Syllabus for M.Sc in Statistics

Session: 2003-2004

The M. Sc course in Statistics is spread over one academic year which is divided into two semesters - Semester I offering 18 credit hour courses and Semester II offering 22 credit hour courses. The M. Sc course is divided into three groups- General group (Gr-A), Project group (Gr-B) and Thesis group (Gr-C). A student of group A will have to take all the courses of Semester-I and courses STA-521, STA-521L, STA-528 and any other two courses including their labs of Semester-II. They will also have to appear at the viva-voce of semester-II. A student of Group-B will have to take all the courses of Semester-I and courses STA-521, STA-521L, STA-528, STA-530 and any other two courses of Semester-II excluding their labs. They will also have to appear at the Viva-voce of Semester-II. A student of Group-C will have to take all the courses of Semester-I and courses STA-521, STA-521L, STA-528, STA-529 and any other two courses of Semester-II excluding their labs. 

Selection of optional courses must be approved by the Department and choice of Thesis  Group and Project Group students will be made by the department.  A student is to pass 40 credits to obtain the M.Sc. degree. Following are the courses:

 Semester I

Course No.

Course Title

    Hours/Week

   (Theory+Lab.)

            Credits

STA-511

Statistical Inference

4 + 0

4.0

STA-511L

Statistical Inference (Lab)

0 + 4

2.0

STA-512

Design and Analysis of Experiments

4 + 0

4.0

STA-512L

Design and Analysis of Experiments (Lab)

0+ 4

2.0

STA-513

Sampling Techniques

0+ 3

3.0
STA-513L Sampling Techniques (Lab)              0+2                   1.0

STA-510

Viva-Voce

0 + 0

2.0

 

Total

8 + 13

18.0

 

 Semester II

Course No.

Course Title

    Hours/Week

    (Theory+Lab.)

Credits

STA-521

Multivariate Analysis

4 + 0

4 .0

STA-521L

Multivariate Analysis (Lab)

0 + 4

2 .0

STA-522

Econometrics

4 + 0

4 .0

STA-522L

Econometrics  (Lab)

0+ 4

2.0

STA-523

Bio-Statistics

4 + 0

4.0
STA-523L   Bio-Statistics (Lab)              0+4               2.0
STA-524  Biometrics              4+0               4.0
STA-524L  Biometrics(lab)              0+4              2.0
STA-525  Advanced Demography              4+0              4.0
STA-525L  Advanced Demography (Lab)              0+4               2.0
STA-526  Stochastic Processes              4+0               4.0
STA-526L  Stochastic Processes (Lab)              0+4               2.0
STA-527  Analysis of Contingency Table & Non    Linear Modeling              4+0               4.0
STA-527L  Analysis of Contingency Table & Non  Linear Modeling(lab)              0+4               2.0
STA-528  Research Methodology              2+0               2.0
STA-529  Thesis              0+6               6.0

STA-530

Project

 0 + 4

4.0

STA-520

Viva-Voce

0 + 0

2 .0

 

Total

16 + 24

22

 

 

 

SEMESTER I

  STA-511 STATISTICAL INFERENCE

Theory: 4Hours/Week 4 Credits

 Point Estimation:

Classical Approach: Principles of point estimation. Exponential family of distributions. Sufficiency, complete sufficient statistic, minimal sufficient statistic. Factorization theorem. Unbiased estimation, locally unbiased estimate. Efficient estimator. Consistent estimator. Cramer-Rao inequality. Rao-Blackwell theorem. Uniformly minimum variance unbiased estimator (UMVUE). Lehmann & scheffe theorem for finding UMVUE.

Asymptotic properties of maximum likelihood estimators. Fisher’s information. Concept of mixture distribution and estimation procedure. Generalized linear models.

Location and scale invariance.

Bayesian Approach: Conjugate family of prior densities. Vague prior knowledge. Loss function. Risk function, Bayes risk, Bayes estimation. Admissible estimator.

Pitman`s estimator for location & scale parameters.

 Interval Estimation: Central and noncentral confidence intervals. General method of finding confidence intervals. Confidence interval for large samples. Joint intervals for several parameters. Bayesian interval. 

Test of Hypothesis: Review of sample hypothesis and test criteria. MP and UMP tests. Unbiasedness and consistency of tests.

Principles of LR test and its applications. Asymptotic distribution of LR statistic. Sequential probability ratio test. Comparison with fixed sample size test. OC function. ASN function.

Nonparametric methods: Sign test, run test, rank sum test, Kruskal-Wallis test, Kolmogrov one sample and two-sample test. 

