#---------------------------------------------------------
# File:   MIT18_05S22_in-class11-script.txt
# Author: Jeremy Orloff
#
# MIT OpenCourseWare: https://ocw.mit.edu
# 18.05 Introduction to Probability and Statistics
# Spring 2022
# For information about citing these materials or our Terms of Use, visit:
# https://ocw.mit.edu/terms.
#
#---------------------------------------------------------
Class 11  Bayesian updating with discrete priors

GET DICE OUT

NOTE: 3 board questions today. If time, do fourth introducing topic 12

Jerry
  Slide 1: XKCD
    Challenge: give a technical explanation of comic
    (Just issue the challenge. Key: P(shell and near ocean)/P(shell) \approx 1
    GOAL UNDERSTAND BAYESIAN UPDATE TABLES COMPLETELY

 Slide 2: Announcements/Agenda (2 minute)

 Slide 3: CLICKER QUESTION (5 minutes)
    PAUSED SLIDE
    Which treatment?
    Main point: Base rates matter
    If we know the base rates this is a probability problem. If not, it's a statistics problem.

 Slide 4: Which die is it demo (6 minutes)
    PAUSED SLIDE 
    Do the demo of rolling the die
       Make sure to choose the 4-sided die: roll e.g. 3, 2, 3, 3
    Go to second part.
    Main point: base rates matter

 Slide 5: Terminology, trees, tables (7 minutes)
    We need to reinforce many times what is meant by hypotheses and how they are used.
   
 Slide 6: BOARD QUESTION Screening tests (Work 10 minutes, discuss 5 minutes)
    This is in the reading
    Don't expect it to be easy for many students
    We should be quick to intervene and help groups get going.
    Bring together to discuss solution

 Slide 7-10 BOARD QUESTION Dice (Work 12 minutes, discuss 6 minutes)
    They should do much better at this one
    Slides 8-10 have the update tables --go through at most 1 carefully
    Amount of writing and detail given should depend on how they did.

Jen
 Slides 11-12 (5 minutes)
    Iterated updates example
    Key points 
      posterior to data 1 = prior to data 2
      Can do in either order or all together --same answer
      no need to normalize until the end

 Slide 13-15 BOARD QUESTION Iterated update (Work 10 minutes, discuss 6 minutes)
      Problem on slide 13
      Solution on slides 14-15
      Gauge how much to say.

 The next slides are just in case there's time. They introduce class 12

 Slide 16 BOARD QUESTION predictive probabilities
     This is just to foreshadow class 12.
     Only do if time
 Slide 17 
     Solution