Simulating

September 23 + 25, 2024

Jo Hardin

Agenda 9/23/24

Why simulate?
What makes a good simulation?
Simulating to calculate probabilities

Small simulation example

1 / 70

Simulating September 23 + 25, 2024 Jo Hardin

Simulating
Agenda 9/23/24
Goals of Simulating Complicated Models
Aside: a few R functions (ifelse())
Aside: a few R functions (case_when())
Aside: a few R functions (sample())
Aside: a few R functions (set.seed())
Why?
Monte Carlo from a population to…
Small simulation example
Sally & Joan
Simulate their meeting
Results
Visualizing the meet up
Simulation best practices
Bigger simulation example
Thoughts on simulating
Roulette
Design the simulation
Step 1: create a roulette wheel
Step 2: spin the wheel
Step 3: update the money
Step 4: keep spinning (function first)
Aside: the accumulate() function
Step 4: run multiple times
Step 4: another function
Step 5: Repeat many times
Step 6: Wrangle the output
Step 6: Wrangle the output
Without magic numbers
Agenda 9/25/24
Modeling
Bias in a model
Goal for admitting students
Plan for accepting students
Flaw in the plan …
What is really different?
Key aspect:
Let’s see what happens …
Two models:
New data
New data
TWO models doesn’t seem right????
How do the error rates change?
What did we learn?
Simulate?
Presidential election
Presidential election
Election Data
Election model
Function to determine who wins
Running the function many times
Caveats
Sensitivity of assumptions
t-test with Poisson data
Non-normal data
t-test function
t-test 10 times
t-test many times
Sensitivity of CI to tech conditions
Plot of data
Capture the slope parameter?
Running a linear model
What happens to the CI of coefficients in repeated samples? (eq var)
Sensitivity of CI to tech conditions
Plot of data
What happens to the CI of coefficients in repeated samples? (uneq var)
Equal variance: type I error?
Unequal variance: type I error?
References