1. A total of 60 credits are to be completed for M. Sc. Degree in Statistics.
2. Six optional courses may be registered form ST-401 to ST-414. However, in case a student registers Course ST-411 then he has to register four other courses from ST-401 to ST-414. The courses offered in other departments can be registered by a student instead of Courses ST-401 to ST-414 with the consent of the Chairperson.
Probability as a set function, Conditional Probability and Bayes’ theorem, Chebychev’s inequality, Random variables, Distribution function and probability density function, Joint distributions and probability density functions of two or more random variables, Marginal and conditional distributions, Stochastic independence, Mathematical expectations, Conditional expectations, Variance and moments, Probability generating functions, Moment generating functions, Characteristics function and their existence properties. Relation between moments and cumulants, Standard Probability distributions, Binomial, Poisson, Hypergeometric, Multinomial, Negative Binomial, Geometric, Uniform, exponential, Beta, Gamma and Normal distributions and their moment generating and characteristic functions, Bivariate Normal distribution, Transformation of variables, Cumulative distribution function and moment generating function techniques, Weak and strong laws of large numbers, Central limit theorem. Practical: Construct of Probability and Probability Distribution for univariate and bivariate cases. Fitting of Poisson, Binomial, Negative Binomial and Gamma Distributions.
BOOKS RECOMMENDED
Stuart, A. and Ord, J. K. Kendalls, Advanced Theory of Mathematical Statistics (volume I), Charles Coriffi & co., London (1998).
Mood, A. M, Graybill, F A. and Boes, D.C. Introduction to the Theory of Statistics, McGraw Hill, New York (1997).
Khan, M. K. Probability with Applications, Maktiba Ilmi, Lahore Pakistan (1996).
Hogg, R. M. and Craig, A. T. Introduction to Mathematical Statistics, MacMillan Co., New York (1995).
Scheaffer, R. L. Introduction to Probability and its Applications, PWS-Kent (1990).
Ho. Cacoullous, T. Exercises in Probability Theory, Springer-Verlag (1989).Feller, W. An Introduction to Probability Theory and its Applications, John Wiley & Sons (1986).
Population, Sample, Parameter, Statistic, Applications of Binomial, Poisson and Normal Distributions, Basic Sampling Distributions (Chi square, T and F), Type I and II errors, confidence interval, estimation, testing, simple and composite hypotheses about means, proportions, variances, regression coefficient and correlation coefficients, power and O.C. Functions, one and two-way analysis of variance, goodness of fit test, Independence in contingency tables, tests of normality and randomness, Diversity Indices, Introduction to the use of one statistical packages-like MINITAB, SPSS, BMDP etc.
BOOKS RECOMMENDED
Steel, R. and Torrie, J. H. Principles and Procedures of Statistics, McGraw Hill, (1997).
Zar, J. H. Biostatistical Analysis, Prentice-Hall, Int. (1993).
Dixon, W.J. and Massey, F. J. Introduction to Statistical Analysis, McGraw Hill, (1983).
Snedecor, G. and Cochran, W. G. Statistical Methods, Iowa State Press, (1962).
Introduction, Simple random sampling, Sampling proportions and percentages, The estimation of sample size, Estimation of parameters for subdomains, Stratified sampling, Allocations of sampling units, Post stratification, Quota sampling, Attribute proportion estimation for a stratified population, Ratio estimation, Regression estimation, Systematic sampling, Sampling with probability proportional to size, Cluster sampling. Practical: Matlab, Mathematica, R and SAS packages will be used to analyse the real data sets under different sampling scheme.
BOOKS RECOMMENDED
Cingi, H and Kadilar, C. Advances in Sampling Theory-ratio method of estimation, Bentham Sciences Publisher (2009)
Sampath, S. Sampling Theory and Methods 2nd edn., Narosa Publishing House (2005).
Sharon, L. L. Sampling Design and Analysis, Duxbury Press, (1999).
Sukhatme, P. V., Sukhatme, B. V., Sukhame, S., and Asok, C. Sampling Theory of Surveys with Applications, Iowa State Uni. Press (1984).
Singh, R., and Mangat, N. S. Elements of Survey Sampling, Kluwer Academic Publishers (1996).
