STA 6866 Fall 2011 Solutions
Andrew Womack & Luis Leon-Novello
Assignment 1: Assigned Aug 22, Due Sep 7
Exercise 1.4:
We can best describe the dierences between order() and rank() through their use. B
Typos from the Og
Christian P. Robert
October 10, 2011
Introducing Monte Carlo Methods with R
1. (Thanks to Kazue Ishida, Japanese translator of the book) The demos for
chapters 2 and 5 do not work, d
STA 6866: Monte Carlo Statistical Methods
Fall 2011
Prerequisite: STA 6166 and 6167 or permission of instructor.
Credits: 3
Course Coordinator Professor George Casella
Instructors:
Dr. Luis Leon-Novel
Random Eects Model Notes
Andrew Womack
November 21, 2011
1
Basic Model
We have the following hierarchical model
yij |j , , 2 , 2 N (j , 2 )
j |, 2 , 2 N (, 2 )
where j = 1, . . . , J is our group inde
Christian Robert
Universit Paris-Dauphine
e
and
George Casella
University of Florida
Introducing Monte Carlo Methods with R
Solutions to Randomly-Numbered Exercises
January 15, 2010
Springer
Berlin He
MC methods: MH. Ch 6
Hw Ch 6. Metropolis-Hasting Algorithm
Explain clearly what you do. When describing the MH algorithm write which is your target
distribution f and the proposal q .
Ex 1.
The negati
Approaches to the Bayesian Linear Model
Andrew Womack
November 14, 2011
1
Introduction
We consider models of the form
y = x +
(1)
where i N (0, 2 ). In general, if we have p possible covariates to inc
Lab 2: Generating Random Variables
Andrew J. Womack
September 2, 2011
1
Probability Inverse Transformation
Write a function which has two inputs (N (a number of draws) and W which is an inverse
CDF F
Lab 6: Optimization
Andrew J. Womack
October 7, 2011
1
One dimensional problem
Create a sample from an exponential distribution make a function evaluating the log likelihood.
1. Use optimize to nd the
Lab 1: Using R
Andrew J. Womack
Aug 26, 2011
1
Estimating the Moments of a Mixture Distribution
I have three measurement devices which you cannot distinguish. With equal probability, I will
hand you a
MC convergence MH. Ch 8. Not to turn in.
Hw Ch 8. Convergence
Explain clearly what you do and why you are making the (convergence) decision.
Ex 1.
According to exercise 1 in MH. Hw 6
a a 1
1
,
p ( | )
EM and Monte Carlo EM Algorithms
Andrew J. Womack
September 26, 28, and 30, 2011
Setup
We have observed data x and parameter . We wish to maximize
the (log) likelihood
L(|x ) = f (x |)
(|x ) = log (L(
Sampling Importance Resampling (SIR)
Another method to simulate (almost) from f based on g
Assumption: f & g known up to a constant, i.e.
f = c1 and
f
g = c2 g
c1 , c2 > 0 unknown.
iid
1. Generate y1
Monte Carlo Methods with R: Monitoring Convergence [1]
Chapter 8: Monitoring Convergence of MCMC Algorithms
Why does he insist that we must have a diagnosis? Some things are not
meant to be known by m
Monte Carlo Methods with R: Gibbs Samplers [1]
Chapter 7: Gibbs Samplers
Come, Watson , come! he cried. The game is afoot.
Arthur Conan Doyle
The Adventure of the Abbey Grange
This Chapter
We cover b
Monte Carlo Methods with R: MetropolisHastings Algorithms [1]
Chapter 6: MetropolisHastings Algorithms
How absurdly simple!, I cried.
Quite so!, said he, a little nettled. Every problem becomes very c
Monte Carlo Methods with R: Monte Carlo Optimization [1]
Chapter 5: Monte Carlo Optimization
He invented a game that allowed players to predict the outcome?
Susanna Gregory
To Kill or Cure
This Chapte
Monte Carlo Methods with R: Monte Carlo Integration [1]
Chapter 3: Monte Carlo Integration
Every time I think I know whats going on, suddenly theres another
layer of complications. I just want this da
Monte Carlo Methods with R: Random Variable Generation [1]
Chapter 2: Random Variable Generation
It has long been an axiom of mine that the little things are innitely the
most important.
Arthur Conan
R Basics
Andrew J. Womack
August 22, 2011
Introduction
What R is:
Statistical Scripting Language
Free
Open Source
Flexible
Objects and Methods
What R is not:
The fastest computing language
Fool proof
STA 6866 Fall 2011 Assignments
Andrew Womack & Luis Leon-Novello
For all problems where coding is necessary, you must submit your code along with your
answers to any questions. Solutions must be well