STAT2002: Linear Models and the Analysis of Variance
STAT7101: Further topics in Statistics and Computing
Ioannis Kosmidis
Contents
1 Preamble
iv
2 Preliminaries
2.1 Statistical models . . . . . . . .
Revision of Basic Probability
The fundamental idea of probability is that chance can be
measured on a scale which runs from zero, which represents
impossibility, to one, which represents certainty.
Sa
YP: STAT2001/3101, 2016 2017
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STAT2001: Probability and Inference (0.5 unit)
STAT3101: Probability and Statistics II (0.5 unit)
Lecturer: Yvo Pokern
Aims of course
To continue the study of probabilit
STAT2002: Linear models and the analysis of variance
STAT7101: Further statistical methods and computing
Chapter 3 of course notes
Connections between the models
Normal population (NP):
Yi = + i
(i =
STAT2002: Linear models and the analysis of variance
STAT7101: Further statistical methods and computing
Chapter 2 of notes
Statistical models
What do we mean by a statistical model?
Why do we need st
YP: STAT2001/3101, 2016-2017
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Exercise Sheet 1
The exercise sheet is subdivided into three parts:
Part A contains warm-up questions you should do in your own time.
You should solve all questions of
YP: STAT2001/3101, 2016-2017
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Exercise Sheet 2
The exercise sheet is subdivided into three parts:
Part A contains warm-up questions you should do in your own time.
You should solve all questions of
YP: STAT2001/3101, 2015-2016
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Exercise Sheet 0: Get Ready!
Mathematics background
For this course you will need a knowledge of basic mathematical tools. The following
is a list of mathematical topics
STAT2002/STAT7101
Autumn term 20162017
Exercises - Sheet 4
To be discussed in the problem class on Friday 4th November. Please note that you
are expected to work on the exercises below before the prob
STAT2002/STAT7101
Autumn term 20162017
Exercises - Sheet 3
To be discussed in the problem class on Friday 28th October. Please note that you are
expected to work on the exercises below before the prob
STAT2002/STAT7101
Autumn term 20162017
Exercises - Sheet 2
To be discussed in the computer workshop on Friday 21st October. Please note that
you are expected to work on the exercises below before the
STAT2002/STAT7101
Autumn term 20162017
Exercises - Sheet 1
To be discussed in the problem class on Friday 14 October. Please note that you are
expected to work on the exercises below before the proble
Probability
3105
Based on lectures by
Dr N Sidorova
typed by John Sylvester
Jan 2012
Contents
1 Rigorous set up
1.1 Probability space, events and random variables . . . . . . . . . . . . . . . .
1.2 D
Concepts from Last Lecture
Condence Interval in a Frequentist Framework
Pivotal quantity
1
7.2 Likelihood-based condence intervals
Suppose that is the maximum likelihood estimator of the unknown par
Concepts from last lecture
Hypothesis Testing
Null and Alternative
Type I and II errors
size and power of a test
1
Classical approach to hypothesis testing:
State of Nature
= 0
d0
= 1
Type II er
3 Likelihood and Suciency
Chapter 3 of Lecture Notes focuses on the important basic statistical concepts of likelihood and suciency, which are central
to statistical inference. It also highlights how
4 Concepts from last lecture
Likelihood Principle
Suciency
Principles of Bayesian Inference
( | x) ()p(x | )
1
4 Frequentist point estimation
Chapter 4 focuses on Frequentist point estimation and d
5 Likelihood and Bayesian methods of point estimation
Chapter 5 of the Lecture Notes describes the principles and basic
methods of Likelihood and Bayesian point estimation.
1
5.1 Maximum likelihood es
Concepts from last lecture
Score function: V (X) = ln L(; X ), with E(V ) = 0 and var(V ) =
cfw_
2
I() = E 2 ln L(; X )
CRLB: If T is unbiased for m():
var(T )
[m()]2
I()
Exponential Family
p(x;
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Solutions to Exercise Sheet 9
1. Let X1 , . . . , Xn be iid from U (0, ) and consider X as well as X(n) as bases for
estimators for . Check whether they are unbiased:
E
STAT2001/STAT3101:
Probability and Inference
Lecturer: Yvo Pokern, Room 144 Dept. of Statistical
Science
Lectures:
Christopher Ingold XLG2 Auditorium on Thursdays
1pm-2pm
Darwin B40 Lecture Theatre
YP: STAT2001/3101, 2012-2013
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Exercise Sheet 6
A: Warm-up question
1. For geometrically distributed variables X and Y we have that P(X > n) = (1 p)n
(no successes in n trials, or sum the GP). Furthe
YP: STAT2001/3101, 2012-2013
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Exercise Sheet 4
A: Warm-up questions
1. From the specication of the bivariate normal distribution for (X, Y ), we can read
o: 1 = 0, 2 = 1, 1 = 1, 2 = 2, = 1 .
2
Theref