Hypothesis Testing
Definition 1
A statistical hypothesis is a statement about the unknown values of the parameters of the population distribution.
Suppose the family of population distributions is indexed by the
d-dimensional vector IRd.
We shall deal wit
STAT743 FOUNDATIONS OF STATISTICS (PART II)
Winter 2011
Assignment 3
Q. 1
Solutions
a) If X1 , . . . , Xn come from a single parameter exponential family distribution then we
can write the joint density (mass) function as
(
fX (x; ) = h(x)c() exp w()
n
X
Bayesian Statistics
Bayesian statistical inference is an alternative to the usual
frequentist inference we have considered up to now.
In frequentist inference the parameters of a distribution are
considered fixed unknown quantities and inference is base
STAT743 FOUNDATIONS OF STATISTICS (Part II)
Assignment 1
Due January 31, 2011
Q. 1 This question describes two ways of generating normal random variates from uniforms.
a) Suppose that U1 and U2 are two independent Unif(0, 1) random variables, show that
th
Interval Estimation
Definition 18
Given a sample X1, . . ., Xn from a distribution with pdf f (x | ),
an interval estimator of the parameter is the random interval
I(X ) = [L(X ), U (X )]. The end-points of the interval are two
statistics such that L(x) 6
STATISTICS 743 (Part 2)
Foundations of Statistics
Angelo J. Canty
Topics to be covered
Lecture 1 Simulation and Monte Carlo Methods
Lecture 2 Computation of the MLE
Lectures 34 Hypothesis testing
Lectures 56 Interval estimation
Lecture 78 Bayesian inferen
STAT743 FOUNDATIONS OF STATISTICS (Part II)
Assignment 1
Due February 28, 2011
Q. 1 Suppose that X1 , . . . , Xn is a random sample from a Normal(1 , 2 ) distribution. Suppose
we take the improper prior distribution
(1 , 2 )
1
2
< 1 < , 0 < 2 <
a) Show
STAT743 FOUNDATIONS OF STATISTICS (Part II)
Assignment 3
Q. 1
Due March 14, 2011
a) Suppose that X1 , . . . , Xn are a random sample from the an exponential family distribution with a single parameter and natural parameter = w() where w is a monotone
func