Stat 411 Lecture Notes 06
Bayesian Analysis
Ryan Martin
www.math.uic.edu/~rgmartin
Version: December 3, 2012
1
Introduction
Up to know, our focus in Stat 411 has been on whats called frequentist statistics. That is,
our main objective was sampling distri
Stat 511 Homework 03
Solutions
iid
1. For X1 , . . . , Xn N(, 2 ), the likelihood function is
n
2
L(, ) =
i=1
1
2 2
e(Xi )
2 /2 2
( 2 )n/2 e(1/2
2)
n
2
i=1 (Xi )
.
Then the log-likelihood (up to an additive constant) is
n log( 2 )
1
(, ) =
2
2
2
n
2
(Xi
Stat 511 Homework 02
Solutions
1. Problem 3 from Notes II. For the exponential family density p (x) = exA() h(x),
with respect to measure , the moment generating function is given by
E (euX ) =
eux exA() h(x) d(x) =
e(+u)xA() h(x) d(x).
Since A() is dened
Stat 511 Homework 01
Solutions
1. Problem 1 from Lecture Notes I. Fix any small , e.g., = 0.05, and write X
1/2
zn
for the standard condence interval for the normal mean . Note that z
depends on in that (z ) = 1 /2, but Ive omitted the dependence in the
Lectures notes on large-sample theory
Ryan Martin
rgmartin@math.uic.edu
Spring 2012
1
Introduction
Large-sample theory was and is crucial to the development of statistical methods. Before
the availability of high-power computing, the only way to solve ma
Stat 511 Lecture Notes IV
Bayesian Inference
Ryan Martin
Spring 2013
1
Introduction
The classical frequentist approach to statistics is one that students are familiar with.
That is, for a given procedureestimator, test, condence interval, etcwe investiga
Stat 511 Lecture Notes II
Exponential Families, Suciency & Information
Ryan Martin
www.math.uic.edu/~rgmartin
Spring 2013
1
Introduction
In statistics, suciency and information are fundamental concepts, no matter what approach one adoptsBayesian, frequen
Stat 511 Lecture Notes I
Introduction and Preparations
Ryan Martin
www.math.uic.edu/~rgmartin
Spring 2013
1
Introduction
Stat 511 is a rst course in advanced statistical theory. This rst set of notes is intended
to set the stage for the material that is
Stat 511 Homework 02
Solutions
1. Problem 3 from Notes II. For the exponential family density p (x) = exA() h(x),
with respect to measure , the moment generating function is given by
E (euX ) =
eux exA() h(x) d(x) =
e(+u)xA() h(x) d(x).
Since A() is dened
Stat 511 Homework 01
Solutions
1. Problem 1 from Lecture Notes I. Fix any small , e.g., = 0.05, and write X
1/2
zn
for the standard condence interval for the normal mean . Note that z
depends on in that (z ) = 1 /2, but Ive omitted the dependence in the
Stat 511 Lecture Notes II
Exponential Families, Suciency & Information
Ryan Martin
www.math.uic.edu/~rgmartin
Spring 2013
1
Introduction
In statistics, suciency and information are fundamental concepts, no matter what approach one adoptsBayesian, frequen