 BOOKS RECOMMENDED:      

1.    Barnet V  Comparative statistical inference (2nd edn),  Wiley, New York

2.    Beaumont  Intermediate mathematical statistics, Chapman and Hall, London

3.    Hogg & Craig Probability and statistical Inference, Maxwell Macmillan International

4.    Larson Introduction to Probability theory and statistical inference, Wiley , New York

5.    Lehman Testing statistical hypothesis , Wiley, New York

6.    Lehman L E Theory of point estimation, Wiley, New york

7.    Mood, Grabyl & Boes introduction to the theory of statistics, McGraw Hill, New York

8.   Saxena H C & Surendran P U Statistical Inference, S Chand & Company India

9.   Siegel  S & Cartellan N J Nnparametric statistics, McGraw Hill, New York

10.  Wald A Sequential analysis, Wiley, New York

11.   Zacks S Theory of statistical inference, Wiley, New York

12.   Mc Cullagh and Nelder Generalized linear models, Chapman and Hall

 

STA-511L STATISTICAL INFERENCE (Lab)

Lab: 4Hours/Week, 2 Credits

 Estimation of parameters (with estimated standard error) by different methods under classical and Bayesian.

Construction of confidence interval and Bayesian interval.

Power function and power curves, SPRT test. Nonparametric tests.

 

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STA-512 DESIGN AND ANALYSIS OF EXPERIMENTS

Theory: 4Hours/Week, 4 Credits

 Two-way non-orthogonal designs. Least squares estimation and analysis. Extensions to multi-way designs

Weighting design: Method of estimation. Use of incomplete blocks, construction and analysis of BIB designs, incomplete block design as weighting designs (Intra and inter-block analysis). Missing plot. Orthogonal latin squares. Youden squares. Lattice designs. Partially balanced incomplete block designs. 

 Factorial experiment: Sn factorial experiments and their analysis. Confounding, complete, partial and simultaneous confounding. Fractional replicates and their construction. Asymmetric factorial experiments.

 Analysis of covariance: Analysis of covariance of non-orthogonal data in two-way classification. Two-step least squares and Analysis of covariance with one and more than one ancillary variables. Covariance and analysis of experiments with missing orbs. transformation.  

 Designs for Bio-assays and Response surfaces: 1st and 2nd order designs. Steepest ascent and canonical equations. Elements of optimal designs. 

Multivariate analysis of variance:Introduction. Omnibus MANOVA tests. Analysis and interpreting MANOVAs.Causal models underlying MANOVA analysis. Complex designs.

 

Booked Recommended:

  1.        P.W.M.John-Statistical Deign and Analysis of Experiments, Mac-Millan.

  2. D.Montgomery – Design and Analysis of Experiments, Wiley.

  3. Cochran and Cox-Experimental Designs, Wiley.

  4. Yates- Factorial Experiment.

  5. Chakrabarty, Laha and Roy- Handbook of Statistics, Vol.II, Wiley.

  6. Seber- Linear Regression Analysis, Wiley.

  7. Sllvey-Optimal Designs.

  8. Searle, S.R.-Linear Models,John Wiley,1971

  9. Federer, W.T.-Experimental Designs

  10. Das M.N. & Giri, N.C.- Design and Analysis of Experiments

  11. Banerjee, K.S.(1962): Weighting design 2nd Edition

  12. Lewis Beck, M.S. (1990): Experimental Design & Methods. SAGE Publication,Vol.3

  

STA-512L DESIGN AND ANALYSIS OF EXPERIMENTS (Lab)

Lab: 4Hours/Week, 2 Credits 

Analysis of non-orthogonal designs, BIBD,PBIBD, Youden square and others design. Analysis of Sn factorial experiments, their confoundings, fractional replicates. Analysis of covariance. Designs for Bio-assays and Response surfaces. Multivariate analysis of variance

 

STA-513 SAMPLING TECHNIQUES

Theory: 3Hours/Week, 3 Credits         

PPS sampling. Comparison with sampling with equal probabilities. Selection of clusters with unequal probability without replacement. Horvitz-Thompson estimator and its standard error. Brewer and Durbin’s methods of selection of sample of size2. Raj, Murthy, Rao-Hartley and Cochran and Samford’s methods of selection. PPS systematic selection. Estimation and standard errors. 

Musltistage sampling - two and three stage-Equal and unequal clusters. Selection of units with equal and unequal probability with or without replacement. Self-weighting estimates.

 Double sampling with PPS selection. Double sampling for stratification, ratio, regression and difference estimations, Repetitive surveys. Sampling on two or more occasions.

