#--------------------------------------------------------- # File: MIT18_05S22_in-class13-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. # #--------------------------------------------------------- Continuous priors Jerry Slide 1: Slide 2: Announcements/Agenda (2 minutes) From last time: CSI blood types (5 minutes) Show slide Go through solution Jen Slide 3: Examples of continuous range of hypotheses (2 minutes) Slide 4: Example review (5 minutes) Use notatation theta_.25 etc See solutions: go through this carefully **Point out how each piece of Bayes formula is in the tables Point out P(data) is the prior predictive prob. of the data Slides 5-9: More coins --leading to need for some notation (2 minutes) Slide 10: Notation to eliminate the number of rows (3 minutes) Slide 11: Big and little letters (2 minutes) Slide 12: f(x)dx = probability (1 minute) This is just a reminder. Present it that way. Don't go into any detail. Slide 13: Coin as example of continuous hypotheses (2 minutes) Point out that the coin is our way of describing a situation with success or failure, e.g. medical treatment Slide 14: Law of total probability (2 minutes) Slide 15: TABLE QUESTION: (work 6 minutes, discussion 5 minutes) Total probability Discussion Slide 16: CONCEPT QUESTION (4 minutes) discrete or continuous Jerry Slide 17: Bayes theorem with densities (2 minutes) Slide 18: Bayesian update tables. (3 minutes) Slide 19: BOARD QUESTION 1, Bayesian update (work 8 minutes, discussion 5 minutes) Students should get this. So the discussion should center on showing how to present the solution carefully and efficiently. I'll have the graphs in the slides we present in class. (Students can find them in the posted solutions.) Slide 20: BOARD QUESTION 2, Bayesian update (work 8 minutes, discussion 5 minutes) The point here is that once you have the likelihood it's just a routine, if tedious, computation to get the posterior. This is preliminary to discussing conjugate priors. Slide 21: Plots for BQ2 This shows that the data is making us more certain of the value of theta ONLY IF TIME Jerry Slide 22 Beta distribution This is looking forward to class 14 --define --Show applet