 Challenge question
 Intro To Probability And Bayes Nets
 Probability / Coin Flip
 Dependence
 quiz: Weather
 Bayes Rule
Week 6 Announcement
This week you should watch Lesson 5, Probability, and read Chapter 13 in AIMA (Russell & Norvig). Assignment 3: Bayes Nets Sampling
Challenge question
 P(x) is the probability of the disease without other constraints

P(Y) is calculated P(Y ~X)P(~X) + P(Y X)P(X)
Intro To Probability And Bayes Nets
 in the above example, we have random variables represents events which are connected by arrows to describe the relationships.
 the arrows indicate that the child nodes are influenced by their parents, and the influence can be a deterministic or probabilistic way.
 Bayes net is a compact representation of the distribution of the large probability distribution of all the variables.
 With Bayes net, we can specify the distribution, observe certain variables and compute probabilities of unobserved variables.
outline
Probability / Coin Flip
 P(T) = 1  P(H)
 since H and T are independent events, P(H,H,H) = P(H) x P(H) x P(H)
 remember, P(H) and P(T) are independent
Summary
Dependence
quiz: Weather
 complementary rule applies for the first 2 quiz questions.
 dependence rule applies to the calculation of P(D2 = Sunny) and P(D3 = Sunny)

P(D2 = Sunny) = P(D2 = Sunny D1 = Sunny) x P(D1 = Sunny) + P(D2 = Sunny D1 = Rainy) x P(D1 = Rainy) 
Simillarly, * P(D3 = Sunny) = P(D3 = Sunny D2 = Sunny) x P(D2 = Sunny) + P(D3 = Sunny D2 = Rainy) x P(D2 = Rainy)
Quiz: Cancer
 joint probability of a and b is P(a, b) = P(a) x P(b)

P(C +) = P( +,C) /(P(+,C) + P(,C))  this is the Bayes rule!
Bayes Rule
 Prior
 Posterior
 Likelihood
 Marginal likelihood (Total probability)
20171006 初稿