 Sampling errors and nonsampling errors. Different methods of estimating nonsampling errors. Nonresponse, interviewer`s bias, interpenetrating subsamples. Familiarity with recent sample surveys in Bangladesh.

 

BOOKS RECOMMENDED :

1  Cochran  Sampling techniques

2  Des Raj Sampling theory

3  Des Raj Sampling designs

4  John & Smith  New developments in survey sampling

5  Kish L  Survey sampling

6  Sukhatme Sampling theory of surveys with application

 

STA-513L SAMPLING TECHNIQUES (Lab)

Lab: 2Hours/Week, 1 Credits

 Estimates and standard errors for sample selected with unequal probabilities. Two or more stage sampling (equal and unequal clusters). PPS sampling. Double sampling. Self weighting estimates.

 

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SEMESTER II

 

 

STA-521 MULTIVARIATE ANALYSIS

Theory: 4Hours/Week, 4 Credits

 Multivariate distributions: Hotelling T2 . Mahalanobish`s  D2 .  Wishart distribution.

Multivariate data: Types of data, unifying concepts, classification of multivariate techniques, data representation. Similarity, dissimilarity and distance. Two dimensional representation of multivariate data. Minimum spanning tree.

Descriptive methods: Principal component analysis. Scaling methods: metric and nonmetric scaling. Correspondence analysis. Canonical correlations.

Parametric methods: Model based multivariate methods. Multivariate normal distribution, estimation and hypothesis testing. Tests for  multivariate normality. Multivariate regression- fitting, inference, adequacy. Multivariate analysis of variance. Multivariate analysis of covariance. Covariance selection. Factor analysis. Discrimination and Classification, Clustering.

  

BOOKS RECOMMENDED:

1. Anderson T W,An introduction to multivariate statistical analysis, John Wiley,  New York

2. Bock R D ,Multivariate statistical methods in behavioural research, McGraw Hill, New York

3. Chatfield C& Collins A J , Introduction to multivariate analysis, Chapman and Hall, London

4. Cureton E E &D’Agostino R B  Factor analysis: an applied approach, Lawrence Erblaum, New Jersy

5. Everitt B S ,Cluster analysis (2nd edn) Heinemann, London

6. Everitt B S ,An introduction to latent variable models, Chapman and Hall,London

7. Greenacre M  Theory and applications of correspondence analysis, Academic  Press, Orlando, Florida

8. Hand D J ,Discrimination and classification

9. Johnson R A & Wichern D W, Applied multivariate statistical analysis, Practice Hall, New Jersey

10. Krzanowski W J Principles of multivariate analysis- a user’s perspective, Oxford University Press, Oxford

11. Manly B F J,  Multivariate statistical methods- a primer, Chapman and  Hall, London

12. Mardia K V, Kent J J& Bibby J M,  Multivariate analysis , Academic Press, New York

13. Morrison , Multivariate statistical methods, McGraw Hill, New York

14. Rao C R , Advanced statistical methods in biometric research, John Wiley, New York

 

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STA-521L MULTIVARIATE ANALYSIS (Lab)

Lab: 4Hours/Week, 2 Credits

 

Behran-Fisher’s test. Test of equality of mean vectors. Test of zero population dispersion matrix.  Principal component analysis. Discriminant analysis and classification.

 

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 STA-522  ECONOMETRICS

Theory: 4 Hours/Week, 4 Credits

 Econometric Modelling: The traditional view on econometric modelling, Leamer’s and Hendry’s approaches to model selection, Testing of non nested hypotheses. 

Dynamic Econometric Model: Lagged variables, Autoregressive and distributed lag-models, Koyck approach to distributed lag-model.

 Models of Simultaneous Relationships: Simultaneous-equation models, Structural and reduced form models, Recursive model, Identification problem, Instrumental variable, ILS, 2SLS and 3SLS methods of estimation.

 Estimating the Parameters of a Set of Error Related Economic Relations: A seemingly unrelated regressions (SUR) model and its estimation, Combining time-series and cross-sectional data.

 Time Series Econometrics: Stationary, Unit root tests, Spurious regression, Cointegration and error correction mechanism, Vector autoregressive (VAR) models, estimation of VAR models, Vector error correction model, Granger causality, Box-Jenkins methodology.

 Nonlinear Least Squares: Nonlinear models, Principles of nonlinear least squares estimation, Properties of the Nonlinear least squares estimator.

 The Bayesian Approach to Estimation and Inference: Concepts and Applications.

 Books Recommended:

Griffiths, W.E. et al: Learning and Practicing Econometrics, John Wiley & Sons, Inc., New York.

