Bayesian Inference

Paper Code: 
24STT423(D)
Credits: 
2
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

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

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT423(D)

Bayesian Inference

(Theory)

CO 148: Explain the importance of non-informative priors in Bayesian inference, effectively demonstrating their role in reducing bias and subjectivity in decision-making processes.

CO 149: Apply Bayes estimation under symmetric loss functions.

CO 150: Identify and evaluate various Bayesian approximation techniques in approximating complex probability distributions.

CO 151: Demonstrate the construction of conjugate prior families and facilitate posterior inference.

CO 152: Evaluate hierarchical priors and partial exchangeability in predictive inference.

CO 153: Contribute effectively in course-specific interaction.

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: 
Fundamentals of Statistical Decision Theory and Bayesian Inference

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: 
Point Estimation and Hypothesis Testing in Bayesian Framework

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: 
Bayesian Approximation Techniques

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: 
Subjective Probability and Prior Distributions

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: 
Hierarchical Priors and Predictive Inference

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.

 

SUGGESTED READINGS:

  • 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.

 

e-RESOURCES:

 

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2024-2025
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