Singh D. and Chaudhary, F. S. Theory and Analysis of Sample Survey Designs, Jhon Wiley & Sons (1986).
Cochran, W. G. Sampling Techniques, Jhon Wiley & Sons (1977).
Counting techniques, Combinations & Permutations, Review of Matrices and Vectors, Matrix Differentiation, Eigenvalues, Eigenvectors and their Properties, Positive definite matrix, semi positive definite matrix, Introduction to quadratic forms, Maximization of Quadratic Forms, Variance-Covariance matrix, Partitioned Matrices, Rank of Matrix. Gamma and Beta functions with their applications, Line integrals, transformation of coordinates (Cartesian & Polar), Change of variables in multiple integrals, Extrema of functions of two variables, Orthogonal polynomials, Complex exponential, Fourier series and Fourier Transforms, Laplace Transforms and their applications, Geometrical interpretation of multiple integrals.
BOOKS RECOMMENDED
Richard, A. Johnson & Dean, W. Wichern Applied Multivariate Statistical Analysis (1998).
Mood, A. M. Grabill, F.A., & Boes, D.C. Introduction to the Theory of Statistics, McGraw-Hill, (1997).
Hogg, R. M. & Craig, A. T. Introduction to Mathematical Statistics, Prentice Hall (1995).
Kaplan, W. C. Advance Calculus, Addison and Wiley, (1984)
Introduction to a programming/language, Random numbers generation, Multiplicative congruential method, Solution of linear equations and matrix computations, Non-Linear equations, Univariate and multivariate roots, Interpolations, Numerical differentiation and integration: Newton cotes formulae, Minimization and maximization methods, especially the steepest gradient method. Practical: Developing soft code for random number generation, soft code for matrix computation, computations for Min/Max., loop structure for integration.
BOOKS RECOMMENDED
Chambers, J. Software for Data Analysis: Programming with R, Kindle Edit. (2008).
Karris, S, T. Numerical Analysis using MATLAB and Excel, 3rd Edit. Orchard Publications (2007).
Froberg, C. E. Numerical Mathematics: Theory and Computer Applications, Benjamin Cunnings (1985).
Conte, S. D. Elementary Numerical Analysis Algorithmic Approach, McGraw Hill (1980).
Ralston, A.and Rabinowitz, P. A First Course in Numerical Analysis, McGraw Hill, (1979).
Knuth, D. E. The Art of Computer Programming, Fundamental Algorithms (1973).
Kuo, S. S., Computer Applications of Numerical Methods, Addison Wesley (1972).
Moment generating and characteristic functions, properties of Cauchy , Laplace, Weibull, Maxwell, Pareto, Raleigh and Log normal distributions with applications in various fields. Inversion and uniqueness theorems, Convolution of Distributions. Order Statistics, Distribution of rth & sth order Statistic, distribution of median, range and quantiles, Methods of deriving exact sampling distribution for a population. Independence of sample mean & variance, Central and Non-central t, F and chi-square distributions, Distribution of Quadratic Forms, Distributions under linear constraints, Standard error of estimates in large samples (Varience, St. Dev. & Corr. Coeff.), Truncated Distributions.
BOOKS RECOMMENDED
Bickel, P. J. & Docksum, K. A. Mathematical Statistics Holden Day Inc (1997).
Hogg, R. T. & Craig, A. T. Introduction to Mathematical Statistics. Macmillan Co. (1995).
Stuart, A. & Ord, J. K. Kedalls Advanced Theory of Mathematical Statistics (volume I), Charles Griffen & Co., London (1991).
Scheaffer, R. L. Introduction to Probability and its Applications, PWS-Kent (1990).
Ho. Cacoullous, T. Exercises in Probability Theory, Springer-Verlag (1989).
Beiman, Probability and Stochastic Process McMillan & Co., London (1986).
Principles of experimental design, Layout analysis and related efficiency of completely randomized, randomized complete block, Latin square, Cross-over and Greco Latin square designs, Estimation of missing observations in three basic designs, Fixed, random and mixed effect models in the basic designs, Factorial experiments, Analysis up to 23 factorial experiments, Multiple comparisons, Effect of violation of assumptions underlying ANOVA and transformation of data, Analysis of covariance up to two covariates. Practical: Practically structuring lay-out plan of basic experiments techniques, collection of data, estimation of parameters and statistical analysis on collected data.