Gujarati, Damodar N.: Basic Econometrics, 3rd ed., McGraw-Hill, Inc., New York. 

Maddala, G.S.: Introduction to Econometrics, 2nd ed., Prentice-Hall, Inc., Sydney.

Johnston, J. and DiNardo, J.: Econometric Methods, 4th ed., The McGraw-Hill Companies, Inc., New York.

Enders, W.: Applied Econometric Time Series, John Wiley & Sons, Inc., New York.

Judge, George G. et al.: The Theory and Practice of Econometrics, 2nd ed., John Wiley & Sons, Inc., New York.

Kmenta, Jan.: Elements of  Econometrics, 2nd ed., Macmillan Publishing Company, New York.

Judge, George G. et al.: Introduction to the Theory and Practice of Econometrics, 2nd ed., John Wiley & Sons, Inc., New York.

Pindyck, R.S., and D.L. Rubinfeld: Econometric Models and Economic Forecasts, 3rd ed.,  McGraw-Hill, Inc., New York.

Chow,Gregory C.: Econometrics, McGraw-Hill, Inc., New York. 

 

STA 522L: ECONOMETRICS (Lab)

Lab: 4 Hours/Week, 2 Credits

 Testing of nonnested hypotheses, Fitting distributed lag models, Detecting autocorrelation in distributed lag models, Identification problem, Fitting of simultaneous-equation models using ILS and 2SLS methods, Tests of stationarity, Estimating cointegration regression, Estimation of VAR models and Granger causality test, Fitting of AR, MA and ARIMA models.

 

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STA-523 BIO-STATISTICS

Theory: 4Hours/Week 4 Credits

 Bio-statistics Overview: Roots, Development and Scope of the discipline, Current focuses and Challenges.

Basic Quantities: Lifetime, Density function, Survival function, Hazard function, Mean residual life function, Interrelationships, Median lifetime. Censoring, Truncation, Right and Left censoring, Type-I and Type-II censoring, Random censoring. Lifetime distributions- Exponential, Gamma, Weibull, Log-normal and Extreme value. 

Nonparametric Methods: Estimation of Survival function, Hazard function, Reduced sample method, Kaplan-Meier or Product limit method, Actuarial method, Estimation and Standard error. Gehan test, Mantel Haenszel Test, Logrank test. 

Parametric Methods: Likelihood construction for censored and truncated data, Inference procedures for Exponential, Gamma, Weibull, Log-normal and Extreme value distribution for complete and censored data.

 Regression and Proportional Hazards Models: Parametric regression models-Exponential and Weibull regression models, proportional hazards models, conditional, marginal and partial likelihood, Logistic regression, Polytomous Logistic regression, Probit models, Estimation and Test of hypotheses.

 Generalized Linear Models (GLIM): Introduction, Fitting of GLIM, Quasi-likelihood, Estimating equations, Generalized Estimating equations (GEE), Self-consistency and EM algorithm. Loglinear Models.

 Competing Risks Theory: Concepts, Crude, Net, Partial crude probabilities, their interrelationships and Estimation. Application of Competing Risks to Current Mortality Data.

 Clinical Trials: Objectives, Protocol of Clinical Trials, Parallel, Crossover and Sequential design. Drug trials: Phase I, Phase II, Phase III and Phase IV, Randomization, Bias, Error, Sample size and Power.

 BOOKS RECOMMENDED:

  1. A.J. Dobson. An introduction to generalized linear models. Chapman & Hall.

  2. S. Piantadosi. Clinical trials: A methodological perspective. Wiley.

  3. J.D. Kalbfleisch and R.L. Prentice. The statistical analysis of failure time data. Wiley.

  4. D.R. Cox and D. Oakes. Analysis of survival data. Chapman & Hall.

  5. J.F. Lawless. Statistical models and methods for lifetime data. Wiley.

  6. R.C. Elandt-Johnson and N.L. Johnson. Survival models and data analysis. Wiley .

  7. D.G. Altman. Practical statistics for medical research. Chapman & Hall.

  8. P. McCullagh and J.A. Nelder. Generalized linear models. Chapman & Hall.

  9. J.P. Klein and M.L. Moeschberger. Survival analysis: Techniques for censored and truncated data. Springer.

 

STA-523L BIO-STATISTICS (Lab)

Lab: 4Hours/Week 2 Credits

 Fitting of parametric models with complete and censored samples: Exponential, Gamma, Weibull distribution, Graphical methods for survival distribution, Estimation and Tests, Goodness of fit tests.

Nonparametric methods: Reduced sample, Actuarial and Product-Limit methods, estimation and Tests.

