Lecture 18: Bayesian ANOVA

Question 1

What is the Bayes factor

Answer 1

Quantifies which model better supports the data than the other

Question 2

What does it mean when the Bayes factor is 1

Answer 2

The models predict equally well, Bayes factor away from 1 means more evidence in favor of one hypothesis —> cannot be negative

Question 3

Marginal likelihood

Answer 3

The average quality of a model’s prediction; how well a model predicts the data; how likely the data are under a certain model

Question 4

What is the formula for Bayesian inference

Answer 4

P(theta|data)=p(theta) * p(data|theta)/p(data)

P(H1|data)/p(H0|data)=p(H1)/p(H0) * p(data|H1)/p(data|H0)

Question 5

What part of the formula is the posterior beliefs about the world

Answer 5

P(theta|data)

Question 6

What part of the formula is the prior beliefs about the world

Answer 6

P(theta)

Question 7

What part of the formula is the predictive updating factor

Answer 7

P(data|theta)/p(data)