#--------------------------------------------------------- # File: MIT18_05S22_in-class20-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 20 Bayes vs Frequentist Jerry Slide 1: Slide 2: Announcements/Agenda (2 minutes) Slide 3: Comparison of Bayes and Frequentist (6 minutes) Class discussion: good and bad aspects of requiring a full specification of the experiment. -- + avoid experimenter bias -- + plan carefully -- - not flexible -- - can lead to silly situations --see stopping rules Key point: Should not view NHST as proving something. It just gives evidence and suggests further experiments. Only with time and an overwhelming amount of accumulated evidence can we declare something proved.. Jen Slides 4: Concept question. (6 minutes) Significance is not total probability of error Slide 5: BOARD question STOP I: (work: 12 minutes, discussion 6 minutes) This is similar to a pset question. In discussion: Start with updating with conjugate priors: B(1,1) --> B(5,2) Then show them how we got this from the table. Remind them carefully that hypotheses are all of the form theta = some value. Jerry Slide 6 Board question STOP II: frequentist p values (work: 15 minutes, discussion: 6 minutes) They may find 2 and 3 confusing to set up. For experiment 2: Use a tree (missing in the solutions) Slides 7-9: Class 18 type one errors (6 minutes) The point is that the fraction of type one errors among all rejections, i.e. P(H0 | reject) can be anywhere from 0 to 1 depending on the prior. Jen Slide 10: Class 19 Board question: chi-square test for independence (work 10 minutes, discussion 5 minutes) There should be plenty of time. If not, we can just make sure each group gets through the problem. As always, the hard part is using H0 and the data to get the probabilities needed to compute expected counts.