Multivariate Distributions: Dirichlet-Multinomial
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 10
1
Dirichlet-Multinomial
I
= (1 , . . . , m ),
I
Xi cfw_1, . . . , m,
Intro to Monte Carlo
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 5
1
Studying for an Exam
1. The PhD notes
2. Homework
3. Lab (its duplicated for a reason)
4. Class m
Intro to Markov Chain Monte Carlo
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 6
1
Intro to Markov chain Monte Carlo (MCMC)
Goal: sample from f (x), or approximate Ef
Intro to Markov Chain Monte Carlo
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 7
1
Gibbs sampling
Instead of moving into the Metropolis algorithm, we now move
into Gib
Metropolis Hastings
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 9
1
The Metropolis-Hastings algorithm is a general term for a family of
Markov chain simulation method
The Multi Stage Gibbs Sampling: Data
Augmentation Dutch Example
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 8
1
Example: Data augmentation / Auxiliary variables
I
A c
Intro to Bayesian Methods: Part II
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 2
1
Last Time
I
Why should we learn about Bayesian concepts?
I
Natural if thinking abo
The Multi Stage Gibbs Sampling
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 8
1
The generalization to more than two variables is straightforward.
We cycle through the
Intro to Decision Theory
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 3
1
Please be patient with the Windows machine.
2
Topics
I
Loss function
I
Risk
I
Posterior Risk
An Introduction to Bayesian Nonparametric
Methods
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 11
1
What is a nonparametric model?
1. A really large parametric model.
Noninformative (Default) Bayes
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 6
1
Exam I
I
Exam Thursday, Feb 11th in class. Be early to class so that
you can start you
Noninformative (Default) Bayes:
A Quick Review
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 7
1
Exam I
I
Exam Thursday, Feb 11th in class. Be early to class so that
y
More on Bayesian Methods: Part II
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 5
1
Todays menu
I
Confidence intervals
I
Credible Intervals
I
Example
2
Confidence inte
More on Bayesian Methods
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 4
1
Todays menu
I
Review of notation
I
When are Bayesian and frequentist methods the same?
I
Exa
The Multivariate Distributions: Normal and
inverse Wishart
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 10
1
I
Moving from univariate to multivariate distributions.
I
Linear Regression
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 10
1
Setup
Lets assume that Di = (xi , yi ) for all i.
Assume
iid
Yi N (wT xi , 2 ).
Assume 2 known and
Intro to Monte Carlo, Part II
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 5
1
Rejection Sampling
Rejection sampling is a method for drawing random samples from
a dist
Intro to Bayesian Methods
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 1
1
I
Course Webpage
I
Syllabus
I
LaTeX reference manual
R markdown reference manual
Please com