BOOKS RECOMMENDED
Clarke, G. M. Kempson, R. E. Introduction to the Design & Analysis of Experiments, Edward Annold (1997).
Montgomery, D. C. Design and Analysis of Experiments, John Wiley, New York (1997).
Boniface, D. R. Experiment Design & Statistical Methods, Chapman & Hall (1995).
Clarke, G. M. Statistics & Experimental Design, Edward Annold (1994).
Mead, R. The Design of Experiments. Cambridge University Press, Cambridge (1988).
Gometz, K. A. & Gometz, A. A. Statistical Procedures for Agricultural Research. John Wiley, New York (1984).
Hicks, C. R. Fundamentals Concepts in Design and Analysis of Experiments. Saunders (1982).
Properties of a good estimator, unbiased, consistent, sufficient, efficient, complete, Minimum variance unbiased estimator, Rao-Black well and Lehmann Sheffe theorem with applications, Cramer-Rao inequality, Methods of Estimation, Maximum likelihood, moments, least squares, minimum chi-square and Bayesian, Estimates based on order observations, Simultaneous confidence intervals.
BOOKS RECOMMENDED
Mood, A. M. Graybill, F. A. & Boes, D. C. Introduction to the Theory of Statistics, McGraw Hill, (1997).
Staurt. A. & Ord. K. Kendall’s Advanced Theory of Statistics (Vol-II), Charles Griffing and Co. (1994).
Lehmann, E. L. Testing Statistical Hypotheses. John Wiley, New York (1986).
Hirai, A. S. Estimation of Statistical Parameters, Ilmi Kitab Khana, Lahore, Pakistan (1973).
Introduction of survey sampling: The purpose of Survey, the development of standardized Questioning, the development of Sampling Methods, the development of data collection. Inference and errors in Surveys, Measurement error, Processing errors, Coverage error, Sampling error, Non-response error. Sampling frames, Sample design, Simple random sampling, Cluster Sampling, Stratification and stratified sampling, Systematic selection, Two stage cluster designs, Methods of data collection, Non-response in sample surveys, Evaluation of survey questions, Survey Interviewing, Post Collection processing of survey data. Probability proportional to size sampling (PPS).
Note: Students are required to conduct a small scale survey as part of this course.
Practical: Students will learn MINITAB, SAS, SPSS and R packages for analysis.
BOOKS RECOMMENDED
Groves, R. M., Fowler, F. J., Couper, M. P., Lepkowski, J. M., Singer, E. and Tourangeau, Survey Methodology 2nd edn., Jhon Wiley & Sons (2009).
Levy, P. S. and Lemeshow, S., Sampling of Populations: Methods and Applications 3rd edn., Jhon Wiley & Sons (1999).
Casley, D. J. and Kumar, K., The Collection, Analysis and Use of Monitoring and Evaluation Data, Jhon Hopkin Press (1988).
Cochran, W. G., Sampling Techniques, Jhon Wiley & Sons (1977).
Murthy, M. N., Sampling Theory and Methods. Statistical Publishing Society (1967).
Simple linear regression: Assumptions and least squares estimates, General linear model: Least squares solution, test of hypotheses and confidence intervals about parameters, Residual Analysis: Testing and dealing with heteroscedasticity and auto-correlation, Solutions to mulitcollinearity, Introduction to dummy variables. Practical: Computer based statistical analysis on a huge set of data, handling auto correlation, multicollinearity, and conducting principal component analysis using R, Excel or other statistical tools.
BOOKS RECOMMENDED
Barreto, H. and Howland, F. M., Introductory Econometrics Using MC Simulation with MsExcel, Cambridge University Press (2006).
Gujrati, D., Basic Econometrics, 4th edn., John Wiley & Sons,. (2003).
Johnston, J., Econometric Method 4th edn., McGraw Hill, (1997).
Draper, N. R. and Smith, H. Applied Regression Analysis, 3rd edn., John Wiley & Sons(1998)
Montgomery, D. C., and Peck, E. Introduction to Linear Regression Analysis, John Wiley & Sons (1982).
