Statistical Computing (Elective-I)

Unit I

Descriptive Statistics & Probability: Diagrammatic representation of data, measures of central tendency, dispersion, skewness and kurtosis, correlation, inference procedure for correlation coefficient, bivariate and multiple correlation, linear regression and its inference procedure, multiple regression. Probability: conditional probability, independent events, Bayes' theorem, random variables, discrete and continuous probability distributions, expectation and variance, Markov inequality, Chebyshev's inequality, central limit theorem.

Unit II

Inferential Statistics & Regression Analysis: Sampling & Confidence Interval, Inference & Significance, Estimation and Hypothesis Testing, Goodness of Fit, Test of Independence, Permutations and Randomization Test, t-test/z-test (one sample, independent, paired), ANOVA, chi-square. Linear Methods for Regression: multiple regression analysis, QR orthogonalization by Householder transformations, singular value decomposition (SVD), linear dimension reduction using PCA.

Unit III

Random Numbers & Monte Carlo: Random number generation, inverse-transform, acceptance-rejection, transformations, multivariate probability calculations. Monte Carlo Integration: simulation, variance reduction, Monte Carlo hypothesis testing, antithetic variables/control variates, importance sampling, stratified sampling. Markov chain Monte Carlo (MCMC): Markov chains, Metropolis-Hastings algorithm, Gibbs sampling, convergence.

Unit IV

Resampling, Density Estimation & Numerical Methods: Cross-validation, Bootstrapping, Jackknife resampling, percentile confidence intervals, permutation tests. Density Estimation: univariate and multivariate density estimation, kernel smoothing. Numerical Methods: root finding, numerical integration, numerical maximization/minimization, constrained and unconstrained optimization, EM (Expectation-Maximization) algorithm, simplex algorithm.

Unit V

R Programming & Statistical Analysis: History of R, R as a scientific calculator, handling packages, workspace, inspecting variables, operators and expressions, data objects and types, vectors, matrices and arrays, lists and data frames, built-in and user-defined functions, strings and factors, flow control and loops, dates and times. Using R for Statistical Analysis: importing/exporting data, outputting results, exporting graphs, graphics in R, descriptive statistics commands, data aggregation, multivariate data representation, code factorization and optimization, statistical libraries in R.