Name of the Programme: M.Sc. in Biostatistics

Total duration: 2years

Scope: Bio-Statistics has emerged as an important branch of statistical sciences and it helps strengthening research in the disciplines of biology, biomedical sciences, health sciences, veterinary and animal sciences. This course is an interdisciplinary postgraduate course combining statistics, bioinformatics, epidemiology and health sciences. The students will be trained in softwares such as SPSS, SAS and R. The course will enable the students to become biostatisticians, bio statistical programmers, SAS programmers, consultants and research associates in industry, hospitals and research departments.

Pattern of course (Semester/annual): Semester

Mode of teaching (Regular/distant): Regular

Language of teaching: English

Colleges/ Institutions offering the programme with number of seats at each college

Eligibility for admission:Bachelor’s degree in Statistics/Mathematics with statistics as subsidiary subject

Mode of selection and admission: Entrance exam and interview

Seat reservations:

Syllabus (Provide as a separate document)/ Link to Syllabus in case of VCI& AICTE

Mode of evaluation: Internal

Attendance requirement: 80%

- Fee structure (semester wise)on as on …………………………. (Date) (as per prospectus 2020)

Name of Programme | Sem 1 | Sem 2 | Sem 3 | Sem 4 |
---|---|---|---|---|

M.Sc. in Biostatistics | 60250 | 52100 | 55200 | 52100 |

**SYLLABUS OF MASTER OF SCIENCE IN BIOSTATISTICS**

**MAJOR**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 511 | Probability Theory | 2+0 |

2 | BSTAT 513 | Statistical Inference | 2+1 |

3 | BSTAT 514 | Demography | 1+1 |

4 | BSTAT 515 | Operations Research | 2+1 |

5 | BSTAT 521 | Sampling Techniques | 2+1 |

6 | BSTAT 522 | Experimental Designs | 2+1 |

7 | BSTAT 523 | Data analysis using SPSS, R and SAS | 1+2 |

8 | BSTAT 524 | Statistical Genetics and Biological Assays | 2+1 |

9 | BSTAT 531 | Survival Analysis | 2+1 |

10 | BSTAT 532 | Multivariate Analysis | 2+1 |

11 | BSTAT 533 | Stochastic Processes | 2+0 |

12 | BSTAT 534 | Time series Analysis | 1+1 |

13 | BSTAT 535 | Regression Analysis | 1+1 |

14 | BSTAT 541 | Statistical Quality control | 2+0 |

15 | BSTAT 542 | Actuarial Statistics | 2+0 |

16 | BSTAT 543 | Statistical computing | 1+1 |

Total |
40 |

** Minor**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 519 | Epidemiology | 2+0 |

2 | BSTAT 529 | Bioinformatics | 2+1 |

3 | BSTAT 539 | Clinical Trials | 1+0 |

Total |
6 |
||

Supporting |
|||

1 | BSTAT 512 | Statistical Methods | 2+1 |

Total |
3 | ||

1 | BSTAT 591 | Seminar | 1 |

2 | BSTAT 599 | Research and dissertation | 10 |

Total |
11 |

**Semester-wise course distribution**

**Semester I**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 511 | Probability Theory | 2+0 |

2 | BSTAT 512 | Statistical Methods | 2+1 |

3 | BSTAT 513 | Statistical Inference | 2+1 |

4 | BSTAT 514 | Demography | 1+1 |

5 | BSTAT 515 | Operations Research | 2+1 |

6 | BSTAT 519 | Epidemiology | 2+0 |

Total |
15 |

**Semester 2**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 521 | Sampling Techniques | 2+1 |

2 | BSTAT 522 | Experimental Designs | 2+1 |

3 | BSTAT 523 | Data analysis using SPSS, R and SAS | 1+2 |

4 | BSTAT 524 | Statistical Genetics and Biological Assays | 2+1 |

5 | BSTAT 529 | Bioinformatics | 2+1 |

Total |
15 |

**Semester 3**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 531 | Survival Analysis | 2+1 |

2 | BSTAT 532 | Multivariate Analysis | 2+1 |

3 | BSTAT 533 | Stochastic Processes | 2+0 |

4 | BSTAT 534 | Time series Analysis | 1+1 |

5 | BSTAT 535 | Regression Analysis | 1+1 |

6 | BSTAT 539 | Clinical Trials | 1+0 |

7 | BSTAT 591 | Seminar | 1 |

Total |
14 |

**Semester 4**

Sl.No. | Catalogue No. | Course Name | Credits |
---|---|---|---|

1 | BSTAT 541 | Statistical Quality control | 2+0 |

2 | BSTAT 542 | Actuarial Statistics | 2+0 |

3 | BSTAT 543 | Statistical computing | 1+1 |

4 | BSTAT 599 | Research and dissertation | 10 |

Total |
16 |

** Total credit load = 60**

**BSTAT 511 PROBABILITY THEORY 2+0**

**Objective**

This is a fundamental course in Statistics. This course lays the foundation of probability theory, random variable, probability distribution, mathematical expectation, etc. which forms the basis of basic statistics.

Theory

UNIT I

Basic concepts of probability.Elements of measure theory: class of sets, field, sigma field, minimal sigma field, Borel sigma field in R, measure, probability measure. Axiomatic approach to probability.definitions of probability. Properties of probability.Addition and multiplication theorems.Conditional probability and independence of events.Bayes theorem.

UNIT II

Random variables: definition of random variable, discrete and continuous, functions of random variables. Probability mass function and Probability density function, Distribution function and its properties. Notion of bivariate random variables, bivariate distribution function and its properties.Joint, marginal and conditional distributions.Independence of random variables. Transformation of random variables (two dimensional case only).

UNIT III

Mathematical expectation: Mathematical expectation of functions of a random variable. Raw and central moments and their relation, covariance, skewness and kurtosis.Addition and multiplication theorems of expectation.Definition of moment generating function, cumulant generating function, probability generating function and statements of their properties.

UNIT IV

Conditional expectation and conditional variance.Characteristic functionand its properties.Inversion and uniqueness theorems.Functions, which cannot be characteristic functions.Chebyshev, Markov, Cauchy-Schwartz, Jenson, Liapounov, holder’s and Minkowsky’s inequalities.Sequence of random variables and modes of convergence (convergence in distribution, in probability, almost surely, and quadratic mean) and their interrelations.Statement of Slutsky’s theorem.Borel –Cantelli lemma and Borel 0-1 law.

UNIT V

Laws of large numbers: WLLN, Bernoulli and Kintchin’s WLLN. Kolmogorov inequality, Kolmogorov‘s SLLNs.

Central Limit theorems: Demoviere- Laplace CLT, Lindberg – Levy CLT, Liapounov CLT, Statement of Lindeberg-Feller CLT and simple applications. Definition of quantiles and statement of asymptotic distribution of sample quantiles.

