36-724 Spring 2006: MCMC and BUGS
Brian Junker
February 20, 2006
Hierarchical Normal Model
Complete Conditionals for Hierarchical Normal
Brief R code for this model
An Alternative to R: BUGS/WinBU
36-724: Applied Bayesian and Computational Statistics
Homework 4: Due Friday March 10, 2006
Announcements:
In Gelman, please look at Chapter 6 (if you havent already).
Please download and examine th
36-724 Spring 2006: Some Basic Concepts
Brian Junker
January 18, 2006
Basic Notation
Applied Bayesian Paradigm
Example: Bernoulli and Binomial data
Example Continued: Posterior Inference
Some Exa
36-724 Spring 2006: Large Samples, Normal
Approximations
Brian Junker
February 6, 2006
Large Sample Desiderata
Normal Approximation
More Refined Result: Laplace Approximation
Some Frequentist Prop
36-724: Applied Bayesian and Computational Statistics
Homework 2: Due Monday February 6, 2005
Announcements:
Please read Chs 2 and 3 of Gelman et al. Also, please download the following paper from ww
36-724 Spring 2006: Metropolis-Hastings Example
Brian Junker
February 22, 2006
The Hierarchical Beta-Binomial
An MCMC solution
Example: Rat Tumors
1
36-724 February 22, 2006
The Hierarchical Beta-B
36-724 Spring 2006: Metropolis-Hastings Example
Brian Junker
February 22, 2006
The Hierarchical Beta-Binomial
An MCMC solution
Example: Rat Tumors
1
36-724 February 22, 2006
The Hierarchical Beta-B
36-724: Applied Bayesian and Computational Statistics
Homework 6: Due Friday April 21, 2006
Announcements:
Class is cancelled for April 10, 12, and 15. We have one more makeup class on April 18,
4:30
36-724 Spring 2006: Posterior Intervals, Non-informative
Priors
Brian Junker
January 25, 2006
Posterior intervals, credible sets
Invariance of Interval Estimates
Noninformative/Improper/Default Pri
36-724 Spring 2006: Large Samples, Normal
Approximations
Brian Junker
February 6, 2006
Large Sample Desiderata
Normal Approximation
More Refined Result: Laplace Approximation
Some Frequentist Prop
HW7 Solutions
36-724: Applied Bayesian and Computational Statistics
May 12, 2006
Problem 1
a) Since we assume separability, we may choose such that y i = sign(T xi ) for all i. Then yi T xi > 0 for
al
HW3 Solutions
36-724: Applied Bayesian and Computational Statistics
March 2, 2006
Problem 1
a Fatal Accidents Poisson()
I will set a prior for to be Gamma, as it is the conjugate prior. I will allow t
36-724 Spring 2006: Simulation, Conjugacy, Posterior
Summaries
Brian Junker
January 23, 2006
Simulation Methods
Importance Sampling
SIR (sampling/importance resampling)
More on Conjugate Priors
P
36-724 Spring 2006: Some general MCMC comments
Brian Junker
February 24, 2006
A Sketch of MCMC Theory
Designing a M-H / Gibbs algorithm
Some Further Design Considerations
Checking Burn-in and Conv
36-724 Spring 2006: Model Checking. . . Generalities
Brian Junker
March 1, 2006
Some Model checking strategies
Posterior Predictive Checks
Bayes Factors
Model Comparison Indices
1
36-724 March 1,
36-724 Spring 2006: An Example
Brian Junker
March 3, 2006
Urban Migration Data
A Model For This Data
Some Modeling Questions
1
36-724 March 3, 2006
Urban Migration Data
Crouchley et al. (1982, Geog
36-724 Spring 2006: Model Checking. . . Generalities
Brian Junker
March 1, 2006
Some Model checking strategies
Posterior Predictive Checks
Bayes Factors
Model Comparison Indices
1
36-724 March 1,
36-724 Spring 2006: An Example
Brian Junker
March 3, 2006
Urban Migration Data
A Model For This Data
Some Modeling Questions
1
36-724 March 3, 2006
Urban Migration Data
Crouchley et al. (1982, Geog
36-724 Spring 2006: Some general MCMC comments
Brian Junker
February 24, 2006
A Sketch of MCMC Theory
Designing a M-H / Gibbs algorithm
Some Further Design Considerations
Checking Burn-in and Conv
36-724: Applied Bayesian and Computational Statistics
Homework 5: Due Wednesday March 29, 2006
Announcements:
Most of what I am doing in these first few lectures after break comes from Hastie Tibshir
36-724: Applied Bayesian and Computational Statistics
Homework 7: Due Monday May 8, 2006
Announcements:
This is the last hw, and the last assignment of any kind, for the course!
Please dont forget to
36-724 Spring 2006: MCMC and BUGS
Brian Junker
February 20, 2006
Hierarchical Normal Model
Complete Conditionals for Hierarchical Normal
Brief R code for this model
An Alternative to R: BUGS/WinBU
36-724 Spring 2006: Posterior Intervals, Non-informative
Priors
Brian Junker
January 25, 2006
Posterior intervals, credible sets
Invariance of Interval Estimates
Noninformative/Improper/Default Pri
36-724 Homework 5
Due: Monday February 27, 14:30, by email to Dansci
([email protected])
Please submit 1) your R code, set to output your computational solutions, with a name like
yourname
#importance sampling demo; sampling a t-distribution with a normal instead.
target <- function(x) dt(x,10)+0.1
proposal <- function(x) dnorm(x)
prop.draw <- function(nn) rnorm(nn)
range <- seq(-3,3,by
#
#
#36-724: Simulating Random Variables and Introduction to R
#
#
#lines preceded with the # symbol are comments.
#Simulating Bernoulli random variables:
#I want 100 of them in a vector.
length <- 10