#---------------------------------------------------------
# File:   MIT18_05S22_in-class24-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.
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#---------------------------------------------------------
Class 24 Bootstrap


Jerry
  Slide 1: Intro
  
  Slide 2: Announcements/Agenda (3 minutes)
     Exam comments: Class ave 90, std dev 9. Will publish results on gradescope soon. 
     Announcements/Agenda 3 minutes

  Slide 3: Empirical distribution (2 minutes)
     Example 2: the histogram is made with n = 100 samples
     
  Slide 4: Review of resampling (3 minutes)
  
  Slide 5: Bootstrap principle for the mean (3 minutes)
      Don't dwell: tell them they will get board practice for this
      
  Slide 6: Empirical percentile bootstrap CI (4 minutes)
      Don't dwell: tell them they will get board practice for this
       
  Slide 7: Empirical basic bootstrap CI  (1 minute)
      This is in notes, we won't do this in class.
      Just say words 'algebraic pivot'
      Will discuss that with parametric bootstrap
      Empirical Percentile CI is more important for us
      
  Slide 8: Which empirical is is best? (2 minutes)
     We'll emphasize the percentile bootstrap
     
  Slide 9: CONCEPT QUESTION (5 minutes)
     Emphasize can be used for any statistic
     
Jen
  Slide 10: BOARD QUESTION (Work: 10 minutes, discuss 6 minutes
     Median: Interpolation: How quantile() works: There are 8 values, the first is at quantile 0, the second is at quantile 1/7 etc. So the .1 quantile is .1/(1/7) of the way from the first element to the second. That is xbar^*_{0.1} = 2.83 + (.1/(1/7))*(4.00-2.83) = 2.83 + .7*(1.17) = 3.65

     Median is similar

  Slide 11: Percentile bootstrapping in R (4 minutes)
     Point out it's essentially 5 lines of working code
     
  Slide 12: Parametric bootstrap ( 4 minutes)
     Similar: generate the samples from parametrized distribution
          estimate variation -delta_start
          pivot to get confidence interval --like algebraic pivot for z CI etc
	  
  Slide 13: R code (4 minutes)
     **Quickly
     Same code except data generation line and use of delta_star
     Note theta_hat requires division by n since mean of binomial is n*theta
     Note pivot in last line
     
  Slide 14: BOARD QUESTION (Work: 10 minutes, Discussion 5 minutes)
    Discussion: (If time) show code from previous slide