**Suggested Readings**

Ash RB. 2000. Probability and Measure Theory. 2nd Ed. Academic Press.

Billingsley P. 1986.Probability and Measure.2nd Ed. John Wiley.

Capinski M &Zastawniah. 2001. Probability Through Problems. Springer.

Dudewicz EJ & Mishra SN. 1988. Modern Mathematical Statistics. John Wiley.

Feller W. 1972.An Introduction to Probability Theory and its Applications. Vols. I., II. John Wiley.

Loeve M. 1978. Probability Theory.4th Ed. Springer.

Marek F. 1963. Probability Theory and Mathematical Statistics.John Wiley.

Rohatgi VK &Saleh AK Md. E. 2005.An Introduction to Probability and statistics.2nd Ed. John Wiley.

**BSTAT 512 STATISTICAL METHODS 2+1**

**Objective**

This course lays the foundation of probability distributions and sampling distributions and their application which forms the basis of Statistical Inference. Together with probability theory, this course is fundamental to the discipline of Statistics. The students are also exposed to correlation and regression. Categorical data analysis is also covered in this course.

Theory

UNIT I

Descriptive statistics: probability distributions: Discrete probability distributions, Bernoulli, Binomial, Poisson, Negative-binomial, Geometric and Hyper Geometric, uniform, multinomial , Properties of these distributions and real life examples. Continuous probability distributions rectangular, exponential, Cauchy, normal, gamma, beta of two kinds, Weibull, lognormal, logistic, Pareto.Properties of these distributions.

UNIT II

Concepts of compound, truncated and mixture distributions (definitions and examples).Pearsonian curves and its various types. Sampling distributions of sample mean and sample variance from Normal population, Chi-Square, t and F distributions, their properties and inter relationships.

UNIT III

Concepts of random vectors, moments and their distributions.Bivariate Normal distribution - marginal and conditional distributions.Cochran theorem.Correlation, rank correlation, Regression analysis, partial and multiple correlation and regression.

UNIT IV

Sampling distribution of correlation coefficient, regression coefficient, Categorical data analysis - loglinear models, Association between attributes. Variance Stabilizing Transformations.

UNIT V

Order statistics, distribution of r-th order statistics, joint distribution of several order statistics and their functions, marginal distributions of order statistics, distribution of range, median, etc.

**Practical**

Fitting of discrete distributions and test for goodness of fit; Fitting of continuous distributions and test for goodness of fit; Computation of simple, multiple and partial correlation coefficient, correlation ratio and intra-class correlation; Regression coefficients and regression equations; Analysis of association between attributes, categorical data and log-linear models.

**Suggested Readings**

Agresti A. 2002. Categorical Data Analysis. 2nd Ed. John Wiley.24

Arnold BC, Balakrishnan N &Nagaraja HN. 1992. A First Course in Order Statistics. JohnWiley.

David HA &Nagaraja HN. 2003. Order Statistics. 3rd Ed. John Wiley.

Dudewicz EJ & Mishra SN. 1988. Modern Mathematical Statistics. John Wiley.

Huber PJ. 1981. Robust Statistics. John Wiley.

Johnson NL, Kotz S &Balakrishnan N. 2000.Continuous Univariate Distributions.John Wiley.

Johnson NL, Kotz S &Balakrishnan N. 2000.Discrete UnivariateDistributions.John Wiley.

Marek F. 1963. Probability Theory and Mathematical Statistics.JohnWiley.

Rao CR. 1965. Linear Statistical Inference and its Applications.JohnWiley.

Rohatgi VK &Saleh AK Md. E. 2005.An Introduction to Probability andStatistics.2nd Ed. John Wiley.

**BSTAT 513 STATISTICAL INFERENCE 2+1**

**Objective**

This course lays the foundation of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They would also be given the concepts of nonparametric test procedures.

**Theory**

UNIT I

Concepts of point estimation: MSE, unbiasedness, consistency, efficiency and sufficiency. Statement of Neyman’s Factorization theorem with applications.MVUE, Rao-Blackwell theorem, completeness.Fisher information, Cramer-Rao lower bound and its applications.

UNIT II

Moments, minimum chi-square, least square and maximum likelihood methods of estimation.Interval estimation-Confidence level.CI using pivots and shortest length CI.CI for the parameters of Normal, Exponential, Binomial and Poisson distributions.

UNIT III

Fundamental notions of hypothesis testing-statistical hypothesis, statistical test, critical region, types of errors, test function, randomized and nonrandomized tests, level of significance, power function, most powerful tests: Neyman-Pearson fundamental lemma, MLR families and UMP tests for one parameter exponential families. Concepts of consistency, unbiasedness and invariance of tests. Likelihood Ratio tests, statement of asymptotic properties of LR tests with applications (including homogeneity of means and variances). Relation between confidence interval estimation and testing of hypothesis.

UNIT IV

Notions of sequential vs fixed sample size techniques. Wald’s SPRT for testing simple null hypothesis vs simple alternative.Termination property of SPRT, SPRT for Binomial, Poisson, Normal and Exponential distributions. Concepts of loss, risk and decision functions, admissible and optimal decision functions, estimation and testing viewed as decision problems, conjugate families, Bayes and Minimax decision functions with applications to estimation with quadratic loss.

UNIT V

Non-parametric tests: Sign test, Wilcoxon signed rank test, Run test for randomness, Kolmogorov – Smirnov test for goodness of fit, Median test and Wilcoxon-Mann-Whitney U-test. Chi-square test for goodness of fit and test for independence of attributes. Kruskal –Wallis and Friedman’s tests. Spearman’s rank correlation and Kendall’s Tau tests for independence.

**Practical**

Methods of estimation - Maximum Likelihood, Minimum χ2 and Moments; Confidence Interval Estimation; MP and UMP tests; Large Sample tests; Non-parametric tests, Sequential Probability Ratio Test.

**Suggested Readings**

Box GEP &Tiao GC. 1992. Bayesian Inference in Statistical Analysis.John Wiley.

Casela G & Berger RL. 2001. Statistical Inference. Duxbury ThompsonLearning.

Christensen R. 1990. Log Linear Models. Springer.

Conover WJ. 1980. Practical Nonparametric Statistics. John Wiley.

Dudewicz EJ & Mishra SN. 1988. Modern Mathematical Statistics. John Wiley.

Gibbons JD. 1985. Non Parametric Statistical Inference. 2nd Ed. Marcel Dekker.

Kiefer JC. 1987. Introduction to Statistical Inference.Springer.

Lehmann EL. 1986. Testing Statistical Hypotheses.John Wiley.

Lehmann EL. 1986. Theory of Point Estimation.John Wiley.

