Roll Number
134197001
Category
EX
Topics for PhD Qualifiers
Compulsory Subject: (i) Optimisation Techniques, (ii) Stochastic Models
Elective1
Discrete Event Simulation:
Overview of basic concepts from probability and statistics concerning random variables, correlation, estimation, confidence intervals, hypothesis testing. Generation and testing of random numbers. Generation of random variates, random vectors, correlated random variates and stochastic processes. Input modeling; useful probability distributions; hypothesizing families of distributions, estimation of parameters, testing goodness of fit. Simulation Output data analysis for a single system; statistical analyses for transient systems and systems in statistical equilibrium. Comparing alternative system configurations; confidence intervals, ranking and selection. Variance reduction techniques. Experimental design, sensitivity analysis and optimization.
References:
A. M. Law and W. D. Kelton (2000), Simulation Modeling and Analysis, 3rd Ed., McGraw Hill
J. Banks, J. S. Carson, B. L. Nelson and D. M. Nicol (2001), Discrete Event System Simulation, 3rd Ed., Pearson Education International Series.
K. S. Trivedi (2001), Probability and Statistics with Reliability, Queuing and Computer Science Applications, Eastern Economy Edition, Prentice-Hall (India).
Overview of basic concepts from probability and statistics concerning random variables, correlation, estimation, confidence intervals, hypothesis testing. Generation and testing of random numbers. Generation of random variates, random vectors, correlated random variates and stochastic processes. Input modeling; useful probability distributions; hypothesizing families of distributions, estimation of parameters, testing goodness of fit. Simulation Output data analysis for a single system; statistical analyses for transient systems and systems in statistical equilibrium. Comparing alternative system configurations; confidence intervals, ranking and selection. Variance reduction techniques. Experimental design, sensitivity analysis and optimization.
References:
A. M. Law and W. D. Kelton (2000), Simulation Modeling and Analysis, 3rd Ed., McGraw Hill
J. Banks, J. S. Carson, B. L. Nelson and D. M. Nicol (2001), Discrete Event System Simulation, 3rd Ed., Pearson Education International Series.
K. S. Trivedi (2001), Probability and Statistics with Reliability, Queuing and Computer Science Applications, Eastern Economy Edition, Prentice-Hall (India).
Elective2
Theory of Estimation:
Population and samples; Parametric and non-parametric models; Exponential and location-scale families; Sufficiency and minimal sufficiency; Complete statistics; Unbiased and UMVU estimation; Asymptotically unbiased estimators; Method of moments; Bayes estimators; Invariance; admissibility of Bayes rule; Minmax Theorem Maximum Likelihood Estimation. consistency and efficiency. UMVU estimators and their properties. Application to normal and exponential one and two sample problems. Information inequality(multiple parameter case) Invariance. Simultaneous estimation. Stein's phenomenon, Shrinkage estimation.
References:
E. L. Lehmann, Theory of Statistical Inference, Wiley, 1983.
S. Zacks, The Theory of Statistical Inference, Wiley, 1971.
Jun Shao, Mathematical Statistics, 2nd Ed., Springer, 2003.
T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach,Academic Press, 1967.
Population and samples; Parametric and non-parametric models; Exponential and location-scale families; Sufficiency and minimal sufficiency; Complete statistics; Unbiased and UMVU estimation; Asymptotically unbiased estimators; Method of moments; Bayes estimators; Invariance; admissibility of Bayes rule; Minmax Theorem Maximum Likelihood Estimation. consistency and efficiency. UMVU estimators and their properties. Application to normal and exponential one and two sample problems. Information inequality(multiple parameter case) Invariance. Simultaneous estimation. Stein's phenomenon, Shrinkage estimation.
References:
E. L. Lehmann, Theory of Statistical Inference, Wiley, 1983.
S. Zacks, The Theory of Statistical Inference, Wiley, 1971.
Jun Shao, Mathematical Statistics, 2nd Ed., Springer, 2003.
T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach,Academic Press, 1967.
PhD. Supervisor (if decided)
Prof. N. Hemachandra
Proposed Research Plan (if decided)
Essays on payment systems