Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian
MTH 511 : Statistical Simulation and Data Analysis
Syllabus:
Simulation of random variables from discrete, continuous, multivariate
distributions and stochastic processes, Monte-Carlo methods. Regression
analysis, scatter plot, residual analysis. Computer Intensive Inference Methods
- Jack-Knife, Bootstrap, cross validation, Monte Carlo methods and permutation
tests. Graphical representation of multivariate data, Cluster analysis,
Principal component analysis for dimension reduction.
I will cover the following topics: Simulation of random variables from discrete, continuous, multivariate distributions and stochastic processes, Monte-Carlo methods. Computer Intensive Inference Methods - Jack-Knife, Bootstrap, cross validation, Monte Carlo methods, Graphical representation of multivariate data, Cluster analysis, Dimension reduction using LASSO, E.M. Algorithm, Markov Chain Monte Carlo.
Grading Scheme: Quiz: 30%, Mid semester exam: 30%, End semester exam:40%
Books:
"Simulation" by Sheldon M. Ross (Academic Press, Fourth Edition), 2006, Chaps. 1-5, Low price Indian edition is available.
Bootstrap from "An Introduction to the Bootstrap" by B. Efron and R.J. Tibshirani (Chapman and Hall), 1994, Chapters 1-6, 12, 13.
Jackknife from "An Introduction to the Bootstrap" by B. Efron and R.J. Tibshirani (Chapman and Hall), 1994, Chapter 11.
Cluster Analysis from "Cluster Analysis" by B.S. Everitt, S. Landau, M. Leese, D. Stahl, (Wiley), 2011, Chapters 1-4
E.M. Algorithm from "The EM Algorithm and. Extensions" by G. M. McLachlan and T. Krishnan, (Wiley), 1997, Chap. 1, (Chapters 2-4 are needed for better understanding).
LASSO from "Regression Shrinkage and Selection via the Lasso" by R. Tibshirani, Journal of Royal Statistical Society, (1996) 58, No. 1, pp. 267-288.
LASSO from "Statistical Learning with Spharsity- The Lasso and Generalizations" by T. Hastie, R. Tibshirani and M. Wainwright, (CRC), 2015, Chapters 1,2, 4
MCMC from
(i) "Markov Chain Monte Carlo in Practice" by W.R. Gilks, S. Richardson, D.J. Spiegelhalter (Chapman and Hall) Chapter 1,
(ii) "Simulation and the Monte Carlo Method" by R.Y. Rubinston and D.P Kroese (Wiley), Chapters 6, and
(iii) "Explaining the Gibbs sampler" by G. Casella and E.I. George, The American Statistician, Vol. 46, Issue 3, 1992, pp. 167-174.
(iv) "Understanding the Metropolis-Hasting Algorithm" by Siddartha Chib and Edward Greenberg, The American Statistician, Vol. 49, Issue 4, 1995, pp. 329-335.
(v) "Simulated Annealing" by Dimitris Bertsimas and John Tsitsiklis, Statistical Science, Vol. 8, No. 1, 1993, pp. 10-15.
(vi) "Bayesian Computation: a summary of the current state, and sample backwards and forwards" by Peter J. Green, K. Latuszynski,M. Pereyra, Christian P. Robert, Statistical Computations, Vol. 25, 2015, pp. 835-862.
Assignaments: