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Bayesian Inference
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
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Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
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Paper Code |
Paper Title |
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STT-423(D) |
Bayesian Inference |
CO 129: Use relative frequencies to estimate probabilities.
CO 130: Calculate conditional probabilities.
CO 131: Calculate posterior probabilities using Bayes’ theorem.
CO 132: Calculate simple likelihood functions.
CO 133: 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 |
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.
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.
Bayesian approximation techniques: Normal approximation, T-K approximation, Monte-Carlo Integration, Accept-Reject Method, Idea of Markov chain Monte Carlo technique.
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
Hierarchical priors and partial exchangeability. Predictive inference, Predictive density function, prediction for regression models, Decisive prediction, point and internal predictors, machine tool problem.
● 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:
· https://epgp.inflibnet.ac.in/
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