Competing risks: Estimation of crude, net and partial crude probabilities, Application of competing risks to current mortality data.

 Logistic regression, application of parametric regression, proportional hazards models.

 

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STA-524 BIOMETRICS   

Theory: 4Hours/Week, 4 Credits

 Generalised linear model: Introduction. Fitting a generalised linear model using maximum likelihood. Goodness of fit and analysis of deviance. Linear logistic and probit models. Bioassay, Parallel line assays, slope ratio assays, quantal response assays.  Estimation of LD50. Fieller’s theorem. Relative potency. Log linear models. Contingency table.

Agricultural experimentation: Field experiments. Block and plot size and shape. Guard rows. Discard areas. Uniformity trials. Soil heterogeneity. Nearest neighbor methods. Intercropping. Competition.

Response surface: Nature of linear and nonlinear response surfaces. Selecting an appropriate type of model.  Fitting linear and nonlinear response surfaces.

Ordered categorical data analysis: Sources. Review of relevant methods of inference. Proportional odds models and Mann-Whitney test. Continuation ratio models and log-rank test. Linear models for ordered  categorical data. Model checking. Sample size calculations. Power and robustness.                  

Clinical trials: Protocol for clinical trials. Parallel group and cross over designs. Allocation to treatment. Sample size determination. Design of clinical trials. Monitoring a clinical trial. Test statistics. Sequential designs. Analysis after a sequential trial. Stratification and covariate adjustment. Applications. Accuracy of theory.

Epidemiological studies: Basic designs for epidemiological studies. Relative risk and odds ratio. Confounding and interaction. Analysis of data from cohort studies using proportional hazards model. Poisson regression model for the analysis of rates. Analysis of data from case-control studies using linear logistic model. Diagnostics for model checking. Matched case-control studies and the use of conditional logistic regression models.

 

BOOKS RECOMMENDED:

1.    Agresti A ,Analysis of ordered categorical data, Wiley, New York

2.   Aitken M, Anderson D A, Statistical modelling in GLIM, Clarendon Press, London

      Francis B & Hinde J P

3.   Box G E P, Hunter W E & Statistics for experiments, John Wiley, New York

      Hunter J S

4.   Box G E P & Draper N R Empirical model and response surfaces, Wiley, New York

5.   Breslow N E & Day N E Statistical methods in cancer research, Vol.I: The analysis of case-control studies, Vol.II The design and analysis of cohort studies, Oxford University Press, Oxford

6.  Collet D  Modelling binary data, Chapman and Hall, London

7.  Cox D R & Snell E J , Analysis of binary data (2nd edn), Chapman and Hall, London

8.  Dobson A J An introduction to generalized linear models, Chapman and  Hall, London

9.  Dyke G V , Comparative experiments with field crops, Griffin, London

10. Everitt B S, The analysis of contingency tables, Chapman and Hall, London

11. Fienberg S E,The analysis of cross classified categorical data, MIT Press, Cambridge, Massachusetts

12. Gomez K A 7 Gomez A, A Statistical procedure for agricultural research, John Wiley, New  York

13. Khuri A I & Comell J A , Response surface, Marcel Decker

14. Lilienfeld A M & Lilienfeld D F   Foundations of epidemiology, Oxford University Press, Oxford

15. McCullagh P & Nelder J A,Generalized Linear models, Chapman and Hall, London

16. Mead R,The design of experiments, Cambridge University Press, Cambridge

17. Pocock S J ,Clinical trials: a practical approach, Wiley, New York

18. Schlesselman J J , Case-control studies: design, conduct, analysis, Oxford University Press, Oxford

19. Whitehead J , The design and analysis of sequential clinical trials, Chichester: Ellis Horwood, England

 

STA-524L BIOMETRICS (Lab)      

Lab: 4Hours/Week, 2 Credits

 Lab: Fitting of linear logistic and probit models. Tests of goodness of fit. Estimation of LD50. Confidence interval for LD50. Relative potency. Loglinear models for contingency table.

Uniformity trials. Soil heterogeneity. Bivariate analysis of intercropping exeperiments.

Fitting linear and nonlinear response surfaces.

Parallel group and cross over designs.

Proportional odds models and Mann-Whitney test. Continuation ratio models and logrank test.

Relative risk and odds ratio.

 

 

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STA-525 ADVANCED DEMOGRAPHY 

Theory: 4Hours/Week, 4 Credits

 

Sources of population data: Concept of traditional and non-traditional sources of demographic data in Bangladesh. Procedure of Sample Registration System in BBS plan. Chandra- Sekhar- Deming method. Procedure for frame preparation of population data. Population policy in Bangladesh.

