DECISION IS TO SEED ==> WIND IS 90 MPH AT
LANDFALL
•SEEDING “CLEARLY” INCREASED THE SPEED, SO SUE THE
GOVERNMENT
70
Oct 3, 2007
d
POLICY
f(x|d)
UNCERTAINTY
X
CONSEQUENCE
(ANECDOTAL) CONCEPTION, PERCEPTION AND
CODIFICATION OF POLICY
“MORAL HAZARD”
•DECISION MAKER DOES NOT SUFFER
CONSEQUENCES
•HURRICANE INSURANCE
•SUB-PRIME LENDING INSTITUTIONS
•“DONORCYCLES”
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Oct 3, 2007