Distributions

Question 1

Binomial Distribution

Answer 1

• models number of successes in n independent trials
• each trial has success probability p

Question 2

Beta Distribution

Answer 2

• models uncertainity in probability of success p
• models proportions, probabilities
• generates values between 0 and 1
• small shape parameters - more uncertain about p

Question 3

Beta-Binomial Distribution

Answer 3

• models number of successes with success probability p drawn from a Beta
• p can vary across groups
• flexible

Question 4

Dirichlet Distribution

Answer 4

• models probability vector p
• ensures p sums to 1
• defined on simplex
• restrictive covariance structure

Question 5

Generalised-Dirichlet Distribution

Answer 5

• more general covariance structure
• more flexible
• each component has own variance

Question 6

Multinomial Distribution

Answer 6

• generalisation Binomial to multiple categories
• models counts of observations in K categories over n trials
• models counts across multiple categories

Question 7

Generalised-Dirichlet-Multinomial Distribution

Answer 7

• combines GD and Multinomial to model compositional counts
• greater flexiblity in covariance structure
• can handle 0 and missing values
• defined as a series of Beta-Binomial distributions

Question 8

GDM Components

Answer 8

• GD - captures prior over compositions - series indepdendent Beta
• Multinomial - models observed counts - series conditional Binomial