Office Hours
TBA
Course Prerequisites:
Probability & Statistics (Random variables, PDFs, Moments, Regression, etc.)
Required Text:
John E.Freund's Mathematical Statistics with Applications by Miller & Miller 7th Ed.
Course Grading:
Exam I : 25%
Exam II : 25%
Project : 25%
HWs/Quizes: 25%
Catalogue Description:
STAT 447. Statistical Theory for Research Workers.
(4-0) Cr. 4. F.S.SS. Prereq: MATH 151 and permission of instructor, or MATH 265
Primarily for graduate students not majoring in statistics. Emphasis on aspects of
the theory underlying statistical methods. Probability, probability density and
mass functions, distribution functions, moment generating functions, sampling
distributions, point and interval estimation, maximum likelihood and likelihood
ratio tests, linear model theory, conditional expectation and minimum mean square
error estimation, introduction to posterior distributions and Bayesian analysis,
use of simulation to verify and extend theory.
Syllabus:
1. Introduction; Sets & Subsets: 1 week (Class Notes: Chapter 1)
2. Actions as Random Variables: 1 week (Class Notes: Chapter 2)
3. Probability & Simulating R.V.s: 1 week (Class Notes: Chapter 3)
4. Marginal, Joint & Conditional Probability: 1 week (Class Notes: Chapter 3)
5. Moments & Their Estimators ; Exam1 1 week (Class Notes: Chapter 3)
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6. Joint Moments & Their Estimators: 1 week (Class Notes: Chapters 3 & 4)
7. Linear & nonlinear regression: 1 week (Class Notes: Chapter 4)
8. Simulating R.V.s & the CLT: 1 week
9. Moments & PDFs of Functions of n-D R.V.s: 1 week
10. Simulating Functions of R.V.s ; Exam 2 1 week
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11. Parameter estimation (MME & MLE): 1 week
12. Confidence intervals & hypothesis test 1 week
13. Simulations and sampling pdfs 1 week
14. ANOVA 1 week
15. More ANOVA ; Special Topics 1 week
Learning Objectives: At the completion of this course the student should be able to:
- 1. Recast data analysis results in terms of random variables.
- 2. Appreciate the assumptions upon which various computed statistics are based, and know how to validate them.
- 3. Have a solid grasp of univariate distributions for that might be suitable for discrete and continus random variables.
- 4. Have a solid grasp of joint and conditional distributions for discrete and continuous random variables.
- 5. Formulate linear and certain nonlinear models, hypothesis tests, confidence intervals in a rigorous fashion.
- 6. Understand and appreciate the value of the conditional expected value as an alternative to linear models.
- 7. Use simulations to probe the distributional nature of complicated functions of random variables and of statistics that do not adhere to standard assumptions.
- 8. Be well-prepared to take more rigorous courses in probability and statistics, as well as courses in application areas (e.g. applied time series and applied Kalman filtering).
NOTE: If you have a documented disability and anticipate needing accommodations in this course, please make arrangements to meet with me soon. Please request that a Student Disability
Resource staff send a SAAR form verifying your disability and specifying the accommodation you will need.