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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.
Vu Dinh MATH 450: Mathematical Statistics
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
Vu Dinh MATH 450: Mathematical Statistics
Homework
Vu Dinh MATH 450: Mathematical Statistics
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.
Vu Dinh MATH 450: Mathematical Statistics
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.
Vu Dinh MATH 450: Mathematical Statistics
Data analysis
Open source statistical system R
http://cran.r-project.org/
Vu Dinh MATH 450: Mathematical Statistics
Tentative schedule
Vu Dinh MATH 450: Mathematical Statistics
About me
PDEsmathematical financeuncertainty quantificationexperimental designcomputational biologystatistical machine learning
Vu Dinh MATH 450: Mathematical Statistics
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
Vu Dinh MATH 450: Mathematical Statistics
Chapter 1: Overview and Descriptive Statistics
Vu Dinh MATH 450: Mathematical Statistics
Living in a world of uncertainties
— Insanity is doing the same thing over and over and expecting adifferent result
Vu Dinh MATH 450: Mathematical Statistics
Modeling uncertainty and randomness
probability → random variables
numerical analysis → uncertainty quantification
electrical engineer → fuzzy logic
theory of evidence, possibility theory
Vu Dinh MATH 450: Mathematical Statistics
Random variable
Vu Dinh MATH 450: Mathematical Statistics
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)
Vu Dinh MATH 450: Mathematical Statistics
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)
Vu Dinh MATH 450: Mathematical Statistics
How are we going to do it?
Vu Dinh MATH 450: Mathematical Statistics
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
Vu Dinh MATH 450: Mathematical Statistics
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)
Vu Dinh MATH 450: Mathematical Statistics
Pictorial and Tabular Methods
Stem-and-Leaf displays
Dotplots
Histograms
Vu Dinh MATH 450: Mathematical Statistics
Stem-and-Leaf displays
44 46 47 49 63 64 66 68 6872 72 75 76 81 84 88 106
Vu Dinh MATH 450: Mathematical Statistics
Dotplots
Vu Dinh MATH 450: Mathematical Statistics
Histograms
Vu Dinh MATH 450: Mathematical Statistics
Histograms: unequaled class width
Vu Dinh MATH 450: Mathematical Statistics
Measures of locations: mean
Vu Dinh MATH 450: Mathematical Statistics
Measures of locations: median
Step 1: ordering the observations from smallest to largest
Vu Dinh MATH 450: Mathematical Statistics
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
Vu Dinh MATH 450: Mathematical Statistics
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