MATH 450: Mathematical Statisticsvucdinh.github.io/Files/lecture1.pdf · Textbook: Modern...

MATH 450: Mathematical Statistics

Vu Dinh

Departments of Mathematical SciencesUniversity of Delaware

August 29th, 2017

Vu Dinh MATH 450: Mathematical Statistics

General information

Classes:Tuesday & Thursday 9:30-10:45 am, Gore Hall 115

Office hours:

Tuesday 1-2 pm, Ewing Hall 312.Wednesday 11am-12pm, Ewing Hall 312.

Website: http://vucdinh.github.io/m450f17

Textbook: Modern mathematical statistics with applications(Second Edition). Devore and Berk. Springer, 2012.


http://vucdinh.github.io/m450f17

Evaluation

Overall scores will be computed as follows:25% homework, 10% quizzes, 25% midterm, 40% final

No letter grades will be given for homework, midterm, or final.Your letter grade for the course will be based on your overallscore.

The two lowest homework scores and the lowest quiz scorewill be dropped.

Here are the letter grades you can achieve according to youroverall score.

≥ 90%: At least A≥ 75%: At least B≥ 60%: At least C≥ 50%: At least D


Homework


Homework

Assignments will be posted on the website every otherTuesday (starting from the first week) and will be due onThursday of the following week, at the beginning of lecture.

No late homework will be accepted.

Two lowest homework scores will be dropped in thecalculation of your overall homework grade.


Quizzes and exams

At the end of every chapter, there will be a short, multiplechoice quiz during class.

The quiz dates will be announced at least one class inadvance.

The lowest quiz score will be dropped.

There will be a midterm on 10/26 and a final exam duringexams week.


Data analysis

Open source statistical system R

http://cran.r-project.org/


http://cran.r-project.org/

Tentative schedule


About me

PDEsmathematical financeuncertainty quantificationexperimental designcomputational biologystatistical machine learning


Topics

Textbook: Modern mathematical statistics with applications(Second Edition).Devore and Berk. Springer, 2012.

Week 1 · · · · · ·• Chapter 1: Descriptive statistics

Week 2 · · · · · ·• Chapter 6: Statistics and SamplingDistributions

Week 4 · · · · · ·• Chapter 7: Point Estimation

Week 7 · · · · · ·• Chapter 8: Confidence Intervals

Week 10 · · · · · ·• Chapter 9: Test of Hypothesis

Week 13 · · · · · ·• Two-sample inference, ANOVA, regression


Chapter 1: Overview and Descriptive Statistics


Living in a world of uncertainties

— Insanity is doing the same thing over and over and expecting adifferent result


Modeling uncertainty and randomness

probability → random variables

numerical analysis → uncertainty quantification

electrical engineer → fuzzy logic

theory of evidence, possibility theory


Random variable


What do we want?

make meaningful statement about the uncertain world(e.g.: Smoking is bad for your health)

saying those statements with confidence(e.g.: I’m 95% sure that smoking is bad for health)

quantify uncertainties

making prediction about uncertain outcomes(I’m 90% sure that the McDonald’s stock is rising)(The weather channel says there is a 90% that it will rain)

using such predictions for our personal gains(I’m bringing an umbrella with me today)


Is it even possible to do so?

The law of large numbers (Chapter 6)

The Central Limit Theorem (Chapter 6)

Asymptotic normality of the maximum likelihood estimator(Chapter 7)


How are we going to do it?


How are we going to do it?

population: a well-defined collection of objects of interest

when desired information is available for all objects in thepopulation, we have what is called a census→ very expensive

a sample, a subset of the population, is selected→ we obtain a data set → make prediction/test hypothesis


Chapter 1: Descriptive Statistics

Goal: describe a data set

By pictures and tables (1.2)

By measures of locations (1.3) and variability (1.4)


Pictorial and Tabular Methods

Stem-and-Leaf displays

Dotplots

Histograms


Stem-and-Leaf displays

44 46 47 49 63 64 66 68 6872 72 75 76 81 84 88 106


Dotplots


Histograms


Histograms: unequaled class width


Measures of locations: mean


Measures of locations: median

Step 1: ordering the observations from smallest to largest


Measures of locations: median

Data set

15.2, 9.3, 7.6, 11.9, 10.4, 9.7, 20.4, 9.4, 11.5, 16.2, 9.4, 8.3

Ordered list

7.6, 8.3, 9.3, 9.4, 9.4, 9.7, 10.4, 11.5, 11.9, 15.2, 16.2, 20.4

Median =9.7 + 10.4

2= 10.05

→ Median is not affected by outliers


MATH 450: Mathematical Statisticsvucdinh.github.io/Files/lecture1.pdf · Textbook: Modern...

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