"Applied statistics at an advanced level"
Syllabus
Topics will generally be selected from the following:
Part I. Introduction
1. What is statistics? Cyclic nature of the scientific method
Part II. Contemporary descriptive statistics
2. Data types, stem-and-leaf, 5-number summary, boxplot, parallel boxplots, scatter plots, pairs(), bagplot(), spin()
3. Summaries of location, spread vs. level plot, empirical Q-Q plot
4. Linear fitting, OLS, WLS, NLS, robust/resistant fitting, residuals
5. Optimization methods, the psi function, fitting by stages
6. Smoothing, loess, splines
7. Two-way arrays, residual analysis, Simpson's paradox
8. Exploratory analysis of variance, terminology, overlays, anova table, rob/res methods.
Part III. Pertinent formalism
9. Models, EDA vs. CDA
10. The classical linear model. Gauss-Markov theorem, regression analysis, diagnostics (residuals, plots, influence,...), interpretation of results, generalized least squares, analysis of variance, effects, factors, random effects variant
11. r-squared, R-squared, lurking variables
12. Multivariate normal, singular case, conditionals, quadratic forms
13. General estimation and testing theory. M-estimates, maximum likelihood, nonlinear regression, quasilikelihood, asymptotic results (when model family incorrect), likelihood ratio, robust methods, computations
14. The generalized linear model, exponential family, IRLS algorithm, analysis of deviance, diagnostics, contingency tables
15. Density estimation, nonparametric regression
16. The generalized additive model, algorithms
17. Nonparametric uncertainty estimation, delta method, jackknife, bootstrap, cross-validation
There will be case studies throughout and the Laboratory will be devoted to analyzing pertinent data sets using the methods discussed in the lectures.
The students are expected to: learn what the above models and techniques are, be able to impliment them on a computer and to justify or reject their applicability in real examples.
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