Bayesian Inference

Paper Code: 
STT 423(D)
Objective: 

This paper gives an insight to use decision making process with the help of  prior and posterior probabilities in various fields. 

 

Students will able to

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-423(D)

Bayesian Inference

CO 114: Use relative frequencies to estimate probabilities.

 

CO 115: Calculate conditional probabilities.

 

CO 116: Calculate posterior probabilities using Bayes’ theorem.

 

CO 117: Calculate simple likelihood functions.

 

CO 118: Describe the role of the posterior distribution, the likelihood function and the posterior distribution in Bayesian inference about a parameter.

Approach in teaching:

Interactive Lectures,

Group Discussion,

Classroom Assignment

Problem Solving Sessions

 

Learning activities for the students:

Assignments

Seminar

Presentation

Subject based  Activities

Classroom Quiz

Assignments

Class Test

Individual Presentation

 

15.00
Unit I: 
UNIT I

Basic elements of Statistical Decision Problem. Expected loss, decision rules (nonrandomized and randomized). Overview of Classical and Bayesian Estimation. Advantage of Bayesian inference, Prior distribution, Posterior distribution, Subjective probability and its uses for determination of prior distribution. Importance of non-informative priors, improper priors, invariant priors.

 

15.00
Unit II: 
UNIT II

Point estimation, Concept of Loss functions, Bayes estimation under symmetric loss functions, Bayes credible intervals, highest posterior density intervals, testing of hypotheses. Comparison with classical procedures.

 

15.00
Unit III: 
UNIT III

Bayesian approximation techniques: Normal approximation, T-K approximation, Monte-Carlo Integration, Accept-Reject Method, Idea of Markov chain Monte Carlo technique.

 

15.00
Unit IV: 
UNIT IV

Subjective probability, its existence and interpretation. Prior distribution, subjective determination of prior distribution. Improper priors, non-informative (default) priors, invariant priors. Conjugate prior families, construction of conjugate families using sufficient statistics of fixed dimension, mixtures of conjugate priors

 

 

15.00
Unit V: 
UNIT V

Hierarchical priors and partial exchangeability. Predictive inference, Predictive density function, prediction for regression models, Decisive prediction, point and internal predictors, machine tool problem.

 

Essential Readings: 
  • Berger, J. O. : Statistical Decision Theory and Bayesian Analysis, Springer Verlag.
  • Robert, C.P. and Casella, G. : Monte Carlo Statistical Methods, Springer Verlag.
  • Leonard, T. and Hsu, J.S.J. : Bayesian Methods, Cambridge University Press.
  • Bernando, J.M. and Smith, A.F.M. : Bayesian Theory, John Wiley and Sons.
  • Robert, C.P. : The Bayesian Choice: A Decision Theoretic Motivation, Springer.
  • Gemerman, D. : Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman Hall.
  • Bansal, A. K. (2007). Bayesian Parametric Inference, Narosa Publishing House, New Delhi.
  • Box, G.P. and Tiao, G. C.: Bayesian Inference in Statistical Analysis, Addison-Wesley.
  • Aitchison, J. and Dunsmore, I.R. (1975). Statistical Prediction Analysis, Cambridge University Press.
  • De. Groot, M.H. (1970). Optimal Statistical Decisions, McGraw Hill.

 

Academic Year: 
2021-2022
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