Randles RH & Wolfe DS. 1979. Introduction to the Theory of Nonparametric Statistics. John Wiley.

Rao CR. 1973. Linear Statistical Inference and its Applications.2nd Ed .John Wiley.

Rohatgi VK &Saleh AK. Md. E. 2005. An Introduction to Probability and Statistics.2nd Ed. John Wiley.

Rohtagi VK. 1984. Statistical Inference. John Wiley

Sidney S & Castellan NJ Jr. 1988.Non Parametric Statistical Methods for Behavioral Sciences.McGraw Hill.

Wald A. 2004. Sequential Analysis.Dover Publ.

**BSTAT 514 DEMOGRAPHY 1+1**

**Objective**

This course is meant for training the students in measures of demographic indices, estimation procedures of demographic parameters. Students would also be exposed to population projection techniques.

**Theory**

UNIT I

Introduction to vital statistics, crude and standard mortality and morbidity rates, Estimation of mortality; Application and methods of constructing life table, abridged life tables; Increment-Decrement Life Tables.

UNIT II

Stationary and stable populations, Migration, Demographic relations in Nonstable populations. Measurement of population growth, Lotka'smodel(deterministic) and intrinsic rate of growth, Measures of mortality and morbidity, Period and Cohort studies. Population projections

UNIT III

Fertility and reproduction: CBR, GFR, GRR and NRR. Measures of reproduction: total fertility rate, gross reproduction rate, net reproduction rate, replacement index, general fertility models.

**Practical**

Problems based on estimation of crude and standard mortality and morbidity rates. Construction of life tables; Estimation of CBR, GFR, GRR and NRR.

**Suggested Readings**

Cox DR. 1957.Demography.Cambridge Univ. Press.

Everitt BS & Dunn G. 1998.Statistical Analysis of Medical Data. Arnold.

Fleiss JL. 1981. Statistical Methods for Rates and Proportions. John Wiley.

Lawless JF. 1982. Statistical Models and Methods for Lifetime Data. John Wiley.

MacMahon B & Pugh TF. 1970. Epidemiology - Principles and Methods. Little Brown.

Mann NR, Schafer RE &Singpurwalla ND. 1974. Methods for Statistical Analysis of Reliabilityand Life Data. John Wiley.64

Miettinen OS. 1985. Theoretical Epidemiology: Principles of Occurrence

Research in Medicine.John Wiley.

Newell C. 1988. Methods and Models in Demography.Guilford Publ.

Preston S, Heuveline P &Guillot M. 2001.Demography: Measuring and ModelingPopulationProcesses. Blackwell.

Rowland DT. 2004. Demographic Methods and Concepts. Oxford Press.

Siegel JS & Swanson DA. 2004. The Methods and Material of Demography. 2nd Ed. Elsevier.

Woolson FR. 1987.Statistical Methods for the Analysis of Biomedical Data.John Wiley.

**BSTAT 515 OPERATIONS RESEARCH 2+1**

**Objective**

This course is meant to teach the students the concepts involved in Operations Research. They would also be exposed to different models in Operations research and their applications.

**Theory**

UNIT I

Basics of Operational Research: Origin & Development of Operational Research, Definition and Meaning of Operational Research, Different Phases of an Operational Research Study, Scope and Limitations of Operational Research, Mathematical Modelling of Real Life Problems. Linear Programming Problem Formulation, solution by Graphical Method, Theory of Simplex Method, Simplex Algorithm, Two phase Method, Charnes-M Method, Degeneracy, Theory of Duality, Dual-simplex method.

UNIT II

Transportation problem (TP) and its formulation. finding basic feasible solution of TP using North-West Corner Rule, Least Cost and Vogel's Approximation Method, MODI method for finding optimal solution for TP, Assignment problem and its formulation, Hungarian method for solving Assignment problem, Transhipment and Travelling salesmen problem

UNIT III

Introduction to inventory systems, inventory classification and its use in controlling inventory. Deterministic inventory models: Economic order quantity (EOQ) model.

UNIT IV

Queueing Systems: General concepts of a queueing system, measures of performance, arrival and service processes, single and multiple server models, channels in parallel and in series with limited and unlimited queues, Little’s formula, Queues with finite waiting room, Queues with impatient customer(Balking and reneging), Markovian queues- M/M/1 with finite and infinite waiting space, M/M/C, Birth and death queueing systems

UNIT V

Decision making without and with experimentation.Decision Trees.Utility theory. Decision under risk: expected value, expected value - variance, aspiration - level, and most likely future criteria. Decision under uncertainty: Laplace and Minimax (Maxmin) criteria.

UNIT VI

Concepts of Game problem.Two- person zero-sum game. Pure and Mixed strategies. Saddle point and its existence. Project Scheduling: PERT and CPM with known activity times. Critical Path Analysis, Various types of floats. Probability considerations in PERT.Updating of PERT charts.Project crashing.Formulation of CPM as a linear programming problem.Resource levelling and resource scheduling.

UNIT VII

Sequencing problem: Introduction to Sequencing problem. Flow shop problem: Processing n jobs through 2, 3 and m machines. General n/m job-shop problem.

**Practical**

Construction of OR models. LP problems.Inventory control problems.Replacement model problems.Problems on queuing theory.Problems on sequencing.Problems on transportation.Problems on assignment. Problems on PERT/CPM .

**Suggested Readings**

Hamdy A. Taha (2010)Operations Research-An Introduction, Prentice Hall, 9th Edition,

Taha H.A. (1982) Operational Research: An Introduction; Macmillan.

K. R. Sharma. Quantitative techniques and operations research

Srivastatva, U. K. ,Shenoy, G. V. , Sharma, S. C. Quantitative techniques for managerial decisions.

Hillier F.S. and Leiberman G.J. (1962) Introduction to Operations Research; HoldenDay.

KantiSwarup, Gupta, P.K. and Singh,M.M.. (1985) Operations Research; Sultan Chand& Sons.

Philips D.T., Ravindran A. and Solberg J.( ) Operations Research, Principles and Practice.

Mckinsey J.C.C. (1952) Introduction to the Theory of Games; McGraw Hill

Wagner H.M. (1973) Principles of O.R. with Applications to Managerial Decisions;Prentice Hall

Gross, D. and Harris,C.M. (1974) Fundamentals of Queueing Theory; John Wiley

**BSTAT 519 EPIDEMIOLOGY 2+0**

**Objective**

This course is to familiarize students with epidemiological concepts.

**Theory**

UNIT I

Basic concepts and Measures of disease frequency: Epidemiology, Emergence of modern epidemiology, causation and causal inference in epidemiology, measures of effect and association, incidence time, incidence rate, other types of rates, incidence proportions and survival proportions, product-limit and exponential formulas, prevalence, standardization.

