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Sensitivity Analysis II
PAD824
Presented by Ignacio J. Martinez and Peter Otto
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Today‘s Presentation
• Clarification
• Traditional Process for Conducting Sensitivity
Analysis
• Parameters in Vensim
• Doing in Class Exercises
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Clarification
• Models often include exogenous parameters
or relations among variables about which our
knowledge is inadequate, thus we make
guesses
• SA is the process of determining which of
these guesses really matter, that is, we try to
determine whether a slight different guess
would make a significant difference in the
behavior of the model
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Types
• Numerical Sensitivity.- Changes the numbers of the
output of the simulation but not the behavioral
pattern.
• Behavioral Sensitivity.- Changes the numbers and
the behavioral pattern of the output of the simulation.
• Structural Sensitivity.- Changes the output when
changing the structure.
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Process for Conducting a
Sensitivity Analysis
• List the exogenous parameters and relations
about which we are making guesses
• Determine the possible range for each
parameter
• Pick the parameter that seems most likely to
be important, while holding everything else
constant, run the model under a full range of
different values for that parameter
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Outcome
• If model behavior changes significantly, the
model is sensitive to the selected parameter,
and we must reformulate the model to
eliminate the parameter, learn what the real
value for the parameter is, or lose confidence
in the model.
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Setting up a Sensitivity
Analysis in Vensim®
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Settings
• Default: Multivariate, causes all selected
constants to be changed together
• Univariate, if selected, causes the first
constant to be changed and then the next,
with the first constant set back to its normal
simulation value (useful option for doing a
series of Vector searches across parameters)
Note: If you enter only one parameter, Univariate and Multivariate searches are the same
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Settings
• Latin Hypercube (change together exhausting
axes ranges), if selected will cause a Latin
Hypercube search to occur. A Latin
Hypercube search is simply a mechanism to
ensure that the full range of each parameter
being varied is explored in the number of
simulations specified. This is desirable for big
models where each simulation takes a long
time.
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Distributions
• Default: Random Uniform (min, max), draws
from a uniform random distribution
• Random Normal (min, max, mean, standard
dev), draws a number from a normal
distribution with the specified mean and
standard deviation
• Vector (min, max, increment), generates a
sequence of numbers from min to max by
increment. This sequence is not random, but
uniformly increasing
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Running Sensitivity in
Vensim®
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Changing Settings and Results
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<BLM>
<BLFM>
Business labor
force multiplier
Business land
multiplier
BCN
Business
construction
Business
structures
Business
demolition
<AJM>
BDN
Area
<HLM>
Land fraction
occupied
Labor to
job ratio
Jobs
Housing land
multiplier
LPBS
LPH
Attractiveness from
jobs multiplier
Labor
force
JPBS
LPF
Population
Housing
Outmigration
Housing
demolition
Housing
construction
HCN
OMN
HDN
BN
Attractvieness from
housing multiplier
HS
<HAM>
IMN
Net births
Households to
housing ratio
DN
Housing
availability
multiplier
Inmigration
<AHM>
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Multivariate with
Random Uniform Distribution
sensi1
urban1
50%
75%
95%
Multivariate with
Random Normal Distribution
sensi2
50%
100%
75%
Population
600,000
Population
400,000
450,000
300,000
300,000
200,000
150,000
100,000
0
0
25
50
Time (year)
75
Sensitivity Run:
BCN = 0.01 – 0.2 (value in the model 0.07)
100
0
0
95%
25
100%
50
Time (year)
75
100
Sensitivity Run:
BCN = 0.01 – 0.2, Mean = 0.1,
Standard Deviation = 0.01
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Latin Hypercube with
Random Uniform Distribution
sensi3
50%
75%
95%
Latin Hypercube with
Random Normal Distribution
sensi4
50%
100%
75%
Population
600,000
Population
400,000
450,000
300,000
300,000
200,000
150,000
100,000
0
0
0
25
50
Time (year)
75
Sensitivity Run:
BCN = 0.01 – 0.2 (value in the model 0.07)
100
0
95%
25
100%
50
Time (year)
75
100
Sensitivity Run:
BCN = 0.01 – 0.2, Mean = 0.1,
Standard Deviation = 0.01
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Univariate with
Vector Distribution
sensi5
50%
75%
95%
Multivariate with
Random Normal Distribution
sensi2
50%
100%
75%
Population
600,000
Population
400,000
450,000
300,000
300,000
200,000
150,000
100,000
0
0
0
25
50
Time (year)
75
Sensitivity Run:
BCN = 0.01 – 0.2, Increment = 0.01
(value in the model 0.07)
100
0
95%
25
100%
50
Time (year)
75
100
Sensitivity Run:
BCN = 0.01 – 0.2, Mean = 0.1,
Standard Deviation = 0.01
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Sensitivity to a Table Function (A kind of Structural Sensitivity)
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Weight on A
<BLFM A>
<BLFM>
<BLFM B>
Business labor
force multiplier
Business
construction
Business
structures
Business
demolition
Jobs
BDN
Labor to
job ratio
Attractiveness from
jobs multiplier
Business
labor force = ("<BLFM A>"(Labor to job ratio)*Weight on A)
+("<BLFM B>"(Labor to job ratio)*(1-Weight on A))
multiplier
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sensi1
50%
75%
95%
100%
Business structures
6,000
4,500
3,000
1,500
0
0
25
Graph for Business structures
50
Time (year)
75
100
6,000
4,500
3,000
1,500
0
0
10
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Business structures : sensi2
Business structures : sensi1
Business structures : urban1
30
40
50
60
Time (year)
70
80
90
100
structure
structure
structure
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sensi1
50%
75%
95%
100%
Housing
100,000
75,000
50,000
25,000
0
sensi1
50%
75%
95%
0
25
50
Time (year)
75
100
100%
Population
400,000
300,000
200,000
100,000
0
0
25
50
Time (year)
75
100
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