Sensitivity and Uncertainty Analysis and Optimization in GoldSim

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Sensitivity and Uncertainty Analysis and
Optimization in GoldSim
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Overview

• Uncertainty Analysis
• Sensitivity Analysis with Monte Carlo simulation
• Options to support uncertainty and sensitivity
  analysis when doing Monte Carlo simulation
• Screening realizations
• Saving distributions at multiple timepoints
• Sensitivity Analysis with deterministic
  simulations
• Optimization

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Uncertainty and Sensitivity Analysis

• Uncertainty analysis answers the question
• Which parameters is the uncertainty in the
  result most sensitive to
• Sensitivity analysis answers the question
• Which parameters is the result most sensitive
  to

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Example

• A Uniform(10,20)
• B Uniform(10,20)
• C Uniform(10,20)
• E Uniform(1,5)
• D Constant10

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Uncertainty Analysis in GoldSim

• GoldSim computes a correlation matrix
• Value (Pearson) correlation indicates a linear
  relationship
• Can capture non-linear relationships with rank
  (Spearman) correlation

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Example

• Run 1000 times
• For X, select Final Values Multivariate
  analysis
• Select a Stochastic
• Add all stochastics
• Variable correlations

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Sensitivity Analysis in GoldSim Using Monte Carlo
Simulation

• Coefficient of determination  This coefficient
  varies between 0 and 1, and represents the
  fraction of the total variance in the result that
  can be explained based on a linear (regression)
  relationship to the input variables (i.e., Result
  aX bY cZ ). The closer this value is to
  1, the better that the relationship between the
  result and the variables can be explained with a
  linear model.
• SRC (Standardized Regression Coefficient)
  Standardized regression coefficients range
  between -1 and 1 and provide a normalized measure
  of the linear relationship between variables and
  the result.  They are the regression coefficients
  found when all of the variables (and the result)
  are transformed and expressed in terms of the
  number of standard deviations away from their
  mean. GoldSims formulation is based on Iman et
  al (1985).

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Sensitivity Analysis in GoldSim Using Monte Carlo
Simulation

• Partial Correlation Coefficient Partial
  correlation coefficients vary between -1 and 1,
  and reflect the extent to which there is a linear
  relationship between the selected result and an
  input variable, after removing the effects of any
  linear relationships between the other input
  variables and both the result and the input
  variable in question.  For systems where some of
  the input variables may be correlated, the
  partial correlation coefficients represent the
  unique contribution of each input to the
  result.  GoldSims formulation is based on Iman
  et al (1985).
• Importance Measure  This measure varies between
  0 and 1, and represents the fraction of the
  results  variance that is explained by the
  variable. This measure is useful in identifying
  nonlinear, non-monotonic relationships between an
  input variable and the result (which conventional
  correlation coefficients may not reveal). The
  importance measure is a normalized version of a
  measure discussed in Saltelli and Tarantola
  (2002).

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Example

• Run 1000 times
• For X, select Final Values Multivariate
  analysis
• Select a Stochastic
• Add all stochastics
• Sensitivity analysis

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Example

• Run 1000 times
• For X, select Final Values Multivariate
  analysis
• Select a Stochastic
• Add all stochastics
• 2D Plot

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Sensitivity Analysis in GoldSim Using
Deterministic Simulation

• Hold all variables at a constant value (typically
  mean), and then vary each parameter over a
  specified range
• X-Y function charts
• Tornado charts
• Visually indicates sensitivity

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Example

• From main menu, select Run Sensitivity
  Analysis
• Add all Stochastics
• Add D
• Select ranges
• Carry out analyses

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Optimization

• Optimize (minimize or maximize) an objective
  function by
• Adjusting optimization variables
• Meeting a Required Condition
• Uses Boxs Complex method to solve

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Optimization

• Specify Objective Function
• Specify Required Condition
• Specify Optimization Variables
• Example

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Optimization

• Common application calibration
• Example the stock market