UNIT II

Types of experimental studies, types of non-experimental (observational) studies, data collection instruments, data preparation. Precision, validity and accuracy considerations in epidemiologic studies: Precision, validity, internal validity, generalizability, improving precision and validity, source of information on exposure and diseases, prevention of confounding.

UNIT III

Fundamentals of epidemiologic data analysis: Elements of data analysis, data editing, data description and summarization, handling of missing values, methods of significance testing and estimation, confidence intervals, confidence limits, multiple comparisons. Vital and health statistics: Population census, registration of vital events, sample registration system in India, hospital statistics, disease registries.

UNIT IV

Case-control studies: Definition of cases and controls, methods of selecting cases and controls, matching, sources of bias, sample size, power calculations, basic methods of analysis of grouped data, basic methods of analysis of matched data.

Cohort studies: Prospective cohort studies: planning and execution, retrospective cohort, nested case-control, case-cohort studies: planning and execution, cohort studies –statistical analysis.

**Suggested Readings**

K. J. Rothman and S. Geenland (ed.) (1998).Modern Epidemiology, Lippincott-Raven.

S. Selvin (1996). Statistical Analysis of Epidemiologic Data, Oxford University Press.

D. McNeil (1996). Epidemiological Research Methods.Wiley and Sons.

J. F. Jekel, J. G. Elmore, D.L. Katz (1996). Epidemiology, Biostatistics and Preventive Medicine. WB Saunders Co.

**BSTAT 521 SAMPLING TECHNIQUES 2+1**

**Objective**

The students would be exposed to elementary sampling techniques. It would help them in understanding the concepts involved in planning and designing their surveys, presentation of survey data analysis of survey data and presentation of results.

**Theory**

UNIT I

Concept of sampling, sample survey vs complete enumeration, planning of sample survey, sampling from a finite population.

UNIT II

Simple random sampling, sampling for proportion, determination of sample size; inverse sampling, Stratified sampling.

UNIT III

Cluster sampling, PPS sampling, Multi-stage sampling, double sampling, systematic sampling; Use of auxiliary information at estimation as well as selection stages.

UNIT IV

Ratio and regression estimators.Construction and analysis of survey designs, sampling and non-sampling errors; Preparation of questionnaire, Non-sampling errors.

**Practical**

Random sampling ~ use of random number tables, concepts of unbiasedness, variance, etc.; simple random sampling, determination of sample size; Exercises on inverse sampling, stratified sampling, cluster sampling and systematic sampling; Estimation using ratio and regression estimators; Estimation using multistage design, double sampling and PPS sampling.

**Suggested Readings**

Cochran WG. 1977. Sampling Techniques. John Wiley.

Murthy MN. 1977. Sampling Theory and Methods. 2nd Ed. Statistical Publ. Soc., Calcutta.

Singh D, Singh P & Kumar P. 1982. Handbook on Sampling Methods.17 IASRI Publ.

Sukhatme PV, Sukhatme BV, Sukhatme S &Asok C. 1984.Sampling

Theory of Surveys with Applications. Iowa State University Press

and Indian Society of Agricultural Statistics, New Delhi.

**BSTAT 522 EXPERIMENTAL DESIGNS 2+1**

**Objective**

This course is an integrated component of research in almost all sciences. The students would be exposed to concepts of Design of Experiments so as to enable them to understand the concepts involved in planning, designing their experiments and analysis of experimental data.

**Theory**

UNIT I

Need for designing of experiments, characteristics of a good design. Basic principles of designs- randomization, replication and local control.

UNIT II

Analysis of variance; Completely randomized design, randomized block design and Latin square design.

UNIT III

Factorial experiments, (symmetrical as well as asymmetrical), Confounding in symmetrical factorial experiments.

UNIT IV

Split plot and strip plot designs; Analysis of covariance and missing plot techniques in randomized block and Latin square designs; Transformations, crossover designs, balanced incomplete block design, resolvable designs and their applications. Response surfaces.

**Practical**

Analysis of data obtained from CRD, RBD, LSD; Analysis of factorial experiments without and with confounding; Analysis with missing data; Split plot and strip plot designs; Transformation of data; Analysis of resolvable designs; Fitting of response surfaces. Analysis with softwares.

**Suggested Readings**

Cochran WG & Cox GM. 1957. Experimental Designs.2nd Ed. John Wiley.

Dean AM & Voss D. 1999.Design and Analysis of Experiments.Springer.

Federer WT. 1985. Experimental Designs. MacMillan.

Fisher RA. 1953. Design and Analysis of Experiments. Oliver & Boyd.

Nigam AK & Gupta VK. 1979. Handbook on Analysis of Agricultural Experiments. IASRI Publ.

Pearce SC. 1983. The Agricultural Field Experiment: A Statistical Examination of Theory and Practice. John Wiley.

**BSTAT 523 DATA ANALYSIS USING SPSS, R and SAS 1+2**

**Objective**

This course is meant for exposing the students in the usage of various statistical packages for analysis of data. It would provide the students and hands on experience in the analysis of their research data.

**Theory**

UNIT I

Introduction to SPSS, R and SAS: different modules in R and SAS, R and SAS program commands. Use of Software packages for: Summarization and tabulation of data; Descriptive statistics; Graphical representation of data, Exploratory data analysis.

UNIT II

Fitting and testing the goodness of fit of discrete and continuous probability distributions; Testing of hypothesis based on large sample test statistics; Testing of hypothesis using chi-square, t and F statistics.

UNIT III

Concept of analysis of variance and covariance of data for single factor, multi-factor, one-way and multi-classified experiments, contrast analysis, multiple comparison.

UNIT IV

Nonparametric tests: Sign test, Wilcoxon signed rank test, Runs test for randomness, Kolmogorov – Smirnov test for goodness of fit, Median test and Wilcoxon-Mann-Whitney U-test. Chi-square test for goodness of fit and test for independence of attributes. Kruskal –Wallis and Friedman’s tests. Spearman’s rank correlation and Kendall’s Tau tests for independence.

**Practical**

Use of software packages for summarization and tabulation of data, obtaining descriptive statistics, graphical representation of data. Robust Estimation, Testing linearity and normality assumption, Estimation of trimmed means etc., Cross tabulation of data including its statistics, cell display and table format and means for different sub-classifications; Fitting and testing the goodness of fit of probability distributions; Testing the hypothesis for one sample t-test, two sample t-test, paired t-test, test for large samples - Chi-squares test, F test, One way analysis of variance , contrast and its testing, pairwise comparisons.

Bivariate and partial correlation, Linear regression, Multiple regression, Regression plots, Variable selection, Regression statistics, Nonparametric tests: Sign test, Wilcoxon signed rank test, Runs test for randomness, Kolmogorov – Smirnov test for goodness of fit, Median test and Wilcoxon-Mann-Whitney U-test. Chi-square test for goodness of fit and test for independence of attributes. Kruskal –Wallis and Friedman’s tests. Spearman’s rank correlation and Kendall’s Tau tests for independence.

