MA3014 · BS elective · 4 credits

Statistical Computing

Simulation, resampling, MCMC and the numerical methods behind modern statistical practice.

Instructor Prof. Dootika Vats Term As offered Prereq MA1004

§ 1Calendar

  • Quiz 1—
  • Quiz 2—
  • End-term examination—

§ 2Previous Year Questions

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§ 3Resources

Course material2

Notes1

MA3014 · BS elective · 4 credits

Syllabus

The official course syllabus, transcribed from the IITM BS Data Science & Applications course booklet.

§ 1Course Description

This course introduces computational methods used in statistical estimation and learning problems

Lectures-Tutorials-Practicals-Credits: 4-0-0-4

§ 2Faculty

  • Prof. Dootika Vats, Assistant Professor, Department of Mathematics and Statistics, IIT Kanpur

§ 3Week-by-week

Week 1: Random number generation; Congruential methods; Discrete sampling (inverse transform, accept-reject); Generating Bernoulli, Poisson, binomial, and geometric variables.

Week 2: Sampling techniques; Composition method; Inverse transform for continuous distributions; Visualization in R.

Week 3: Advanced sampling methods; Accept-reject optimization; Box-Muller method for Gaussian variables; Proposal selection strategies.

Week 4: Ratio-of-uniforms method; Multivariate and mixture sampling; Specialized distributions (beta, Dirichlet); Multidimensional sampling.

Week 5: Monte Carlo methods; Importance sampling; Variance reduction; Optimal proposal distributions; R-based implementations.

Week 6: Weighted importance sampling; Likelihood functions; Maximum likelihood estimation (MLE); Linear regression via MLE.

Week 7: Penalized regression; Ridge regression; Likelihood visualization; Taylor series approximations; Simulation in R.

Week 8: Numerical optimization; Newton-Raphson methods (univariate and multivariate); Logistic regression via MLE; Convergence behavior.

Week 9: Gradient-based optimization; Gradient ascent; MM (Majorize-Minimize) algorithms; Applications in regression and estimation.

Week 10: Expectation-Maximization (EM) algorithm; Gaussian mixture models; Multivariate clustering; Handling missing/censored data.

Week 11: Model evaluation and selection; Cross-validation; Bootstrapping; Resampling methods; Choosing hyperparameters and model complexity.

Week 12: Applications of SGD with code. Simulated annealing: examples, codes, and challenges