Week 4 — Inference
Introduction
Probability
Joint and Conditional Probability
Continuous Probability
Week 4 Quiz
Submit the Week 4 quiz by Monday night.
Distributions
Resources
- The Probability Distribution notebook
- Wikipedia has a good list of probability distributions
Sampling and the Data Generation Process
Resources
Confidence
Confidence in Confidence
Read Having confidence in confidence intervals by Ellie Murray.
The Bootstrap
Testing Hypotheses
Cartoon
Read XKCD #882: Significant.
This is called p-hacking: running tests until we find one that is significant.
Penguin Inference
The Penguin Inference notebook shows confidence intervals and hypothesis tests on the penguin data.
Further Reading
If you want to dive more deeply into probability theory, Michael Betancourt's case studies are rather mathematically dense but quite good:
- Probability Theory (For Scientists and Engineers)
- Conditional Probability
- Product Placement (probability over product spaces)
For a book:
- Introduction to Probability by Grinstead and Snell
- An Introduction to Probability and Simulation - a hands-on online book using Python simulations
Extra Reading (Philosophy)
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Abandon Statistical Significance, by McShane, Gal, Gelman, Robert, and Tackett. While the title is provocative, this article is not advocating against computing statistical significance measures. It advocates using them as one piece of evidence among many, instead of as an end-of-the-story bright-line rule for establishing discovery.
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Interpretations of Probability. I primarily operate from somewhere in the subjective school.
Assignment 2
Assignment 2 is due on September 27.