Delivering Integrated, Sustainable,
Water Resources Solutions
Institute for Water Resources
2010
Probabilistic Scenario Analysis
Charles Yoe, PhD
cyoe1@verizon.net
“ Building Strong “
Delivering Integrated, Sustainable,
Water Resources Solutions
Why Are Decisions Hard?
•
•
•
•
Complex
Inherent uncertainty
Conflicting objectives
Differences in perspectives, i.e., risk
attitudes
• Scenarios can address these aspects
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Bundle of Tools and Techniques
• Probabilistic scenario analysis is not
scenario planning
– Two different techniques for addressing
uncertainty
• HEC FDA, Beach FX, Harbor Sim are all
examples of PSA
• We’ll use event trees to better understand
the idea
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Scenarios
• Literally an outline
or synopsis of a
play
• Scenarios can be
used to describe
present
• Most often used to
describe possible
futures
• Corps scenarios
– Without
condition(s)
– With conditions
– Base year
– Existing condition
– Failure
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Scenario Comparison
HUs
Cost
Without condition
5,000
0
With condition
Plan A
Change due Plan
A
With condition
Plan B
Change due Plan
B
7,500
One Million
+2,500
+1,000,000
25,000
One billion
+20,000
+1,000,000,000
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Scenario Analysis
• Deterministic scenario analysis
– Examine specific scenarios
– Organize and simplify avalanche of data into
limited number of possible future states of the
study area or infrastructure
• Probabilistic scenario analysis
– Characterize range of potential futures and
their likelihoods
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Some New Scenario Types
• As-planned scenario
• Failure scenarios
• Improvement scenarios
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As-Planned Scenario
• Surprise free scenario--free of any failures
• Risk free scenario--every feature of
system functions as planned—no
exposure to hazard
As planned
Yes
Yes
Terrorist
Attack on
Infrastructure
As planned
No
Plot
Detected
As planned
Yes
No
Attack
Foiled
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No
Structure
Undamaged
Successful Attack
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Failure Scenarios
• Tell story how various elements of system
might interact under certain conditions
• Challenge notion system will function as
planned
• One common failure scenarios is “worstcase” scenario
• Corps “without condition”
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Worst-Case Scenario
• Introduces conservatism into analysis--a
deliberate error
• Given any worst case an even worse case
can, paradoxically, be defined
• Possible is not necessarily probable
• Failure in the better than worst-case world
is still possible
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Improvement Scenarios
• Risk analysis often results in new risk
management options to reduce risks
• Develop an improvement scenario for
each management option considered
– Used to evaluate risk management options
– Used to select the best option.
• Corps “with condition”
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Scenario Comparisons
• Most likely future condition absent risk
management,
– Status quo or "without condition“--basic failure
scenario
– Every new risk management option evaluated
against this
• Most likely future condition with specific risk
management option
– “With condition“--improvement scenarios
– Each option has its own unique with condition
• Compare "with" and "without" conditions for
each new risk management option
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Methods of Comparison
Risk Effect of Interest
With & Without
Option Comparison
Baseline
Before & After
Comparison
Existing
Target
Gap Analysis
Time
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DSA Limits
• Limited number can be considered
• Likelihoods are difficult to estimate
• Cannot address full range of outcomes
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Some Scenario Tools
• Event trees
– Forward logic
• Fault trees
– Backward logic
• Decision trees
– Decision, chance, decision, chance
• Probability trees
– All branches are probabilities
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Event Tree
2.0%
48.5
Stall Occurs
Yes
Lockage
0.02
48.5
10.0%
10.0
Delay Occurs
2.125
90.0%
No
1.3
Yes
No
98.0%
0
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0.098
10.0
0.882
1.3
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Tree Symbols
• Trees are composed of nodes and
branches
– Circles=>chance or probability nodes
– Squares=>decision nodes
– Triangles=>endpoints
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Tree Time
• Nodes represent points in logical time
– Decision node=>time when decision maker makes
decision
– Chance node=>time when result of uncertain
event becomes known
– Endpoint=>time when process is ended or
problem is resolved
• Time (logic) flows from left to right
– Branches leading into a node have already
occurred
– Branches leading out of or following a node have
not occurred yet
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Temporal Logical
Adequate Maintenance
57.1429%
Private
26.6667%
35.7143%
33.3333%
Private
16.6667%
46.6667%
300
Bayes Theorem Example2
Bayes Theorem Example1
Federal construction
Inadequate Maintenance
300
Private
140
7.1429%
Chance
100
50
Yes
80.0%
26.6667%
80
Chance
3.3333%
10
Adequate Maintenance
50.0%
16.6667%
50
Inadequate Maintenance
Locally constructed
12.5%
Private
33.3333%
31.25%
Inadequate Maintenance
Adequate Maintenance
16.6667%
90.0%
30.0%
90
Private
160
Federal construction
Federal construction
50.0%
50
16.6667%
50
53.3333%
Chance
100
6.6667%
20
Locally constructed
No
6.6667%
20
80
Locally constructed
20.0%
56.25%
30.0%
90
33.3333%
Chance
100
Inadequate Maintenance
10.0%
10
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3.3333%
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Branches
• Branches from chance node are possible
outcomes of uncertain events
– You have no control over these
• Branches from decision node are the
possible decisions that can be made
– You can control these
• Branches have values
– Probabilities are listed on top
• They are conditional on all preceding events!
