# Week 4 — Inference (9/13–17)¶

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

## Revision Log¶

Thu, Sep. 16

updated quiz to reflect changed release/deadline

## 🧐 Content Overview¶

Element Length

🎥 Inference Intro

10m36s

🎥 Probability

13m46s

🎥 Joint and Conditional

11m50s

🎥 Continuous Probability

11m48s

📃 Notes on Probability

349 words

🎥 Distributions

9m24s

🎥 Sampling and the DGP

17m53s

🎥 Confidence

13m6s

📃 Having confidence in confindence intervals

225 words

🎥 The Bootstrap

7m26s

This week has 1h36m of video and 574 words of assigned readings. This week’s videos are available in a Panopto folder and as a podcast.

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.

• Week 3 Quiz on Monday, Sep. 20 at 12PM

## 📃 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 $$n$$.

## 📃 Confidence in Confidence¶

Read Having confidence in confidence intervals by Ellie Murray.

## 🚩 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.

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: