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Graduate Course Proposal Form Submission Detail - PHC7067
Tracking Number - 2156
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Submission Type: New
Course Change Information (for course changes only):
Comments: SCNS approved 6/9/09; assigned number 7067
- Date & Time Submitted: 2008-03-26
- Department: Epidemiology and Biostatistics
- College: PH
- Budget Account Number: 6403000
- Contact Person: Yangxin Huang
- Phone: 9748209
- Email: firstname.lastname@example.org
- Prefix: PHC
- Number: 7067
- Full Title: Probability Models
- Credit Hours: 3
- Section Type: C -
Class Lecture (Primarily)
- Is the course title variable?: N
- Is a permit required for registration?: Y
- Are the credit hours variable?: N
- Is this course repeatable?:
- If repeatable, how many times?: 0
- Abbreviated Title (30 characters maximum): Probability Models
- Course Online?: -
- Percentage Online:
- Grading Option:
R - Regular
- Prerequisites: College level calculus, introductory public Health knowlege, statistical software experience such as SPlus/SAS
- Corequisites: none
- Course Description: Probability theory and models with applications in Public Health. Contents: fundamental probability theories; stochastic process; probability modeling with application to health data.
- Please briefly explain why it is necessary and/or desirable to add this course: The content of this course offers doctoral students as well as advanced masters' degree students in our programs a specific course in the concepts, theories and models of probability as it relates to the analysis of mathematical and probability models for
- What is the need or demand for this course? (Indicate if this course is part of a required sequence in the major.) What other programs would this course service? This course will be a requirement for doctoral students in the Biostatistics concentration. It will also serve as an elective for Masters' degree students in the Biostatistics and Epidemiology concentrations.
- Has this course been offered as Selected Topics/Experimental Topics course? If yes, how many times? yes, once (Spring 2006)
- What qualifications for training and/or experience are necessary to teach this course? (List minimum qualifications for the instructor.) Ph.D. with concentration in Statistics or Biostatistics related field.
- Objectives: The objective of this course is to build on previous exposure to probability and gain an understanding of probability theory and models. Students will gain a solid understanding of probability theory with regard to distributions, characteristic functions, relationships between distributions and limit theorems as well as probability model buildings for health data. They will also explore simple stochastic processes. This course will prepare our students to better utilize probability foundations in analysis of health related data. This course is offered as bridge between college calculus and biostatistical inference. It is served as foundation for biostatistical inference and other related biostatistical courses. The class material consist of mainly four parts: (1) basic review materials that each of students has previous exposure: probability spaces as models of chance experiments, axioms, conditional probability; (2) random variables, distributions, densities, mass functions, sum of independent random variables; random vectors, joint and marginal distributions, conditioning, laws of large numbers, moment generating functions and central limit theorems, convergence of random variables; (3) simple stochastic processes including random walk and Poisson process; this part is perhaps less familiar to the students and requires more efforts and group discussion. (4) probability modeling with application to health data; some health data examples are used to illustrate probability modeling.
- Learning Outcomes: By the end of this course students should be able to:
1. Set up plausible models of probability spaces for a variety of chance experiments;
2. Recognize where and when standard probability distributions are applicable;
3. Find probabilities and other properties associated with random variables and vectors;
4. Use indicator variables and the idea of conditional expectation, appropriately;
5. Apply the Laws of Large Numbers and the Central Limit Theorem;
6. Apply extinction criteria and describe the long-term behavior of branching process;
7. Understand the main properties of one-dimensional simple random walks and Poisson process;
8. Set up transition matrices of Markov Chains describing their long-term behavior;
9. Apply the ideas to gambling, optimal growth strategy, insurance models and similar.
10. Build probability models for health related data.
- Major Topics: Probability space, Conditional Probability and Independence, Common Probability Distributions, Discrete Random Variables, Continuous Random Variables, Sum of Random Variables, Convergence and Limit Theorems, Markov Chains and Random Process, Stochastic Process in Discrete Time, Stochastic Process in Continuous Time, Probability models for health data and Markov chain Monte Carlo (MCMC) algorthms with application to health data
- Textbooks: 1 Required:
John Haigh. 2002. Probability Models. Springer-Verlag. ISBN: 1-85233-431-2
2. Reference text books:
S Ross. 2002. Introduction to Probability Models. 8th edition, Academic Press. ISBN: 0-12-598055-8
KL Chung. 2001. A Course in Probability Theory. 3rd edition, Academic Press. ISBN: 0-12-174151-6.
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