Wooldridge, J. M., Introductory Econometrics, 4th edn., Thomson South-Western (2006).
Stock, J. and Watson, Introduction to Econometrics, 2nd edn., Addison Wiely (2008).
Factorial Experiments, 2n, 3n and mixed levels factorial experiments: model, estimation of parameters with applications, Linear, quadratic and higher order components of main effects and interactions, Confounding and its types, fractional replication, Introduction to Quasi-Latin squares, Split-plot and split block designs, Balanced Incomplete Block Design (BIB): Balanced Lattices, Balanced Incomplete Designs, Lattice squares, Euden Square; models and Analysis, Partially balanced incomplete block designs: models and analyses recovery of inter block information, 1st and 2nd order response surface designs, their models and applications.
Practical: Conducting statistical analysis of factorial experiments, interaction, confounding, split-plot design, and incomplete block design etc., using computer softwares like R, with a huge set of data.
BOOKS RECOMMENDED
Montgomery, D. C. Design and Analysis of Experiments, John Wiley, New York (1997).
Clarke, G. M. Kempson, R. E. Introduction to the Design & Analysis of Experiments, Edward Annold, (1997).
Boniface, D. R. Experiment Design & Statistical Methods, Chapman & Hall (1995).
Clarke, G. M. Statistics & Experimental Design, Edward Annold (1994).
Mead, R. The Design of Experiments. Cambridge University Press, Cambridge (1988).
Dad, M. N., & Giri, N. C. Design and Analysis of Experiment, John Wiley, New York, (1986).
Gometz, K. A., & Gometz, A. A. Statistical Procedures for Agricultural Research, John Wiley, New York (1984).
Hicks, C. R. Fundamental Concepts in Design and Analysis of Experiments. Saunders (1982).
Neyman-Pearson Theorem, Uniformly most powerful tests, Likelihood ratio tests, The sequential probability ratio test, Interval estimation and confidence sets, Relation between testing and confidence intervals, asymptotic testing, estimation, confidence intervals, optimality criteria, consistency.
BOOKS RECOMMENDED
Barloszynski, R. & Niewladomska-Bugaj M. Probability and Statistical Inference, John Wiley (1996).
Hogg, A.V. Probability and Statistical Inference. McMillan Co. (1995).
Stuart, A. & Ord, K. Kendall’s Advanced Theory of Statistics (Vol. II), Charles Griffin and Co, (1994).
Mood, A. M. Grabill, F. A. and Boes, D. C. Introduction to the Theory of Statistics, McGraw Hill (1974).
Statistical quality control: measurement and control of quality, control charts for P, X, R, Sigma, C and U., O.C. curves associated with control charts, CUSUM Charts, Leaf and Stem plots, Box Plot, Producer’s risk and consumer’s risk, Acceptance sampling: single and double sampling plans, introduction to multiple sampling plans, Intentional quality standards and their certification, Quality management through quality circles, re-engineering etc., Case Study. Practical: Computer simulation based experiments on techniques discussed in theory.
BOOKS RECOMMENDED
1. Montgomery, D. C. Introduction to Quality Control, John Wiley and Sons (1994).
Begchi, T. P. ISO 9000 Concepts, Methods and Implementations, (1994).
Ryan. T. P. Statistical Methods for Quality Improvements, John Wiley & Sons (1989).
Grant, E. L. & Leavenworth, R. S. Statistical Quality Control (1980).
Polynomial regression: orthogonal polynomials, Use of instrumental, lagged and dummy variables. Model selection: Simple to general (S2G) and general to specific (G2S), Step-wise regression, GLM, Dummy dependent variables: Logit and probit models, Poisson regression models, Generalized least square, Panel data analysis, Introduction to Monte Carlo simulation and Bootstrap simulation, Seemingly unrelated regression. Instrumental variables, Simultaneous equations models, Two-stage and three–stage least squares, Generalized method of moments. Practical: Experiments about model selection, step-wise regression, logit and probit models, Monte Carlo simulation and Bootstrap simulation etc., using some statistical tool like R.
