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Simulation: Modeling Uncertainty with Monte Carlo

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There are no right answers. Our goal: Understand and model it -- make better decisions ... Homework 2 Dam, revisited. Examples Using Monte Carlo. 13 ... – PowerPoint PPT presentation

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Title: Simulation: Modeling Uncertainty with Monte Carlo


1
Simulation Modeling Uncertainty with Monte Carlo
  • 12-706 / 19-702

2
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

3
First Reading PDFs CDFs
  • What information can we get from simply looking
    at a PDF or CDF?

4
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)

5
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

6
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

7
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

8
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!

9
Distribution Examples?
10
Homework 2 Grades
11
Examples for other distributions
  • Uniform
  • Normal
  • Triangular
  • Binomial
  • Discrete
  • Poisson
  • Exponential
  • Lognormal

12
Examples Using Monte Carlo
  • Using examples familiar to us
  • Instead of point estimates, use probabilistic
    functions
  • Pick up penny?
  • Homework 2 Dam, revisited

13
Lets walk through a Monte Carlo problem -
distribution by distrubtion
14
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
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