• They must sum to one.
– Quantitative values are listed on bottom
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Constructing Trees (cont.)
• Use Yes and No branches when possible
– Not always possible or desirable
• Separates elements of problem in
structured way
• Different trees yield different insights
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Endpoints
• Mutually exclusive
• Collectively exhaustive
• Endpoints define sample space, i.e., all
possible outcomes of interest
• Value/units of measure
– Be consistent throughout model
• Can be multiple objectives (payoff matrix)
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1. Identify all possible endpoints
of interest.
2. Collect relative endpoints to get
desired information.
50.0%
Head
12.5%
HHH
Coin 3
HHT
Tail
50.0%
Head
50.0%
Head
50.0%
12.5%
50.0%
12.5%
HTH
50.0%
12.5%
HTT
50.0%
12.5%
THH
50.0%
12.5%
THT
50.0%
12.5%
TTH
50.0%
12.5%
TTT
Coin 2
Head
50.0%
Tail
Coin 3
Tail
Coin 1
Three Coin Toss
Head
50.0%
Head
Coin 3
Tail
Tail
50.0%
Coin 2
Head
Tail
50.0%
Coin 3
Tail
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Constructing Trees Rapidly
• Know the question
• Know relevant
endpoints
• Keep it simple
– Rainfall  Dam
failure
– Does that answer
your questions?
• Don’t attempt
complex model all at
once
• Rapid iteration
prototyping
• Make sure all
possible endpoints
and important paths
are included
• Analyze pros and
cons of details only
after considering
alternatives
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– Avoid temptation to
become enamored of
one or a few
endpoints early in
the process
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5 Steps to Event Tree
• ID the problem
– Write down the question(s) model is to answer
– Endpoints define sample space
• ID major factors/issues to address—
details!
• ID alternatives for each factor/issue
• Construct tree portraying all important
alternative scenarios, start with “asplanned” scenario
• Collect evidence to quantify model
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How Much Detail?
• You need all possible relevant endpoints
and all important pathways to those
endpoints
• How much detail in the pathways is the
question=>more detail=more pathways
• Will more complex model change
outcome values that much?
• Will extra detail mean extra insight?
• Do you want a model enabling a good
choice or a model of reality?
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Many Scenarios
• Because of variability and uncertainty
there are many possible scenarios
• It is not possible to describe them all
• Some may be important to the decision
process
• Probability can be added to a scenario in a
variety of ways
– Monte Carlo process
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Monte Carlo Simulation
• Simulation model that
uses the Monte Carlo
process
• Deterministic values
replaced by
distributions
• Values randomly
generated for each
probabilistic variable
& calculations
completed
• Process repeated
desired # times
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Some Language
• Simulation-technique for
calculating a
model output value
many times with
different input
values. Purpose is
to get complete
range of all
possible
scenarios.
• Iteration--one
recalculation of the
model during a
simulation.
Uncertain
variables are
sampled once
during each
iteration according
to their probability
distributions.
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Monte Carlo Simulation
0.08
0.4
=
X
0.00
0
10
20
20
30
0.0
5.0
40
8.8
12.5 16.3
10
0.02
Simulation
0.00
0
Iteration
100
200
300
400
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20.0
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How Many Iterations?
•
•
•
•
Means often stabilize quickly (102)
Estimating probabilities of outcomes (103)
Defining tails of output distribution (104)
If extreme events are important (105)
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Take Away Points
• PSA is a class of tools that relies on
– Scenarios
– Probabilities
• PSA’s take many forms
– Most IWR tools are PSA’s
– Event trees & fault trees
– Process models & Flow diagrams
• PSA’s are very powerful and useful tools
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Questions?
Charles Yoe, Ph.D.
cyoe1@verizon.net
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