Advanced Statistical Algorithms

Code: MA691 | L-T-P-C: 3-0-0-6

Prerequisites: MA 471 or equivalent

Introduction to probability distributions. Basics of estimation and testing of hypothesis( frequentist approach, bayesian approach ). Discrete and continuous multivariate distributions (multinomial, multivariate normal etc); Different Censoring algorithms and its application (Type-I , Type-II, hybrid, progressive.); Advanced EM algorithm (higher dimensional estimation); Bayesian filters ( Kalman Filter, Extended Kalman, Particle Filter and their applications). Advanced Monte Carlo Techniques: Importance sampling, Monte Carlo Markov Chain and its variations (EM MCMC, Slice sampling, Hamiltonian Monte Carlo etc). Basics of Hidden Markov Model (forward backward algorithm, Viterbi algorithm, Baum-welch algorithm). Deep learning techniques (Back propagation, autoencoder, restricted Boltzmann machine etc); Genetic Algorithm: single objective GA, multi - objective NSGA.

Texts:

1. D. Kundu, Statistical Computing :existing methods and recent development, Alpha Science International, 2004.
2. B.P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, 2004.
3. C. M. Bishop, Pattern Recognition and Machine Learning, Springer, 2006.

References:

1. J.E. Gentle, Elements of computational Statistics, Springer Series in Statistics and computing,2002
2. T. Say, Analysis of Financial Time Series, Wiley Series in Probability and Statistics, 2nd Edn., 2005
3. W. Zucchini and I. L. MacDonald, Hidden Markov Model for time series: an introduction using R, 2nd Edn., CRC Press, 2016.
4. R. C. Mitsno, Genetic Algorithm and Engineering Optimization, Wiley Series in EDA, 2000.