 Fertility : Basic concepts of fertility and its related measures. Indirect method of estimation viz P/F ratio method, Parity progression ratio, Gompertz model, Chandra-Sekhar-Deming method. Bongaart`s proximate determinants of fertility and estimation of its indices. Pattern of transition in developing countries.

 Morbidity and mortality : Basic concepts of morbidity and its different measures. Level and trend in mortality in developing countries especially in Bangladesh. Techniques involve in the estimation of infant, child, adult and maternal mortality. Mathematical models in mortality. Graduation of mortality curves.

 Life table : General idea of ordinary life table, properties and interrelationships.  

UN model life tables, Coale-Demeny model life table. Brass logit life table system,

Greville`s formula and Read & Merrell's formulae for construction of an abridged life table. Sampling distribution of life table functions. Estimation of survival probability by the method of maximum likelihood.

 Stable Population theory: Concept of stable, semi stable and stationary population. Stable age distribution. Interrelationships of demographic variables in stable population. Intrinsic rate of natural increase. Mean length of generation. Lotka`s integral equation and solution for intrinsic rate of growth. Net maternity function. Graduation of net maternity function.

 Population projection : Computational procedure for projecting Population by component method. Development of Leslie projection matrix, Forward and Backward operation of population projection. The momentum of population growth.

 Some demographic models: Nuptiality models- Coale's parameters of nuptiality, Coale- Mc Nicol model .

Migration models- Push-pull hypothesis, Ravenstein's  Seven laws of migration, Lee's theory of migration

 

 BOOKS RECOMMENDED

1. Barclay G W, Techniques of population analysis, Wiley, New York

2.   Biswas S, Stochastic processes in demography and applications, Wiley Eastern, India

3.   Bouge D J, Principles of demography, Wiley, New York

4.   Coale A J & Demny P, Regional model life tables and stable population, Princeton University Press, New York

5.   Cox D R, Demography, Cambridge University Press, Cambridge

6.   Journals: Population studies, Demography, Population and Development review, Studies in family planning, ESCAP population journal, GENUS, Biosocial science, Journal of family welfare.

7.   Keyfitz, N, Introduction to the mathematics of population, Wiley, New York

8.   Keyfitz, N, Applied Mathematical Demography, Wiley, New York

9.   Pollard J H, Matheamtical models for the growth of human populations, CambridgeUniversity Press, Cambridge

10. Rogers A, Introduction to Multi-regional Mathematical demography, Wiley Inter science, New York

11.  Shryock H, Siegel J, The method and materials of demography, Academic Press, New York

12.  UN publications, Manual IV and Manual X, Population Bulletins, Population Debate.

13.  UNFPA (1993), Population Research Methodology, vols: 1-10, Chicago

 

STA-525L ADVANCED DEMOGRAPHY (Lab)

Lab: 4Hours/Week, 2 Credits

Application of various indirect techniques for estimating fertility, mortality, marriage and migration. Problems and issues related to population growth. Problem of construction of abridged life table, UN model life table. Projection of fertility and mortality, Population projection, Application of UN model life table in population projection.

 

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 STA-526 STOCHASTIC PROCESSES

Theory: 4Hours/Week, 4 Credits

 Queueing Theory: Introduction. Preliminaries: Cost equations, Steady-state probabilities. Exponential models: A single-server exponential queueing system, A single-server exponential system having finite capacity. A shoeshine shop, A queueing system with bulk service. Network of queues: Open systems, Closed systems, The system M/G/I. Variations on the M/G/I. The model G/M/I. Multiserver queues: Erlang's loss system. The M/M/k queue, The G/M/k queue, The M/G/k queue.

Renewal processes: Introduction, Distribution of N(t), Limit theorem and their applications, Renewal reward processes, Regenerative processes: Alternating renewal processes, Semi-Markov processes, The inspection paradox, Computing the renewal function.

Martingales: Filtration, Martingales, Stopping times, Sub-martingales, Super-martingales, Optional Stopping theorem, Doob's Martingale Inequalities, Doob's Martingale Convergence theorem, Uniform Integrability and L' Convergence of Martingales.

Brownian Motion: Definition and Basic properties, Increments of Brownian Motion, Sample paths, Doob's Maximal L2 Inequality for Brownian Motion, Geometric Brownian Motion, Integrated Brownian Motion, Brownian Motion with drift.

Ito Stochastic Calculus: Ito Stochastic Integral: Definition. Properties of the Stochastic Integral, Stochastic Differential and Ito Formula, Stochastic Differential Equations.

