Contents

2019-07-14

Contents

Under construction!

1. Exchangeability and De Finetti’s Theorem

1.1 Exchangeability
1.2 De Finetti’s Theorem

2. Bayesian Finite Mixture Model

2.1 Finite Mixture Model
2.2 Bayesian Finite Mixture Model
2.3 Inference of Bayesian Finite Mixture Model
2.4 Model Selection for Finite Mixture Models

3. Dirichlet Process

3.1 Definition
3.2 Properties
3.2.1 Expectations, Variances, and Co-variances
3.2.2 Tail-freeness
3.2.3 Self-similarity & Neutral-to-the-right Property
3.2.4 Conjugacy
3.2.5 Marginal and Conditional Distribution
3.2.6 Discreteness
3.2.7 Support
3.3 Constructions
3.3.1 Construction via a Stochastic Process
3.3.2 Construction through a Distribution Function
3.3.3 Construction through a Gamma Process
3.3.4 Construction through Polya Urn Scheme
3.3.5 Stick-breaking Representation(Sethuraman Representation)

4. Dirichlet Process Mixture Model

4.1 Going Nonparametric
4.2 Stick-breaking Process
4.? Inference of Dirichlet Process Mixture Model
4.?.1 Algorithm 1 4.?.2 Algorithm 2 4.?.3 Algorithm 3

Reference