On Monday this week we will discuss the meaning of conditional probabilities and how they differ from joint probabilities. We’ll also get some practice computing joint, marginal, and conditional probabilities from tables. On Wednesday we will discuss the law (or rule) of total probability and Simpsons paradox.

You will also have your first knowledge check this week, covering the syllabus. I will send a Canvas announcement when it is available.

In-class activities, case studies, exercises for this week

We will work on these in breakout rooms. I suggest having one person share their screen and serve as note-taker, or quickly sharing a Google doc so you can work together. All the activities will be a component of the homework you hand in next week.

Activity 1 (Monday): Come up with at least two examples of conditional probabilities that illustrate the asymmetry of conditional probability – that is, $P(A\mid B)\neq P(B\mid A)$ in general. No more than one should be from your readings.

Activity 2 (Monday): Work through the Berkeley case study on gender bias in graduate admissions

Activity 3 (Wednesday): Randomized response and the law of total probability. Optional related readings on randomized response and differential privacy:

• Wired article on Apple’s use of differential privacy
• Google’s use of randomized response in Chrome
• A lengthier take on both by an academic cryptographer (Matthew Green).

Activity 4 (Wednesday): Revisit this post from FiveThirtyEight I posted last week, about how they “check their work” (i.e., verify that their probabilistic forecasts are accurate and well-calibrated): How Good Are FiveThirtyEight Forecasts?. Answer the questions below:

a. Describe in your own words how a calibration plot is constructed. (The example calibration plot on that page is the one entitled “MLB games, 2016-2018”)

b. Why is a calibration plot a more meaningful assessment of a forecaster than simply checking whether the forecaster’s prediction of the most likely outcome actually occurred?

c. Using the dropdown list just under the title of the post, pick a forecast category and check out its calibration plot. From the calibration plot, does FiveThirtyEight seem to be doing a good job forecasting these kinds of events? When you hand in this assignment, include a screenshot of the plot you looked at.

Some reference materials used in class this week

You may find these links helpful for our activities; see also the material on the Week 1 post.

Monday:

• Probability and conditional probability (DSGI)

Wednesday:

• Simpson’s paradox and the rule of total probability (DSGI)

Readings, videos, and activities to do for next week

For Monday:

• Read Bayes Rule
• Watch this video from the author of your text: https://youtu.be/uPXz0_Vf2T4. You may skip the first ~4:20 minutes.

For Wednesday:

• Read Probability Models page 181-184 and the subsection “The normal distribution” on p 194-202

Exercises and other things due next week

Due next Wendesday, Feb 3:

• Complete Activities 1-4 above, if you haven’t already
• Complete these exercises: Exercises