BOOKS RECOMMENDED
Green, W. H., Econometrics Analysis, 6th edn. Prentice Hall (2009).
Wooldridge, J. M., Introductory Econometrics, 4th edn., Thomson South-Western (2006).
Stock, J. and Watson, M., Introduction to Econometrics. 2nd edn., Addison Wiely (2008).
Draper N. R. and Smith, H. Applied Regression Analysis, 3rd edn., Jhon Wiley & Sons (1998).
Population and Demographic Methods, Sources of Demographic data, Testing of accuracy of demographic data, Basic demographic measures, Life tables, Population estimates and projections, Application of Stationary Population Models.
Official Statistics: Statistical Systems in Pakistan, Statistics Divisions and Bureaus of Statistics: their functioning and publications.
National Accounts: measures of production, income and expenditure, The national income and product, Gross Domestic product, Saving and Wealth, Index Numbers Social Indicators.
BOOKS RECOMMENDED
Govt. of Pakistan, Provisional Results of Fifth Population and Housing Census held in March 1998, P.C.O. Islamabad.
Abel, A. B. & Bermake, B. S. Macroeconomic, Addison-Wesly Publishing Company, New York (1995).
Rukanuddin A. R. Farooqi, N. M. L. The State of Population in Pakistan-NIPS Islamabad. (1987).
Pollard, A. H. Yausaf, F. Pollard, Demographic Techniques, Pergaman Press (1982).
Speigleman, M. Introduction to Demography, Cambridge University Press, Revised Edition (1968).
Publications of Statistics Division I, State Bank of Pakistan, provisional Bureaus of Statistics and other Departments.
Braclay, G. W. Techniques of Population Analysis, John Wiley, New York.
Utility, rewards, consequences and decision function, Game theoretic interpretation of Statistical estimation and testing, Admissibility of Bayesian procedures, the complete class theorem, the minimax theorem, Randomization in one game theory, difference from Bayesian approach, Invariance and minimaxity, admissibility of invariant rules, Location and scale invariance, Pitman estimators.
BOOKS RECOMMENDED
Berger, J. O. Statistical Decision Theory & Bayesian Analysis, Springer Verlag (1985).
Lindgern, B. W. Elements of Decision Theory, Macmillan, New York (1971).
DcGroot, M. H. Optimal Statistical Decisions, McGraw-Hill (1970).
Blackwell, D. & Grishick, M. A. Theory of Games and Statistical Decision, John Wiley, New York (1966).
Stochastic Process, Stationery time-Series: auto-correlation and auto-covariance, estimates functions and standard error of the auto-correlation function (ACF), Spectral Analysis: Periodogram, spectral density functions, comparison with ACF, Linear stationery models: Auto-regressive, Moving average and mixed models, Non-stationery models, general ARIMA notation and models, Introduction to forecasting, important considerations for forecasting: objective, cost function, model specification, forecast construction using ARMA models, forecasting trend, other types of forecast: exponential smoothing, Forecast Evaluation: recursive estimation, model specification, model comparison and testing. Spurious Regressions, introduction to cointegration, Error correction representation, Granger representation theorem.
Practical: Statistical analysis on Auto-regressive models, moving average models, ARMA models, forecasting and smoothing and error correction, using huge set of data with computer softwares.
BOOKS RECOMMENDED
Chatfield, C., The Analysis of Time Series: An Introduction, Chapman and Hall (1996).
Box, G. E. P., Jenkins, G. M. and Reinsel, C. G., Time-Series Analysis, Forecasting and Control, 4th edn., Person Education (2009).
Walter, E., Applied Time Series Econometrics 3rd edn., Addison Wiely (2010).
Diebold, F. X., Elements of Forecasting with Economic Applications Card and Info. Trac, 4th edn., South-Western College Publishing (2008).
Granger, C. W. J., Forecasting in Business and Economics, 2nd edn., Academic Press (1989).
Multivariate Normal Distribution, Distribution of linear function of normal variates, Distribution of Quadratic forms, Wishart distribution, Hotelling’s T2-distribution, Canonical variate Analysis, Discriminant Analysis, Principal Component and Factor Analysis, Factor analysis versus principle component analysis, Cluster Analysis, MANOVA.
