IIT Madras Statistical Computing Lectures
BSMA301457 lectures11 weeks
Weeks
- Week 16 lecturesIntroduction to R | getting started with r & rstudio · Pseudorandom number generation | congruential methods & uniform sampling · Discrete inverse transform method | generating bernoulli & poisson variables · Discrete Accept Reject Algorithm · Discrete accept-reject algorithm | random variable generation & sampling · Discrete accept-reject examples | binomial & geometric sampling cases
- Week 24 lecturesDiscrete: composition method · Continuous: inverse transform method | generating continuous random variables · R: visualizing inverse transform method | exponential & cauchy sampling in r · Continuous: Inverse Transform Method
- Week 35 lecturesAccept-reject examples | beta & normal sampling with proposals in r · Accept-reject: circle mp4 · Accept reject: choosing proposals mp4 | when it fails & how to optimize proposals · R-optimal proposal demonstration mp4 | gamma & exponential sampling in r · Box-muller method | generating gaussian random variables
- Week 45 lecturesRatio-of-uniform: theory | generating continuous random variables · Ratio-of-uniform: examples | exponential & normal sampling in r · R: visualizing ratio-of-uniforms | exponential & normal sampling in r · Miscellaneous sampling methods | binomial, beta, dirichlet & mixture distributions · Multidimensional sampling | multivariate gaussian & conditional methods
- Week 54 lecturesIntroduction to importance sampling | monte carlo integration & efficiency · Examples of importance sampling | gamma moments with exponential proposals · Optimal proposals in importance sampling | variance reduction with gamma & normal · R: optimal importance sampling proposal | gamma & gaussian examples in r
- Week 65 lecturesWeighted importance sampling | estimating expectations with incomplete distributions · R - Weighted importance sampling | comparing sis & wis with gamma examples · Likelihood functions | introduction to maximum likelihood estimation · MLE examples | bernoulli & exponential MLE with fisher information · Linear regression | MLE for regression coefficients & variance in r
- Week 75 lecturesR: Visualizing likelihood functions · Ridge regression | addressing singularity with penalized regression · R: ridge penalty visualization | lambda, data simulation & regularization in r · No closed form MLEs · Review of taylor series approximations
- Week 86 lecturesNewton raphson algorithm | optimization with taylor eeries · Newton raphson algorithm non concave function | cauchy MLE & convergence challenges · R: newton raphson | cauchy MLE, convergence & divergence in r · Multivariate newton raphson algorithm | logistic regression & multi-parameter MLE · Logistic regression | MLE with newton-raphson & computational implementation · R: logistic regression with newton-raphson | titanic dataset example
- Week 95 lecturesGradient ascent algorithm explained | optimization vs newton-raphson · Gradient ascent in higher dimensions | logistic regression · Gradient ascent in r | cauchy & logistic regression examples · MM algorithm explained | majorize-minimize optimization & bridge regression example · R: MM algorithm implementation | location cauchy & bridge regression examples
- Week 105 lecturesEM algorithm | expectation-maximization introduction · Gaussian mixture models | EM algorithm & parameter estimation · R: gaussian mixture models · Multivariate gaussian mixture models | EM algorithm for multivariate clustering · EM algorithm for censored data | maximum likelihood estimation with missing data
- Week 116 lecturesChoosing number of clusters | gaussian mixture models · Loss functions | resampling methods, cross-validation, and bootstrapping · Cross-validation | estimating test error & choosing tuning parameters · R: cross validation | ridge regression & lambda selection in r · Bootstrapping | resampling methods for confidence intervals & parameter estimation · R: bootstrapping | coefficient of variation & confidence intervals in r