 

Books Recommended:

  1. G.R. Grimmett and D.R. Stirzaker. Probability and Random Processes, Oxford Science Publications.

  2. R.B. Ash. Real analysis and Probability, Academic Press.

  3. N.T.J. Baily, The Element of Stochastic Processes, Wiley.

  4. M.S. Bartlett, An Introduction to Stochastic Processes, Wiley.

  5. P. Billingsley, Probability and Measure, Wiley.

  6. K.L. Chung, Elementary Probability Theory with Stochastic Processes.

  7. D.R. Cox and W. Miller, The Theory of Stochastic Processes, Chapman and Hall.

  8. S. Karlin and H.M. Taylor, A First Course in Stochastic Processes, Academic Press.

  9. H.M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, Academic Press.

  10. S.M. Ross, Introduction to Probability Models, Academic Press.

  11. S. Ross, Stochastic Processes, Wiley.

  12. U.N. Bhat, Elements of Applied Stochastic Processes, Wiley.

  13. Zdzislaw Brzezniak and Tomasz Zastawniak -Basic Stochastic Processes-Springer-Verlag London limited 1999.

  14. Lawrence C. Evans-An Introduction to Stochastic Differential Equations Version-1.2, Department of Mathematics, UC Berkley.

  15. Ioannis Karatzas, Steven E. Shreve- Brownian  Motion and Stochastic Calculus, Springer-Verlag New York Inc. 1988.

  16. Steven Shreve- Stochastic Calculus and Finance, Lecture Notes, Oct. 6, 1997.

 

STA-526L STOCHASTIC PROCESSES (Lab)

Lab: 4Hours/Week, 2 Credits

The Syllabus for the course will be designed by the course teacher.

 

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STA-527 Analysis of cross-classified categorical data and multilevel modeling

Theory: 4 Credits / Lab: 2 Credits

 

Introduction to cross-classified categorical data: The analysis of categorical data. Forms of multivariate analysis. Two dimensional tables: The model of independence. The loglinear model. Sampling models. The cross-product ratio and 2´2 tables. Interrelated two-dimensional tables. Three dimensional tables: The general loglinear model. Estimated expected values. Iterative computation of expected values. Goodness-of-fit statistics. Hierarchical models. Selection of a model: General issues. Conditional test statistics. Partitioning chi-square. Using information about ordered categories. Four- and higher-dimensional contingency tables: The loglinear models and MLEs for expected values. Using partitioning to select a model. Stepwise selection procedures. Looking at all possible effects. Fixed margins and logit models: Logit models and ordered categories. Linear logistic response models. Logistic regression vs. discriminant analysis. Polytomous and multivariate response variables. Casual analysis involving logit and loglinear models: Path diagrams. Recursive systems of logit models. Nonrecursive systems of logit models. Fixed and random zeros: Sampling zeros and MLEs in loglinear models. Incomplete two-dimensional contingency tables. Incompleteness in several dimensions.

Introduction to multilevel data: Multilevel data. Sample survey methods. Repeated measures data. Event history models. Discrete response data. Multivariate models. Nonlinear models. Measurement errors. Random cross classifications. Structural equation models. Levels of aggregation and ecological fallacies. Two-level: The 2-level model and basic notation. Parameter estimation for the variance components model. The general 2-level model including random coefficients. Estimation for the multilevel model. Other estimation procedures. Residuals. The adequacy of Ordinary Least Squares estimates. Checking model assumptions. Checking for influential units. Higher level explanatory variables and compositional effects. Hypothesis testing and confidence intervals. Fixed parameters. Random parameters. Residuals. Variance structure: Complex variance structures. Variances for subgroups defined at  level 1. Variance as a function of predicted value. Variances for subgroups defined at higher levels. A 3-level complex variation model. Parameter Constraints. Multilevel: Multivariate Multilevel models. The basic 2-level multivariate model. Rotation Designs. Nonlinear models: The models. Nonlinear functions of linear components. Estimating population means. Nonlinear functions for variances and covariances. Examples of nonlinear growth and nonlinear level 1 variance. Multivariate Nonlinear Models. Modeling linear components. Modeling variances and covariances as nonlinear functions. Likelihood values. Repeated measures: Models for repeated measures. A 2-level repeated measures model. Discrete response: Models for discrete response data. Proportions as responses. Models for multiple response categories. Models for counts. Ordered responses. Mixed discrete – continuous response models.

