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• Programming languages, data structures, programming using R, C/C++, and Perl, HTML and CGI., Calling C/C++ from R., Writing R extensions (called packages)., Grid graphics; interactive and dynamic graphics., Static and dynamic memory management
• numerical libraries and optimization in R, Parallel computing in R., Massive data challanges and solutions., Image processing., Hierarchical models., cluster analysis, Random Number Generation, Pseudo random numbers, linear congruential generator, properties of PRNGs, inverse transform method, basic rejection sampling, envelope rejection sampling, transformation of random variables.
• Monte Carlo Methods, Monte Carlo estimates, bias, mean square error, estimating probabilities, choice of sample size,, importance sampling, antithetic variables, variance reduction, applications in statistical inference, Markov Chain Monte-Carlo Methods, Markov Chains with discrete/continuous state space, random walk, transition matrices, transition densities, stationary distributions
• Metropolis-Hastings algorithm, convergence of MCMC methods,, burn-in period, application to Bayesian inference, MH with discrete state space, detailed balance condition, Metropolis algorithm, random-walk Metropolis, independence sampler., Bootstrap Methods, Empirical distributions, the bootstrap principle, bootstrap estimate for the bias,, bootstrap estimate of the standard error
• Introduction to statistical computing, Least squares (regression), Penalized and weighted least squares, Density estimation and smoothing, Matrix computations, Optimization (likelihood estimation), Newton-Raphson, Fisher scoring, Combinatorial optimization, Integration (probabilities), Quadrature, Laplace approximation, Resampling and Monte Carlo inferences, Jackknife and Bootstrap, Permutation procedures, Monte Carlo simulation, Statistical graphics