Week 4 — Inference (9/12–16)#

These are the learning outcomes for the week:

  • Understand the elements of probability

  • Interpret and write conditional probabilities for events

  • Understand the key relationships between discrete and continuous probability

  • Compute and interpret a confidence interval

🧐 Content Overview#

Element Length

🎥 Inference Intro


🎥 Probability


🎥 Joint and Conditional


🎥 Continuous Probability


📃 Notes on Probability

349 words

🎥 Distributions


🎥 Sampling and the DGP


🎥 Confidence


📃 Having confidence in confindence intervals

225 words

🎥 The Bootstrap


This week has 1h32m of video and 574 words of assigned readings. This week’s videos are available in a Panopto folder.

This week is at the upper end for total video of any week in the course, and also has some of the trickier concepts. The next week — Week 5 — is significantly lighter in terms of new material, and we’ll take a step back to try to solidify the things we’ve learned so far in the class before proceeding to Week 6.

📅 Deadlines#

  • Week 4 Quiz on 9/15 at 8AM

🎥 Introduction#

🎥 Probability#

🎥 Joint and Conditional Probability#

🎥 Continuous Probability#

📃 Notes on Probability#

My notes on probability provide a linear, summary treatment of the concepts of probability that we have discussed, along with pointers for further reading.

I expect you will likely need to return to the probability material as we progress through the semester and use it more and more. A few particularly important things you need to be able to understand are:

  • What does a probability \(\P[A]\) mean?

  • What does a conditional probability \(\P[A|B]\) mean?

  • What does a joint probability \(\P[A,B]\) mean?

  • What does an expected value \(\E[X]\) mean?

In my teaching of later material, I use probability notation a lot, as it is a concise but (relatively) unambiguous way to communicate many important concepts. Also, while the philosophy of probability is largely out of scope of this course, my own philosophy of probability (roughly, instrumentalism) means that I use probabilities to describe things that a strict philosophical frequentist likely would not. One of the most practical implications for this class is that I will use conditional probability as a shorthand for fractions of events or observations:

\[ \P[A|B] = \frac{|A \cap B|}{|B|} \]

You can derive this fraction yourself from \(\P[A] = \frac{|A|}{n}\), where \(n\) is the total number of possible events or observations, and cancelling the \(n\).

🎥 📓 Distributions#


🎥 Sampling and the Data Generation Process#


🎥 Confidence#

This video introduces confidence intervals.

📃 Confidence in Confidence#

Read Having confidence in confidence intervals by Ellie Murray.

🎥 The Bootstrap#

🚩 Week 4 Quiz#

The Week 4 quiz is on Canvas, and is due at 12pm (noon) on Monday, Sep. 20.

📓 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:

For a book:

📚 Extra Reading (Philosophy)#

  • Moving to a World Beyond “p < 0.05”, by Wasserstein, Schirm, and Lazar.

  • 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.

  • Interpretations of Probability. I primarily operate from somewhere in the subjective school, with a strong dose of instrumentalism.

📩 Assignment 2#

Assignment 2 is due on 9/25.