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[size=+2]OUTLINE of Course TOPICS
statistics705_umd_slud.zip
(4.83 MB)
1. Introduction to R:
Starting and quitting R, on-line help, R operators and functions, creating
R objects, data types (vectors, matrices, factors, functions, lists), managing
data (combining objects, subsetting, creation of frames), R graphics.
2. Monte Carlo and Simulation in R:
Basic random number generation, applications of LLN and CLT in simulations,
numerical integration, importance sampling, empirical distributions, Markov Chain
Monte Carlo. Managing loops in R.
3. Numerical Optimization in Statistics:
Objective functions in statistics, and managing functions in R. Linear and nonlinear
least squares, special considerations in maximizing likelihoods, penalized likelihood,
steepest descent, quasi-Newton-Raphson methods, constrained maximization, EM
algorithm. Diagnostics for misspecified models.
4. Linear and Generalized Linear Models:
Regression summaries, model fitting, prediction, model updating, analysis of residuals,
model criticism, ANOVA, generalized linear models, specifying link and variance
functions, stepwise model selection, deviance analysis.
Comparisons of implementations in R and SAS. Fitting mixed-effect (generalized)
linear models in R.
5. Bootstrapping Methodology:
Parametric bootstrap, empirical CDF, bootstrap standard errors and confidence intervals,
estimation of bias, jackknife, application to regression.
6. Smoothing & Nonparametric Regression:
Spline smoothing, kernel smoothing, selecting tuning parameters by cross-validation.
Graphical aspects of smoothing.
7. MCMC and the Gibbs Sampler.
Definitions and basic ideas of MCMC ad Gibbs-Sampler simulation methodology,
including a brief introduction to `Bayesian Computing' using BUGS through R.
8. Mixed and Multilevel Models fitted and interpreted via
Likelihood methods and Bayes (MCMC) methods in R.
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