STAT 440/840 CM 761: Computational Inference
Introduction to R
R is a free, open-source software environment for statistical computing and graphics. It is
essentially the standard statistical software used in the academic community and has gaining
conside
STAT 440/840 CM 761: Computational Inference
The Gibbs Sampler
1. Motivation
The usual setup is that we wish to sample from an unfamiliar distribution p(x) = cr(x), x
Rd , where r(x) is known but the normalizing constant c is not. When x is low dimension
STAT 440/840 CM 761: Computational Inference
The Bootstrap Method
1. Motivation: Condence Intervals
iid
Suppose that we have data Y = (y1 , . . . , yn ) modeled as yi p(y | ) with unknown parameter
2 R. We would like to obtain a condence interval for the
STAT 440/840 CM 761: Computational Inference
An Introduction to Bayesian Inference
1. Recap of Frequentist Inference
iid
Suppose that we have data X1 , . . . , Xn f (x | ). A somewhat automatic receipe for statistical inference is:
Point estimate for : =
STAT 440/840 CM 761: Computational Inference
The Metropolis-Hastings Algorithm
1. Metropolis-Hastings Algorithm
Same setup: we wish to sample from a distribution p(x) = c r(x) of which only r(x) is
known. I like to think of the Gibbs sampler as a reduce o
STAT 440/840 CM 761: Computational Inference
The Expectation-Maximization Algorithm
1. Motivation: Missing Data
Consider the usual linear regression problem
iid
i N (0, 1).
yi = xi + zi + i ,
Now suppose that some of the zi are missing. Let
The data matri
STAT 440/840 CM 761: Computational Inference
Basic Methods of Posterior Sampling
1. Motivation
Bayesian inference is a useful tool for many problems where the MLE fails:
is on the boundary of its range, i.e., `0 ( | y) 6= 0 (usually when = 0 or 1)
`( |
STAT 440/840 CM 761: Computational Inference
The Metropolis-Hastings Algorithm
1. The Metropolis-Hastings Algorithm
Same setup: we wish to sample from a distribution p(x) = c r(x) of which only r(x) is
known. I like to think of the Gibbs sampler as a redu