Statistical Models and Analysis

a
Course
Postgraduate
Semester
Sem. II
Subject Code
MA625
Subject Title
Statistical Models and Analysis

Syllabus

An overview of basic probability theory and theory of estimation; Bayesian statistics; maximum a posteriori (MAP) estimation; conjugate priors; Exponential family; posterior asymptotics; linear statistical models; multiple linear regression: inference technique for the general linear model, generalised linear models: inference procedures, special case of generalised linear models leading to logistic regression and log linear models; introduction to non-linear modelling; sampling methods: basic sampling algorithms, rejection sampling, adaptive rejection sampling, sampling and the EM algorithm, Markhov chain, Monte Carlo, Gibbs sampling, slice sampling.

Text Books

Same as Reference

References

  1. Dobson, A.J. and Barnett,A.G., An Introduction to Generalised Linear Models, 3rd ed., Chapman and Hall/ CRC (2008).
  2. Krzanowski, W.J., An Introduction to Statistical Modeling, Wiley (2010).
  3. Hastie, T., Tibshirani, R., and Friedman, J., The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer (2002).
  4. Bishop,C.M., Pattern Recognition and Machine Learning, Springer (2006).

Course Outcomes (COs):
CO1: Explain the theory of general linear models and generalized linear models.

CO2: Outline the algorithms used for estimation for these models and teach the methodology to test the sutability of a particular model with specific number of parameters.

CO3: Perform statistical analysis, such as estimation, hypothesis testing, and analysis of variance, under thesemodels.

CO4: Teach the students how to choose an appropriate model that fits reasonably well to a particular practical problem and analyse it by using the methods and algorithms that they studied.