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# File:   MIT18_05S22_in-class12-script.txt
# Author: Jeremy Orloff
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# MIT OpenCourseWare: https://ocw.mit.edu
# 18.05 Introduction to Probability and Statistics
# Spring 2022
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# https://ocw.mit.edu/terms.
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Class 12: Prediction and Odds

Jen
  Slide 1: 

  Slide 2: Announcements/Agenda (2 minutes)

  Slide 3: Probabilistic prediction ( 2 minutes)
    Basically just read the slide

  Slides 4-5: Words of estimative probability (3 minutes)
     This is a small digression
     Main point: for policy making translate numbers to words
     BUT use words with a clear meaning.
     Avoid vague statements like: might, could, possibly.
     NOTE: the Bin Laden memo says 'determined to strike in US'

  Slide 6: Predictive probabilities (3 minutes)
     We saw this on Tuesday.
     Main point: make clear that we now use prior and posterior in two contexts.

  Slide 7: CLICKER question  3 Coins (4 minutes)
     Guess the predictive probability 
     Discussion: no calculation --why does the data move the prior towards
     the .5 coin
     This is just a warm up for the board question

  Slide 8. BOARD question (Work 10 minutes, discussion 5 minutes)
     Compute the predictive probability for 3 coins
     If every group got it, we'll skip the discussion
     If not, use one of group's work

  Slide 9: CLICKER question (4 minutes)
     Order doesn't matter
     Can use one of the update tables in student work to see the factor of 5 choose 1 won't change the posterior
     Avoid the temptation to repeat the explanation. It doesn’t work for this type of calculation. Tell them to ask us for clarification during the next board question

Jerry
  Slide 10:  Odds summary (2 minutes)
     Definition of odds.
     Point out the key formula. Don't try to prove it here. 
     We discuss it on the next slides

  Slide 11:  Odds examples (2 minutes)
     Highlight P(E) \approx O(E) if E is rare

  Slide 12 Marfan prior and posterior probability (3 minutes)
     We can point out the prior and likelihood values in the table.
     The Bayes numerator and posterior are just the usual arithmetic
     Point out that the posterior probability of M is still small, but
     a factor of 10 larger than the prior.

  Slides 13-14: Marfan prior and posterior odds (4 minutes)
     Slide 13: Everything is on the slide. But I think it's still worth writing the entire posterior odds equation and explaining each step. 
     Slide 14: With the formula from 13 on the board you can circle the Bayes factor and the prior odds. 
     Be sure to use the term likelihood ratio also

  Slide 15 BOARD question: screening, (Work 8 minutes, discussion 5 minutes)
     This should be relatively easy for them. 
     Discussion 
      Probably no need to redo the calculation
      Fast calculation: True positive rate \approx 1. False pos. rate = 0.05
      --> likelihood ratio \approx 20. 
     Prior prob = 0.005 is small, so prior odds \approx 0.005
     So posterior odds \approx 20\time 0.005 = 0.1  
     (4) The evidence is strong, but not conclusive

  Slide 16,17  BOARD question CSI blood types (Work 10 min., discussion 5 min.)
     Show hint slide 17 while they work
     Discussion
       The tricky part is getting the likelihoods. 
       Look at solutions: it's easy to miss the factor of 2 in the denominator 

PROBABLY WON'T GET BEYOND HERE
  Slide 18 Updating again and again (3 minutes)
     Do this if more than 5 minutes left else skip to slide 19
     Do not try to explain the independence. If anyone asks we can go through it after class. (We have already assumed this when we did repeated updating in class 11)

  Slide 19 Legal thoughts (3 minutes)
     Interesting to poll peoples instinctive reaction to this.
      less than 5 minutes left

  Slide 20 Marfans more symptoms (3 minutes) 
     Repeated updating example