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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
• 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
• 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
• 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
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