 

STA-527L Analysis of cross-classified categorical data and multilevel modeling (Lab)

Theory: 4 Credits / Lab: 2 Credits

Framingham longitudinal study of coronary heart disease.  Test for associations and continuity correction in two-dimensional tables. The loglinear model.Iterative computation of expected values in two- and higher dimensional tables. Partitioning of chisquares. Parameter estimation for the variance components model. Model fitting for the general 2-level model including random coefficients. Hypothesis testing and confidence intervals. Complex variance structures.

Books Recommended:

  1. Aitkin,M., Anderson,D., Francis,B. and Hinde,J. (1989). Statistical Modelling in GLIM. Oxford, Clarendon Press.

  2. Beaton, A.E. (1975). The Influence of Education and Ability on Salary and Attitudes. In F. T. Juster (ed), Education, Income, and Human Behavior. New York, McGraw-Hill.

  3. Bishop, Y.M.M., Fienberg, S.E., and Holland, P.W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, Massachusetts, and London, The MIT Press.

  4. Bliss, C.I. (1967). Statistics in Biology, Vol. 1. New York, McGraw-Hill.

  5. Bock, R.D. (1975). Multivariate Analysis of Qualitative Data. New York, McGraw-Hill.

  6. Bryk,A.S., and Raudenbush,S.W. (1992). Hierarchical Linear Models. Newbury Park, Sage.

  7. Cochran,W.G. (1983). Planning and Analysis of Observational Studies. New York, Wiley.

  8. Cook,R.D.and Weisberg,S. (1982). Residuals and Influence in Regression. London, Chapman and Hall.

  9. Duncan, O.D. (1975). Structural Equations Models. New York, Academic Press.

  10. Fienberg, S.E. ((1980). The Analysis of Cross-classified Categorical Data. Cambridge, Massachusetts, and London, The MIT Press.

  11. Fleiss, J.L. (1973). Statistical Methods for Rates and Proportions. New York, John Wiley.

  12. Fuller, W.A. (1987). Measurement Error Models. New York, Wiley.

  13. Gokhale, D.V. and Kullback, S. (1978). The Information in Contingency Tables. New York, Marcel Dekker.

  14. Goldstein,H. (1979). The Design and Analysis of Longitudinal Studies, London, Academic Press.

  15. Goldstein,H. (1987b). Multilevel Models in Educational and Social Research. London, Griffin.

  16. Haberman, S.J. (1978). Analysis of Qualitative Data. Volume 1: Introductory Topics. New York, Academic Press.

  17. McCullagh,P. and Nelder,J. (1989). Generalised Linear Models (2nd edition), London, Chapman and Hall.

  18. Plackett, R.L. (1974). The Analysis of Categorical Data. London, Griffin.

  19. Searle,S.R., Casella,G. and McCulloch,C.E. (1992). Variance Components. New York, Wiley.

  20. Skinner,C.J., Holt,D. and Smith,T.M.F (1989). Analysis of Complex Surveys, Chichester:Wiley.

 

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STA 528:  RESEARCH METHODOLOGY

Theory: 2 Hours/Week, 2 Credits

 Approaches to knowledge, Definition of Research, Assumptions, operations and aims of  Scientific Research.

The Research Process: Conceptual, Empirical and Analytical Phases of Research;

Elements of Research: Concepts, Definitions, Variables, Hypotheses, Theory and Fact

Formulating Research Problem: Features of a Good Research

Types of Research: Formulative, Descriptive, Explanatory, Exploratory, Evaluative, and Methodological Research

Formulating Research Hypotheses:  Sources of Hypotheses, Relevance of Theory in Hypotheses Formulation, Conceptual Frameworks

Research Design: Definition of Research Design, Components of Research Design; Sampling: Choice of correct sampling methods and Sample Size determination.

Methods of Data Collection: Interview Method, Mail Method, Telephone Surveys; Questionnaire Design and Construction - Types of Questions, Framing of Questions, Sequencing Questions, Construction of a Model Questionnaire for Collecting Basic Demographic and Socio-economic Data (with examples from DHS); Qualitative Methods of Data Collection - Observation, In-depth Interviews, Case Studies, Focus Group Discussions; Key Informant Interview

Planning and Implementation of Research Study, Time and Financial Budgeting, Logistics of Data Collection - Recruitment and Training of the Interviewers, Fieldwork Supervision and Controlling the Quality of  Data. Data Processing and Analysis: Editing, Coding, Data Entry, Validation check, Imputation of Variables, Tabulation Plan, data analysis.

Report Writing: Types of Reports, Design and Structure of Reports, Introductory Section, Main Body, Concluding Section, Tables and Graphical Presentations, References and Bibliography.

 

Books Recommended:

 

1.  C. R. Kothari: Research Methodology- Methods and Techniques

 

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