probabilistic scenario analysis institute for water resources 2009 charles yoe, phd...
TRANSCRIPT
Why Are Decisions Hard?
• Complex
• Inherent uncertainty
• Conflicting objectives
• Differences in perspectives, i.e., risk attitudes
• Scenarios can address these aspects
Know what q
uestions y
ou’re try
ing to answ
er.
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
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
Scenario Comparison
HUs Cost
Without condition 5,000 0
With condition Plan A
7,500 One Million
Change due Plan A
+2,500 +1,000,000
With condition Plan B
25,000 One billion
Change due Plan B
+20,000 +1,000,000,000
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
Some New Scenario Types
• As-planned scenario
• Failure scenarios
• Improvement scenarios
As-Planned Scenario
• Surprise free scenario--free of any failures
• Risk free scenario--every feature of system functions as planned—no exposure to hazard
TerroristAttack onInfrastructure
Plot Detected
As planned As planned As planned
Yes YesYes
No NoNo
AttackFoiled
StructureUndamaged
Successful Attack
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 “worst-case” scenario
• Corps “without condition”
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
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”
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
Methods of ComparisonRi
sk E
ffect
of I
nter
est
Baseline
Existing
Future No Action
Future with Option ABefore & AfterComparison
With & WithoutOption Comparison
Target Gap Analysis
Time
DSA Limits
• Limited number can be considered
• Likelihoods are difficult to estimate
• Cannot address full range of outcomes
Some Scenario Tools
• Event trees– Forward logic
• Fault trees– Backward logic
• Decision trees– Decision, chance, decision, chance
• Probability trees– All branches are probabilities
Event Tree
2.0% 0.02
48.5 48.5
Stall Occurs
10.0% 0.098
10.0 10.0
98.0% Delay Occurs
0 2.125
90.0% 0.882
1.3 1.3
Lockage
Yes
No
Yes
No
Tree Symbols
• Trees are composed of nodes and branches– Circles=>chance or probability nodes– Squares=>decision nodes– Triangles=>endpoints
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
Temporal Logical
57.1429% 26.6667%
80
35.7143% 16.6667%
50
46.6667% Private
140
7.1429% 3.3333%
300 10
Inadequate Maintenance
12.5% 6.6667%
20
31.25% 16.6667%
50
53.3333% Private
160
56.25% 30.0%
90
Bayes Theorem Example2
Yes
Locally constructed
Federal construction
Private
No
Private
Locally constructed
Federal construction
20.0% 6.6667%
20
33.3333% Chance
100
80.0% 26.6667%
300 80
Chance
50.0% 16.6667%
50
33.3333% Chance
100
50.0% 16.6667%
50
90.0% 30.0%
90
33.3333% Chance
100
10.0% 3.3333%
10
Bayes Theorem Example1
Private
Adequate Maintenance
Inadequate Maintenance
Locally constructed
Adequate Maintenance
Inadequate Maintenance
Federal construction
Adequate Maintenance
Inadequate Maintenance
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
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
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)
50.0% 12.5% HHH
50.0% Coin 3
HHT50.0% 12.5%
50.0% Coin 2
50.0% 12.5% HTH
50.0% Coin 3
50.0% 12.5% HTT
Coin 1
50.0% 12.5% THH
50.0% Coin 3
50.0% 12.5% THT
50.0% Coin 2
50.0% 12.5% TTH
50.0% Coin 3
50.0% 12.5% TTT
Three Coin Toss
Head
Tail
Head
Head
Tail
Tail
Head
Tail
Head
Head
Tail
Tail
Head
Tail
1. Identify all possible endpointsof interest.2. Collect relative endpoints to getdesired information.
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– Avoid temptation to
become enamored of one or a few endpoints early in the process
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 “as-planned” scenario
• Collect evidence to quantify model
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?
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
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
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.
Monte Carlo Simulation
0.00
0.08
0 10 20 30 40 0.0
0.4
5.0 8.8 12.5 16.3 20.0
X =
0.00
0.02
0 100 200 300 400
20 10
Simulation
Iteration
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)
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
