1 / 11

Bayes' Rule and Probability Relationships

Learn how Bayes' Rule and probability relationships work in various scenarios, such as AIDS, Arnold supporter demographics, and randomized response techniques. Practice calculations and apply the Law of Total Probability.

carlettar
Download Presentation

Bayes' Rule and Probability Relationships

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Stat 321 – Day 9 Bayes’ Rule

  2. Last Time • Multiplication Rule • P(A  B) = P(A|B)P(B) or P(B|A)P(A) • If the events are independent, simplifies to P(A  B) = P(A)P(B) • Can use this relationship to numerically check for independence • AIDS Problem • P(AIDS|+) = P(+  AIDS)/P(+) = P(+|AIDS)P(AIDS)/P(+) How do we find P(+) when we know P(+|AIDS), P(+|no AIDS)?

  3. Day 8 Example 1

  4. Day 9 Example 1 • Slightly different question, given I have an Arnold supporter, what is the probability the person is white? • P(white|A) = P(white  A)/P(A) Law of Total Probability P(A|white)P(white)

  5. Example 1: Governator Votes .364 .0102 .0558 .0222 .4522 P(W|A) = P(W  A)/P(A) = .364/.4522 = .805 > .7 .70 .06 .18 .06 1.00

  6. Example 2: SPAM filters

  7. Example 3: Shadyside case • Defendant has same genetic markers and only .32% of male population has these markers, how would you “update” the probability of guilt for this defendant? • Want P(G|E) • Know P(E|G) = 1, P(E|G’) = .0032 • P(G|E) = P(G)/[P(G)+.0032(1-P(G))

  8. Example 2: Randomized Response • Technique for asking sensitive questions • Randomly decide which question respondents will answer: sensitive or boring • Work backwards with probability rules to estimate proportions for sensitive question

  9. Example 2: Randomized Response • Flip fair coin • Heads: answer sensitive question • Tails: answer boring question=“does your home phone number end in even digit?” • Determine proportion of “yeses” • Define events • Y=“response is yes” • S=“respondent answered sensitive question”

  10. Example 2: Randomized Response • Respondents are ensured confidentiality • Can still obtain estimate for P(Y|S)

  11. For Monday • HW 3 due Tuesday • Check out review sheet online this weekend • (Today’s handout – Day 9 - online has a Ch. 2 summary)

More Related