CE679 Regression and Stochastic Methods (Fall 2009)


Instructor: Nikolay S. Strigul
E-mail: nstrigul@stevens.edu
Office Hours: by appointment

Lectures: Kidde 228, Monday 6:15 pm -8:45 pm

Grading:

Course program Course program (PDF)

General comments:

CE679 is an introduction to the practical statistical methods for students majoring in sciences and engineering using R. Statistical reasoning plays a critical role in the modern sciences, as much of real-life problems naturally involve a large amount of uncertainty and randomness. This course will teach students to use statistical methods on particular real-life examples (taken mostly from environmental sciences) using R and OpenBugs. Particular topics include: Bayesian approach, causal inference, linear and multiple linear regression, non-linear regression models, dose-response models, analysis of variances, optimal experimental design. Students will need to install two free programs R (http://www.r-project.org/) and OpenBugs (http://mathstat.helsinki.fi/openbugs/). It is also convenient to operate R using code editors, such as Tinn-R for Windows (http://sourceforge.net/projects/tinn-r) and RKWard for Linux (http://rkward.sourceforge.net/).

Textbooks

1) John Maindonald and John Braun, 2006. Data Analysis and Graphics Using R: An Example-based Approach. Cambridge University Press, 2nd edition, ISBN 052186116.
2) Andrew Gelman and Jennifer Hill, 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, ISBN 0521867061.
3) Benjamin M. Bolker, 2008. Ecological Models and Data in R. Princeton University Press, ISBN 0691125228.

Course program:



Lecture 1. - Probability Theory

1. The empirical background.
2. The sample space, events.
3. Random variables.
4. Introduction to R.

Lecture 2. - Discrete probability distributions

5. Discrete uniform distribution
6. Binomial and negative binomial distributions
7. Hypergeometric distribution
8. Poisson distribution

Lecture 3. - Continuous probability distributions

9. The normal distribution
10. Lognormal distribution
11. Gamma distribution
12. Beta distribution
13. Student's t distribution
14. F distribution

Lecture 3. - Fitting probability distributions.

15. Example: fitting the poisson distribution
16. Parameter estimation
17. The method of moments
18. The method of maximum likelihood
19. Efficiency

Lecture 4. - Statistical Hypotheses.

20. Goodness of fit
21. The Neyman-Pearson paradigm
22. Confidence intervals and hypothesis tests
23. Likelihood ratio tests
24. Examples

Lecture 5. - The analysis of variance

25. The one-way layout
26. Normal theory and F test
27. The two-way layout
28. Normal theory for the two-way layout

Lecture 6. - Simple linear regression

29. The simple linear regression model
30. Least squares
31. Properties of the least squares estimators
32. Inferences conserning the regression coefficients

Lecture 7. - Multiple linear regression

33. General form of a multiple regression model
34. Model assumptions
35. Inferences in multiple linear regression

Lecture 8. - Nonlinear regression

36. Transformation to a linear model
37. Non-linear least squares
38. Numerical methods

Lecture 9. - Nonlinear regression models

39. Exponential regression models
40. Michaelis Menten model
41. Monod model
42. Sigmoidal Models

Lecture 10. - Dose response models

43. Logistic model .
44. Dose finding toxicity model
45. Applications and examples

Lecture 11. - Optimal experimental designs

46. Linear regression models
47. Optimality criteria
48. Nonlinear regression models
49. Local and minimax optimal designs

Lecture 12. - Bayesian statistics

50. Bayes formula
51. Posterior analysis
52. Markov Chain Monte Carlo (MCMC) methods
53. The Metropolis-Hastings algorithm and Gibbs sampling

Lecture 13. - Applications of Bayesian methods

54. Introduction to OPENBUGS
55. Bayesian inferences for the normal distribution
56. Hierarchical models
57. Examples

Lecture 14. - Bayesian regression

58. Bayesian linear regression
59. Hierarchical linear models
60. Generalized linear models
61. Nonlinear models

Final exam.

back