**Suggested Readings**

Anderson CW &Loynes RM. 1987.The Teaching of Practical Statistics.John Wiley.

Atkinson AC. 1985. Plots Transformations and Regression. Oxford University Press.

Chambers JM, Cleveland WS, Kleiner B &Tukey PA. 1983. Graphical Methods for Data Analysis. Wadsworth, Belmount, California.

Chatfield C & Collins AJ. 1980. Introduction to Multivariate Analysis. Chapman & Hall.

Chatfield C. 1983. Statistics for Technology.3rd Ed. Chapman & Hall.

Chatfield C. 1995. Problem Solving: A Statistician's Guide. Chapman & Hall.

Cleveland WS. 1985. The Elements of Graphing Data. Wadsworth, Belmont, California.

Ehrenberg ASC. 1982. A Primer in Data Reduction. John Wiley.

Erickson BH &Nosanchuk TA. 1992. Understanding Data. 2nd Ed. Open University Press, Milton Keynes.

Snell EJ & Simpson HR. 1991.Applied Statistics: A Handbook of GENSTAT Analyses.Chapman & Hall.

Sprent P. 1993.Applied Non-parametric Statistical Methods.2nd Ed. Chapman & Hall.

Tufte ER. 1983. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Conn.

Velleman PF &Hoaglin DC. 1981. Application, Basics and Computing of Exploratory Data Analysis. Duxbury Press.

Weisberg S. 1985. Applied Linear Regression.John Wiley.

Wetherill GB. 1982. Elementary Statistical Methods. Chapman & Hall.

Wetherill GB.1986. Regression Analysis with Applications.Chapman & Hall.

**BSTAT 524 STATISTICAL GENETICS AND BIOLOGICAL ASSAYS 2+1**

**Objective**

This course is meant to prepare the students in applications of statistics in quantitative genetics and breeding. The students would be exposed to the physical basis of inheritance, detection and estimation of linkage, estimation of genetic parameters and development of selection indices.

**Theory**

UNIT I

Basic biological concepts in genetics, Mendel’s law,genetic diseases, Hardy Weinberg equilibrium, Mating tables, estimation of allele frequency (dominant/ co-dominant cases), Approach to equilibrium for X-linked gene. The law of natural selection, mutation, genetic drift, equilibrium when both natural selection and mutation are operative.

UNIT II

Non-random mating, inbreeding, phenotypic assortative mating. Analysis of family data - relative pair data, 1, T, 0 matrices, identity by descent, Family data- estimation of segregation ratio under ascertainment bias, pedigree data-Elston-Stewart algorithm for calculation of likelihoods.

UNIT III

Linkage, estimation of recombination fraction, inheritance of quantitative traits.Models and estimation of parameters.Sequence similarity.Homology and alignment.Algorithms for pairwise sequence alignment and multiple sequence alignment, construction of phylogenetic trees, UPGMA, neighbour joining, maximum parsimony and maximum likelihood algorithms.

UNIT IV

Bioassays- direct and indirect, indirect assays based on quantal dose response, parallel line and slope ratio assays. Logit and Probit analysis.

**Practical**

Test for the single factor segregation ratios, homogeneity of the families with regard to single factor segregation; Detection and estimation of linkage parameter by different procedures. Direct assays.parallel line and slope ratio assays.

**Suggested Readings**

Collett, D (2003). Modelling Binary Data, Chapman & Hall.

Durbin, R., Eddy, Krogh, A. and Mithison, G.(1998). Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids.

Ewens, W.J. (2004). Mathematical Population Genetics, Springer

Finney. D.J. (1971). Statistical Method in Bioassay, Griffin

Govindarajulu, Z (2000). Statistical Techniques in Bioassay, S. Kargar

Lange, K (2002). Mathematical and Statistical Methods for Genetic Analysis, Springer

Nagylaki, T.(1992). Introduction to Theoretical Population Genetics, Springer

Sham, P (1997).Statistics in Human Genetics, Arnold Publications.

**BSTAT 529BIOINFORMATICS 2+1**

**Objective**

Bioinformatics is a new emerging area. It is an integration of Statistics, Computer applications and Biology. The trained manpower in the area of Bioinformatics is required for meeting the new challenges in teaching and research in the disciplines of biological Sciences. This course is meant to train the students on concepts of basic biology, statistical techniques and computational techniques for understanding bioinformatics principals.

**Theory**

UNIT I

Introduction to Bioinformatics:Bioinformatics Overview, Bioinformatics Concepts:- Functional Genomics, Comparative genomics, Structural biology, Medical information, Objectives of Bioinformatics. Applications, Challenges in Molecular biology, Skills required by Bioinformatics, Major databases & tools, Bioinformatics in India.

UNIT II

Genomics:Data Mining – UNIGENE, EST, ORF, Pubmed, Phylogenetic Analysis, MSA, Gen BANK, COG Cluster, OMIM, Genome assembly & annotation, Gene Mapping, Sequence Assembly & Expression, Alignment of MS, Gene Annotation.

UNIT III

Proteomics:Macromolecules, Protein Structure& Purification, Visualization & prediction of Protein Structure, Methods used in protein structure prediction, PROSITE, PRODOM, Metabolic pathways-kyoto Encyclopedia of Genes and Genomes, Concept of E-Cell, DNA Micro array (DNA chip).

UNIT IV

Tools in Bioinformatics:Web based Bioinformatics Applications, Desktop based softwares, Online Analysis Tools & Servers, Exploration of Databases like NCBI, EBI standford MB Workbench, DDBJ, PDB, TIGR, SWISS-PROT, CATH, Annotation Systems-DAS, Homology Tools –BLAST, FASTA, SSEARCH, Multiple Alignment-CLUSTALW & PHYLIP, Molecular visualization software-Swisspdb viewer, Rasmol Gene Prediction Softwares- Genescan, McPromoter, Protein, Modelling software-SWISSMODEL.

UNIT V

Computational Biology:Genetic Algorithms, HMMR, Artificial Intelligence, Brute force, Dynamic Programming Algorithm. Local & Global Alignment Algorithm, Needleman- Wunsch Algorithm, Smith –Waterman Algorithm, Heuristic Algorithm like BLAST, FASTA-Multiple Segment Alignment Algorithm, Gene finding Algorithm, Protein secondary structure prediction Algorithm. Programming in Perl Language, Data analysis using GOLD and Autodock software packages.

**Practicals**

Applications and analysis with softwares.

**Suggested Readings**

Bergeron, B.(2003). Bioinformatics Computing, Prentice Hall of India.

