Simulation: Modeling Uncertainty with Monte Carlo

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Simulation Modeling Uncertainty with Monte Carlo

• 12-706 / 19-702

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Notes on Uncertainty

• Uncertainty is inherent in everything we do
• There are no right answers
• Our goal
• Understand and model it --gt make better
  decisions
• We internalize uncertainty using ranges or
  distributions of our inputs
• This is a computationally intensive idea

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First Reading PDFs CDFs

• What information can we get from simply looking
  at a PDF or CDF?

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Monte Carlo History

• Not a new idea Statistical sampling
• Fermi, Ulam, working on Manhattan Project in
  1940s
• Developed method for doing many iterations of
  picking inputs to generate a distribution of
  answers
• Finally have fast computers
• Later, named after Monte Carlo
• (famous for gambling)

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Monte Carlo Method

• Monte Carlo analysis 3 steps
• Specify probability distributions in place of
  constants/variables
• Trial by random draws
• Repeat for many trials
• Doing Monte Carlo does not give you the answer!
• Produces some distribution of results
• Law of large numbers says convergence
• hundreds or thousands

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Monte Carlo Simulations

• Well use _at_RISK (part of DecisionTools Suite)
• Adds special probability functions to Excel
• Excel has some, but these are better
• Bunch of distributions Binomial, Discrete,
  Exponential, Normal, Poisson, Triangular, Uniform
  (more on these in a moment)
• Has a lot of nice post-simulation analysis
• Statistics, graphs, reports
• Again, these are not answers

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Lets Test It

• Look at test-montecarlo-07.xls
• Can random draws from a normal distribution give
  us the parameters of that distribution?
• See Excel formula to do so (and link on web page
  for more)
• What difference does 10, 100, 1000 or 10000
  trials make?
• Dont worry about mechanics yet tutorial on
  Friday

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Lets talk about distributions

• You (should) have seen these before
• Uniform, Normal, Triangular, Binomial, Discrete,
  Poisson, possibly Exponential, Lognormal
• Important part of MC is picking correct
  distributions parameters
• Be careful of over-thinking this choice!

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Distribution Examples?
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Homework 2 Grades
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Examples for other distributions

• Uniform
• Normal
• Triangular
• Binomial
• Discrete
• Poisson
• Exponential
• Lognormal

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Examples Using Monte Carlo

• Using examples familiar to us
• Instead of point estimates, use probabilistic
  functions
• Pick up penny?
• Homework 2 Dam, revisited

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Lets walk through a Monte Carlo problem -
distribution by distrubtion
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Wrap Up

• We have much better models - and knowledge of our
  results now
• Important take away messages
• Dont introduce unnecessary uncertainty with your
  input choices
• Monte Carlo doesnt give you the answer
• Interpreting output (PDFs/CDFs) gives you an
  answer