- Challenge question
- Intro To Probability And Bayes Nets
- Probability / Coin Flip
- 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
- 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.
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
- 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)
- 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!
- Marginal likelihood (Total probability)