Bozdogan, H (2003). Statistical Data Mining & Knowledge Discovery, CRC Press

Chen, Z (2001). Intelligent Data Warehousing, CRC Press

Ewens, W.J. and Grant, G.R. (2002).Statistical Methods in Bioinformatics, Springer.

Waterman, M.S.(2000). Introduction to Computational Biology, CRC Press.

**BSTAT 531 SURVIVAL ANALYSIS 2+1**

**Objective**

The course deals with study of survival times and their statistical properties along with the factors affecting them.

**Theory**

UNIT I

Concept of survival data, definition and associated probability density function, survival function, hazard function, Censoring in survival time.

UNIT II

Estimation of survival function by life table analysis, Kaplan and Meier Method.

UNIT III

Survival and failure time distributions: family of exponential and Weibull models.

UNIT IV

Analytical and graphical method for choosing best fitted distribution, Parametric and non-parametric tests for comparison of survival functions.

UNIT V

Concomitant variables in lifetime distribution models, Cox-proportional hazard models, Cox-proportional hazard models with time dependent covariates.

**Practical**

Estimation of survival functions - life table analysis; Kaplan and Meier Method. Estimation of survival functions in case of censored observations - life table method, Kaplan and Meier method; Fitting of survival and failure time distributions: family of exponential and Weibull models (For uncensored and censored observations); Regression and Maximum Likelihood Method of fitting and choosing appropriate distribution to the survival times; Graphical method for choosing best fitted distribution, Parametric and Non-Parametric tests for comparison of survival functions; Parametric tests for comparison of survival functions in the presence of censored survival times; Non parametric tests for comparing survival functions in the presence of uncensored survival times; Concomitant variables in lifetime distribution models. Fitting of Cox-proportional hazard models.

**Suggested Readings**

Anderson B. 1990.Methodological Errors in Medical Research. Blackwell.

Armitage P & Berry G. 1987.Statistical Methods in Medical Research. Blackwell.

Collett D. 2003.Modeling Survival Data in Medical Research.Chapman & Hall.

Cox DR & Oakes D. 1984.Analysis of Survival Data.Chapman & Hall.

Elandt-Johnson RC & Johnson NL. 1980. Survival Models and Data Analysis. John Wiley.

Everitt BS & Dunn G. 1998.Statistical Analysis of Medical Data. Arnold. 62

Hosmer DW, Lemeshow S & May S. 2008.Applied Survival Analysis:

Regression Modeling of Time-to-Event Data.2nd Ed. John Wiley.

Klein JP & Moeschberger ML. 2003. Survival Analysis: Techniques for Censored and Truncated Data. 2nd Ed. Springer.

Kleinbaum DG & Klein M. 2002. Logistic Regression. Springer.

Kleinbaum DG & Klein M. 2005. Survival Analysis.A Self Learning Text.2nd Ed. Springer.

Lee ET & Wang JW. 2003. Statistical Methods for Survival Data Analysis.John Wiley.

Therneau TM &Grambsch PM. 2000.Modeling Survival Data: Extending the Cox Model.Springer.

**BSTAT 532 MULTIVARIATE ANALYSIS 2+1**

**Objective**

This course lays the foundation of Multivariate data analysis. Most of the data sets in life sciences are multivariate in nature. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis.

**Theory**

UNIT I

Concept of random vector, its expectation and Variance-Covariance matrix.Marginal and joint distributions.Conditional distributions and Independence of random vectors.Multinomial distribution.Multivariate Normal distribution, marginal and conditional distributions. Sample mean vector and its distribution. Maximum likelihood estimates of mean vector and dispersion matrix. Tests of hypothesis about mean vector.

UNIT II

Wishart distribution and its simple properties.Hotelling’s T2 and Mahalanobis D2 statistics.Null distribution of Hotelling’s T2.Rao’s U statistics and its distribution.Wilks’ λ criterion and statement of its properties.

UNIT III

Concepts of discriminant analysis, computation of linear discriminant function, classification between k ( ≥2) multivariate normal populations based on LDF and Mahalanobis D2.

UNIT IV

Principal Component Analysis, factor analysis (simple and multi factor models). Canonical variables and canonical correlations. Cluster analysis, similarities and dissimilarities, Hierarchical clustering. Single and Complete linkage methods.

**Practical**

Maximum likelihood estimates of mean-vector and dispersion matrix; Testing of hypothesis on mean vectors of multivariate normal populations; Cluster analysis, Discriminant function, Canonical correlation, Principal component analysis, Factor analysis; Multivariate analysis of variance and covariance, multidimensional scaling.Analysis with softwares.

**Suggested Readings**

Anderson TW. 1984. An Introduction to Multivariate Statistical Analysis. 2nd Ed. John Wiley.

Arnold SF. 1981.The Theory of Linear Models and Multivariate Analysis.John Wiley.

Giri NC. 1977. Multivariate Statistical Inference. Academic Press.

Johnson RA &Wichern DW. 1988. Applied Multivariate Statistical Analysis. Prentice Hall.

Kshirsagar AM. 1972. Multivariate Analysis. Marcel Dekker.

Muirhead RJ. 1982. Aspects of Multivariate Statistical Theory. John Wiley.

Rao CR. 1973. Linear Statistical Inference and its Applications.2nd Ed. John Wiley.

Rencher AC. 2002. Methods of Multivariate Analysis.2nd Ed. John Wiley.

SrivastavaMS &Khatri CG. 1979. An Introduction to Multivariate Statistics. North Holland.

**BSTAT 533 STOCHASTIC PROCESSES 2+0**

**Objective**

This is a course which aims at describing basic theory and applications of stochastic process. This also helps prepare students for applications of this important subject to biological sciences.

**Theory**

UNIT I

Basics of stochastic processes.Random walk models.Markov chains and their applications. Discrete branching processes.

UNIT II

Markov processes in continuous time: Poisson process, Random-variable technique. Birth and death processes like pure birth process, linear birth and death process, immigration-birth-death process.

UNIT III

Epidemic processes: Simple deterministic and stochastic epidemic model. General epidemic models, Recurrent epidemics.

UNIT IV

Chain binomial models. Diffusion processes. Diffusion limit of a random walk and discrete branching process.Forward and backward Kolmogorov diffusion equations and their applications.

**Suggested Readings**

Adke SR &Manjunath SM. 1984.Finite Markov Processes.John Wiley.

Bailey NTJ. 1964. Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley Eastern.

Bartlett MS. 1955.Introduction to Stochastic Processes.Cambridge Univ. Press.

Basawa IV &PrakasaRao BLS. 1980. Statistical Inference for Stochastic Processes. Academic Press.

Bharucha-Reid AT. 1960. Elements of the Theory of Markov Processes and their Applications. McGraw Hill.

Bhat BR. 2000.Stochastic Models; Analysis and Applications.New Age.

