STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 10
The sample variance
Last time we see that for i.i.d. data from a normal distribution
with unknown mean and variance, the estimator
2 =
1
n
n
(Xi X )2
i=1
is the MLE.
We see that this is biased, a
Chapter 1 - continued
Chapter 1 sections
1.4 Set Theory
SKIP: Real number uncountability
1.5 Denition of Probability
1.6 Finite Sample Spaces
1.7 Counting Methods
1.8 Combinatorial Methods
1.9 Multinomial Coefcients
SKIP: 1.10 The Probability of a Union o
STA 611: Introduction to Mathematical Statistics
Instructor: Meng Li
TueThu 4:40pm - 5:55pm, Old Chemistry Building 116
August 25, 2014
STA 611 (Lecture 01)
Introduction to Probability
August 25, 2014
1 / 16
Introduction
About me
About TAs
About this cour
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 1
What is statistics and why study it?
What is statistics and why study it?
Statistics is the prime information science.
What is statistics and why study it?
Statistics is the prime information scie
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 4
First in-class close-book, close-notes quiz next Tuesday. You
may bring a scientic calculator.
Policies on quizzes and the midterm.
Policies on homeworks and labs.
Last class
The three-step proced
STA 114/MTH 136 Intro to Mathematical
Statistics
Lecture 3
Last class
Bayes Theorem and the ideal approach to inference.
Example: A political poll (a binomial experiment).
Political poll example revisited
An organization randomly selected 100 democrats an
STA 114/MTH 136 Intro to Mathematical
Statistics
Lecture 6
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The sampling (or frequentist) view point
Both Bayesians and frequentists agree on the need to build
models for the distribution of the data given certain
parametersf (x| ) or p(x| ).
Freque
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 2
1 / 35
Probability modeling and statistical inference
Probability models are assumptions (or hypotheses) that
characterize the randomness that arises in the data
Statistical inference goes the oth
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 5
Point estimation
A very common statistical problem is to guess the value of a
parameter based on observed data X = (X1 , X2 , . . . , Xn ).
Functions of the data that are used for guessing the val
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 8
Reminder
Quiz next Tuesday (2/11).
Summary of what we have learned so far
The general inference procedure based on Bayes Theorem.
How to construct point estimates/estimators based on the
posterior
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 9
Two interpretations of the likelihood function
From Bayes Theorem
( |x) ( )f (x| )
we know that if our prior ( ) is at, then
( |x) f (x| ) = L( ).
Under this interpretation, the MLE, , is the po
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 11
If we have n i.i.d. N (0, 1) random variables U1 , U2 , . . . , Un , then
the probability distribution of their sum
2
2
2
Z = U1 + U2 + + Un
is called the 2 (or Chi-square) distribution with n de
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 12
Central limit theorem allows us to directly approximate the
sampling distribution of an estimator if it can be written as the
sum of i.i.d. random variables.
This scenario occurs very often. For
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 13
Reminder: Midterm on March 4 in class
Closed book, closed notes.
Bring your calculator and a double-sided letter-sized cheat-sheet.
Formulas of common distributions will be provided.
If for any r
STA 250/MTH 342 Intro to Mathematical
Statistics
Lecture 7
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More general criteria for selecting good estimators
Recall from last time the goal of constructing an estimator (X) so
that (X) will likely to be close to .
Again, we need a notion of dista
STA 611: Introduction to Mathematical Statistics
Fall 2015
Tue-Thu 4:40-5:55pm in 116 Old Chemistry Building (Old Chem.)
Course Website: https:/stat.duke.edu/courses/Fall15/sta611.01/
Instructor: Meng Li
Ofce: 211A Old Chem.
Email: [email protected]
Ofc