Practical: Fitting a multivariate Normal distribution, Wishart distribution, Hotelling’s T2-distribution. Statistical analysis on huge data set for Discriminant Analysis, Principal Component and Factor Analysis using computer softwares.
BOOKS RECOMMENDED
Richard A. Johnson & Dean. W. Wichern Applied Multivariate Statistical Analysis, Prentice Hall (1998).
R. Gnanadesikan Methods for Data Analysis of Multivariate observations, (2nd Ed.) John Wiley and Sons (1997).
Anderson T. W. An Introduction to Multivariate Statistical Analysis. John Wiley, (1985).
Chatfield, C. & Collin, A. J. Introduction to Multivariate analysis, Chapman and Hall (1980).
Mardia, K.V. & Kent, J. T. and Bibby J. M. Multivariate Analysis, Academic press (1979).
Morrison, D. F. Multivariate Statistical Methods (2nd Ed.) McGraw Hill (1979).
Evritt, B. J. Cluster Analysis, McGraw Hill (1974)
Historical study of operation research, Linear Programming: Methods to solve LP models, The simplex methods: Degeneracy and cycling, artificial variables, Further topics in linear programming: Duality, the dual simplex method, sensitivity analysis, Methods of solving transportation and assignment problems, Game theory, Network analysis: Solution of CPM and PERT problems by mathematical methods and using CP model queuing theory.
Practical: Solution of LP models, sensitivity analysis, transportation models, assignment models, network models and queuing models, Using TORA, GAMS and Excel.
BOOKS RECOMMENDED
Taha, H. A. Operation Research, Macmillan, London, (1998).
Bhatti, S.A. & Bhatti, N. A. Operations Research, An Introduction, A-one publishers, Lahore (1998).
Gupta, P. K. & Hira,, D. S. Operations Research, S. Chand & Co., New Delhi (1994).
Hillier, F. & Lieberman, G. Introduction to Operations Research, Holden-Day (1992).
Sposity, V. A. Linear Programming with Statistical Applications, Iowa State University Press (1985).
Wagner, H. M. Principle of Operation Research with Applications to Managerial Decisions, Prentice Hall (1975).
Prior information, Prior distributions, Methods of elicitation of prior distributions, Posterior distributions: The posterior means, medians (Bayes estimators under loss functions) and variances of univariate and bivariate posterior distributions, Non informative priors: Methods of elicitation of non-informative priors, Bayesian Hypotheses Testing: Bayes factor; The highest density region; Posterior probability of the hypothesis.
BOOKS RECOMMENDED
O. Hagan A. Kendall’s Advanced Theory of Statistics (Vol. 2B), Bayesian Inference, Cambridge, The University Press (1994).
Bernardo, J. M. & Smith, A. F. M., Bayesian Theory, John Wiley, New York (1994).
Lee, P. M. Bayesian Statistics, An Introduction, Oxford University Press, New York (1991).
Berger, J. O. Statistical Decision Theory and Bayesian analysis (2nd Ed.), New York, Springer-Verlag (1985).
Box, G. E. P & Tiao, G. C. Bayesian Inference in Statistical Analysis, Reading Addison-Wesley (1973).
Survival data, censoring, covariates, basic distribution theory, survival function, hazard function; Special distributions: exponential, extreme value, Weibull, gamma and log logistic distributions with special reference to survival analysis, ML inference for parametric model with single sample, Non-Parametric estimation of survival function; life table method, Product-limit method; diagnostic plots; K-sample non-parametric tests, Modeling dependence on covariates: proportional hazard model; Weibull model; accelerated life models, log logistic model; Graphical methods for checking models, Inference for semi-parametric proportional hazards model, Time-dependent covariates; grouped survival times; several types of failure.
BOOKS RECOMMENDED
Muller, R. G. & Xian Zhou, Survival Analysis with long-term Survivors, John Wiley, New York (1996).
Parmer, M. K. B & Maclin, D. Survival Analysis, A Practical Approach, John Wiley, New York (1995).
Lee, E. T. Statistical Methods for Survival Data Analysis, John Wiley, New York (1992).
Yamaguchi K. Event History Analysis, Newbury Park, Sage (1991).