Cox DR & Miller HD. 1965.The Theory of Stochastic Processes. Methuen.

Draper NR & Smith H. 1981.Applied Regression Analysis.Wiley Eastern.

France J &Thornley JHM. 1984. Mathematical Models in Agriculture. Butterworths.

Karlin S & Taylor H.M. 1975.A First Course in Stochastic Processes. Vol. I. Academic Press.

Lawler GF. 1995. Introduction to Stochastic Processes. Chapman & Hall.

Medhi J. 2001. Stochastic Processes.2nd Ed. Wiley Eastern.

Parzen E. 1962. Stochastic Processes.Holden-Day.

Prabhu NU. 1965. Stochastic Processes. Macmillan.

PrakasaRao BLS &Bhat BR.1996.Stochastic Processes and Statistical Inference.New Age.

Ratkowsky DA. 1983. Nonlinear Regression Modelling: a Unified Practical Approach. Marcel Dekker.

Ratkowsky DA. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker.

Seber GAF & Wild CJ. 1989. Non-linear Regression. John Wiley.

**BSTAT 534 TIME SERIES ANALYSIS 1+1**

**Objective**

This course is meant to teach the students the concepts involved in time series data. They would also be exposed to components of time series, stationary models and forecasting/ projecting the future scenarios based on time series data. It would also help them in understanding the concepts involved in time series data presentation, analysis and interpretation.

**Theory**

UNIT I

Components of a time-series. Autocorrelation and Partial autocorrelation functions, Correlogram and periodogram analysis.

UNIT II

Linear stationary models: Autoregressive, Moving average and Mixed processes. Linear non-stationary models: Autoregressive integrated moving average processes.

UNIT III

Forecasting: Minimum mean square forecasts and their properties, Calculating and updating forecasts.

UNIT IV

Model identification: Objectives, Techniques, and Initial estimates. Model estimation: Likelihood function, Sum of squares function, Least squares estimates. Seasonal models.Intervention analysis models and Outlier detection.

**Practical**

Time series analysis, autocorrelations, correlogram and periodogram; Linear stationary model; Linear non-stationary model; Model identification and model estimation; Intervention analysis and outliers detection.

**Suggested Readings**

Box GEP, Jenkins GM and Reinsel GC. 2007. Time Series Analysis: Forecasting and Control. 3rd Ed. Pearson Edu.

Brockwell PJ and Davis RA. 2002. Introduction to Time Series and Forecasting. 2nd Ed. Springer.

Chatterjee S, Hadi A and Price B.1999. Regression Analysis by Examples.John Wiley.

Draper NR and Smith H. 1998.Applied Regression Analysis.3rd Ed. John Wiley.

Johnston J. 1984.Econometric Methods.McGraw Hill.

Judge GG, Hill RC, Griffiths WE, Lutkepohl H and Lee TC. 1988. Introduction to the Theory and Practice of Econometrics. 2nd Ed. John Wiley.

Montgomery DC and Johnson LA. 1976. Forecasting and Time Series Analysis. McGraw Hill.

**BSTAT 535 REGRESSION ANALYSIS 1+1
**

**Objective**

This course is meant to prepare the students in linear and non-linear regression methods useful for statistical data analysis. They would also be provided a mathematical foundation behind these techniques and their applications.

**Theory**

UNIT I

Simple and Multiple linear regressions: Least squares fit, Properties and examples. Polynomial regression: Use of orthogonal polynomials.

UNIT II

Assumptions of regression; diagnostics and transformations; Examination of residuals, Studentized residuals, applications of residuals in detecting outliers, identification of influential observations. Lack of fit, Pure error. Testing homoscedasticity and normality of errors, Durbin-Watson test.Use of R2 for examining goodness of fit.

UNIT III

Concepts of Least median of squares and its applications; Concept of multicollinearity, Analysis of multiple regression models, estimation and testing of regression parameters, sub-hypothesis testing, restricted estimation.

UNIT IV

Weighted least squares method: Properties, and examples. Box-Cox family of transformations. Use of dummy variables, Selection of variables: Forward selection, Backward elimination. Stepwise and Stage wise regressions.

UNIT V

Introduction to non-linear models, nonlinear estimation: Least squares for nonlinear models.

**Practical**

Multiple regression fitting with three and four independent variables; Estimation of residuals, their applications in outlier detection, distribution of residuals; Test of homoscedasticity, and normality, Box-Cox transformation; Restricted estimation of parameters in the model, hypothesis testing, Step wise regression analysis; Least median of squares norm, Orthogonal polynomial fitting.

**Suggested Readings**

Barnett V and Lewis T. 1984.Outliers in Statistical Data.John Wiley.

Belsley DA, Kuh E and Welsch RE. 2004. Regression Diagnostics- Identifying Influential Data and Sources of Collinearity. JohnWiley.

Chatterjee S, Hadi A and Price B. 1999. Regression Analysis by Examples.John Wiley.

Draper NR and Smith H. 1998.Applied Regression Analysis.3rd Ed. John Wiley.

McCullagh P and Nelder JA. 1999. Generalized Linear Models. 2nd Ed. Chapman & Hall.

Montgomery DC, Peck EA and Vining GG. 2003. Introduction to Linear Regression Analysis. 3rd Ed. John Wiley.

Rao CR. 1973. Linear Statistical Inference and its Applications.2nd Ed. John Wiley.

**BSTAT 539 CLINICAL TRIALS 1+0**

**Objective**

The course introduces Pre-clinical trials and clinical trails.

**Theory**

UNIT I

Design and analysis of pre-clinical invitro studies, preclinical invitro studies on rodents and non rodents, preclinical toxicological studies and chronic safety studies in animals.

UNIT II

Introduction to clinical trials: the need and ethics of clinical trials, data management, objectives and end points of clinical trials, bias and random errors in clinical studies, conduct of clinical trials, overview of phase I-IV trials, multi-center trials. Design of clinical trials: parallel vs cross-over designs, cross-sectional vs: longitudinal designs.

UNIT III

Design and analysis of Phase-I, Phase -II and Phase-III trials. Design of bio-equivalence trials.Analysis of categorical outcomes from Phase I-III trials, analysis of survival data from clinical trials, analysis of surrogate endpoint data, meta-analysis of clinical trials.

**Suggested Readings**

Fleiss,J.L. (1989). The design and Analysis of Clinical Experiments, John Wiley & Sons.

Friedman, L.M., Fuburg,C., and Demets, D.L. (1998). Fundamentals of Clinical Trials, Springer Verlag.

Marubeni, E. and Valsecchi (1994).Analyzing Survival Data from Clinical Trials and Observational Studies, Wiley and Sons.

Moyé, L.A.(2003). Multiple Analyses in Clinical Trials, Springer.

