Multivariate Distributions: Dirichlet-Multinomial
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Module 10
1
Dirichlet-Multinomial
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= (1 , . . . , m ),
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Xi cfw_1, . . . , m,
P
i i = 1.
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Assume that
ind
X | Multinomial()
or
ind
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 modules
5. Questions you ask me
2
How I write the exam
1
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 [h(X)].
Recall that f (x) is very complicated and hard
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 Gibbs sampling, which is a special case of it.
We will ret
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 methods that are useful for drawing
samples from Bayesian pos
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
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A commonly-used technique for designing MCMC samplers is
t
Intro to Bayesian Methods: Part II
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 2
1
Last Time
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Why should we learn about Bayesian concepts?
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Natural if thinking about unknown parameters as random.
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They naturally give
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 variables, sampling each from its conditional
distribut
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
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Loss function
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Risk
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Posterior Risk
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Bayes risk
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Bayes estimator
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Minimax estimators
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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.
2. A parametric model where the number of parameters
in
Noninformative (Default) Bayes
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 6
1
Exam I
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Exam Thursday, Feb 11th in class. Be early to class so that
you can start you exam on time.
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You will need pencil and paper. No cal
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
you can start you exam on time.
I
You will need pencil a
More on Bayesian Methods: Part II
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 5
1
Todays menu
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Confidence intervals
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Credible Intervals
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Example
2
Confidence intervals vs credible intervals
A confidence interval for a
More on Bayesian Methods
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 4
1
Todays menu
I
Review of notation
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When are Bayesian and frequentist methods the same?
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Example: Normal-Normal
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Posterior predictive inference
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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.
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The multivariate normal (MVN) distribution.
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Conjugate
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 = w.
What is the MLE?
M LE = arg max p(D | )
2
What is
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 distribution whose p.d.f. can be evaluated up to a constant
Intro to Bayesian Methods
Rebecca C. Steorts
Bayesian Methods and Modern Statistics: STA 360/601
Lecture 1
1
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Course Webpage
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Syllabus
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LaTeX reference manual
R markdown reference manual
Please come to office hours for all questions.
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Office h