Cox D. R. & Oakes D. Analysis of Survival Data, Chapman and Hall, (1984)
R. G. Miller Survival Analysis, John Wiley, New York (1981).
Kalbfleisch, J. D. & Prentice R. L. The Statistical Analysis of Failure Time Data, John Wiley & Sons, New York (1980).
Lawless, J. F. Statistical Models and Methods for Life Time Data, John Wiley, New York.
A practical statistical project involving non-trivial statistical methodology. The project may stress a phases of the statistical process from the design aspects or data collection to data analysis and the complete analysis must be written in a formal way. A good review of literature.
Definition of Biostatistics, viz-a-viz the type of variables and observations in biological, health and medical sciences, uniqueness in terms of behavior of variables their domain, and units; Categorical, numerical and censored data. Populations, Target populations and samples; Role of Sampling in biostatistics, Size of Sample of various type of studies, Proportions, rates and ratios; incidence, prevalence and odds.
Distributional behaviour of biological variables (Binomial, Poisson and Normal), Role of transformation for analysis of biological variables. Probit and logit transformations and their analysis, Evolution of p values, its importance and role. Confidence interval in simple and composite hypothesis testing.
Multivariate Models: Binary logistic regression, Introduction Multiple Logistic Regression. Proportional Hazard Model. Methods of Survival data analysis, Kaplan Maier Estimates.
BOOKS RECOMMENDED
Zar, J. (2000). Biostatistical Analysis, 5th Edition, John Wiley and Sons.
Shoukri, M. M. & Pause, C. A. (1998). Statistical Method for Health Sciences. 2nd Edition, CRC Press, Florida.
Daniel, W.W. (1996) Biostatistics: A foundation for the Health Sciences, 6th Edition, John Wiley, New York.
Dunn, G. and Everit, B. (1995) Clinical biostatistics. Edward Arnold, London.
Rosner, B. (1994). Fundamentals of Biostatistics, 4th Edition, Duxbury, Duxbury Press.
Zolman, J. F. (1993). Biostatistics: Experimental Design and Statistical Inference, Oxford University Press, New York.
Lee, E. T. (1992) Statistical Methods for Survival Data Analysis. 2nd Edition, John Wiley, New York.
Altman, G. (1991). Practical Statistics for Medical Research. Chapman & Hall, London.
Application of multilevel models; Multilevel data structures; Linear multilevel and logistic multilevel models; Random intercept and random slope models; Contextual effects and cross level interactions; Diagnostic checking and model specification; Binary response models; Repeated measures analysis and non-nested data.
Note: The course will have a practical emphasis with computer workshops.
BOOKS RECOMMENDED
Snijders, T and Bosker, R. (2012): An Introduction to Basic and Advanced Multilevel Modelling, Sage Publications, London.
Background and Motivation: Types of Data, Basic Properties, Preliminary Concepts (Spatial Structures and Modeling), Objectives and Applications, Challenges. Spatial processes, Classical methods used for Prediction and interpolation of spatial processes. Characterizing spatial process: the Assumption of stationary in spatial process. Estimation and modeling of spatial correlations: Estimating variogram. Fitting parametric models: Matern family of covariance models. Generalized linear models for geostatistical data: poisson linear model, Binomial logistics linear model, spatial survival analysis and Cox Processes. Parameter estimation: Maximum likelihood estimation and restricted maximum likelihood estimation. Prediction and Kriging based on Lagrange multiplier approach.
BOOKS RECOMMENDED
Diggle P. J. (2006), Model-Based Geostatistics, Springer.
Le N.D. and Zidek J.V. (2006), Statistical Analysis of Environmental Space-Time Processes, Springer.
Webster R. and M.A. Oliver (2007), Geostatistics for environmental scientists, 2nd edition, John wiley & sons Ltd.
Cressie N. (1993). Statistics for Spatial Data. Wiley & Sons.
Banerjee S., Carlin B. P. and Gelfand A.E. (2004). Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall.
Haining R. P. (2003), Spatial Data Analysis: theory and practice, University Press, Cambridge.
Untitled Document
Department of Statistics, Quaid-i-Azam
University Islamabad, 45320, Pakistan.