**BSTAT 541 STATISTICAL QUALITY CONTROL 2+0**

**Objective**

This course is meant for exposing the students to the concepts of Statistical Quality Control and their applications. This course would enable the students to have an idea about the statistical techniques used in quality control.

**Theory**

UNIT I

Introduction to Statistical Quality Control; Control Charts for Variables – Mean, Standard deviation and Range charts; Statistical basis; Rational subgroups.

UNIT II

Control charts for attributes- ‘np’, ‘p’ and ‘c’ charts.

UNIT III

Fundamental concepts of acceptance, sampling plans, single, double and sequential sampling plans for attributes inspection.

UNIT IV

Sampling inspection tables for selection of single and double sampling plans.

**Suggested Readings**

Cowden DJ. 1957. Statistical Methods in Quality Control. Prentice Hall of India.

Dodge HF and Romig HG. 1959. Sampling Inspection Tables. John Wiley.

Duncan A.J. 1986.Quality Control and Industrial Statistics.5th Ed. Irwin Book Co.

Grant EL and Leavenworth RS. 1996. Statistical Quality Control. 7th Ed. McGraw Hill.

Montgomery DC. 2005. Introduction to Statistical Quality Control. 5th Ed. John Wiley.

Wetherhil G.B. 1977. Sampling Inspection and Quality Control.HalstedPress.

**BSTAT 542 ACTUARIAL STATISTICS 2+0**

**Objective**

This course is meant to expose to the students to the statistical techniques such as probability models, life tables, insurance and annuities. The students would also be exposed top practical applications of these techniques in computation of premiums that include expenses, general expenses, types of expenses and per policy expenses.

**Theory**

UNIT I

Insurance and utility theory, models for individual claims and their sums, survival function, curtate future lifetime, force of mortality.

UNIT II

Life table and its relation with survival function, examples, assumptions for fractional ages, some analytical laws of mortality, select and ultimate tables.

UNIT III

Multiple life functions, joint life and last survivor status, insurance and annuity benefits through multiple life functions evaluation for special mortality laws. Multiple decrement models, deterministic and random survivorship groups, associated single decrement tables, central rates of multiple decrement, net single premiums and their numerical evaluations.

UNIT IV

Distribution of aggregate claims, compound Poisson distribution and its applications.

UNIT V

Principles of compound interest: Nominal and effective rates of interest and discount, force of interest and discount, compound interest, accumulation factor, continuous compounding.

UNIT VI

Insurance payable at the moment of death and at the end of the year of death-level benefit insurance, endowment insurance, deferred insurance and varying benefit insurance, recursions, commutation functions.

UNIT VII

Life annuities: Single payment, continuous life annuities, discrete life annuities, life annuities with monthly payments, commutation functions, varying annuities, recursions, complete annuities-immediate and apportionable annuities-due.

UNIT VIII

Net premiums: Continuous and discrete premiums, true monthly payment premiums, apportionable premiums, commutation functions, accumulation type benefits. Payment premiums, apportionable premiums, commutation functions, accumulation type benefits. Net premium reserves: Continuous and discrete net premium reserve, reserves on a semi-continuous basis, reserves based on true monthly premiums, reserves on an apportionable or discounted continuous basis, reserves at fractional durations, allocations of loss to policy years, recursive formulas and differential equations for reserves, commutation functions.

UNIT IX

Some practical considerations: Premiums that include expenses-general expenses types of expenses, per policy expenses. Claim amount distributions, approximating the individual model, stop-loss insurance.

**Suggested Readings**

Atkinson ME & Dickson DCM. 2000. An Introduction to Actuarial Studies. Elgar Publ.

Bedford T & Cooke R. 2001.Probabilistic Risk Analysis. Cambridge.

Booth PM, Chadburn RG, Cooper DR, Haberman S & James DE. 1999.

Modern Actuarial Theory and Practice.Chapman & Hall.

Borowiak Dale S. 2003. Financial and Actuarial Statistics: An Introduction. 2003. Marcel Dekker.

Bowers NL, Gerber HU, Hickman JC, Jones DA & Nesbitt CJ. 1997.

Actuarial Mathematics.2nd Ed. Society of Actuaries, Ithaca, Illinois.

Daykin CD, Pentikainen T & Pesonen M. 1994. Practical Risk Theory for Actuaries.Chapman & Hall.

Klugman SA, Panjer HH, Willmotand GE & Venter GG. 1998. Loss Models: From data to Decisions. John Wiley.

Medina PK & Merino S. 2003.Mathematical Finance and Probability: A Discrete Introduction. Basel, Birkhauser.

Neill A. 1977. Life Contingencies.Butterworth-Heinemann.

Rolski T, Schmidli H, Schmidt V &Teugels J. 1998.Stochastic Processes for Insurance and Finance.John Wiley.

Rotar VI. 2006. Actuarial Models. The Mathematics of Insurance.Chapman & Hall/CRC.

Spurgeon ET. 1972. Life Contingencies. Cambridge Univ. Press.

**BSTAT 543 STATISTICAL COMPUTING 1+1**

**Objective**

This course is meant for exposing the students in the concepts of computational techniques. Various statistical packages would be used for teaching the concepts of computational techniques.

**Theory**

UNIT I

Introduction to statistical packages and computing: data types and structures, pattern recognition, classification, association rules, graphical methods. Data analysis principles and practice

UNIT II

ANOVA, regression and categorical data methods; model formulation, fitting, diagnostics and validation; Matrix computations in linear models.Analysis of discrete data.

UNIT III

Numerical linear algebra, numerical optimization, graphical techniques, numerical approximations, numerical integration and Monte Carlo methods.

UNIT IV

Spatial statistics; spatial sampling; hierarchical modeling. Analysis of cohort studies, case-control studies and randomized clinical trials, techniques in the analysis of survival data and longitudinal studies, Approaches to handling missing data, and meta-analysis.

**Practical**

Data management, Graphical representation of data, Descriptive statistics; General linear models ~ fitting and analysis of residuals, outlier detection; Categorical data analysis, analysis of discrete data, analysis of binary data; Numerical algorithms; Spatial modeling, cohort studies; Clinical trials, analysis of survival data; Handling missing data.

Suggested Readings

Agresti A. 2002. Categorical Data Analysis.2nd Ed. John Wiley.

Everitt BS and Dunn G. 1991.Advanced Multivariate Data Analysis.2nd Ed.Arnold.

Geisser S. 1993. Predictive Inference: An Introduction. Chapman & Hall.

Gelman A and Hill J. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models.Cambridge Univ. Press.

Gentle JE, Härdle W and Mori Y. 2004.Handbook of Computational Statistics - Concepts and Methods.Springer.

Han J &Kamber M. 2000.Data Mining: Concepts and Techniques. Morgan.

Hastie T, Tibshirani R and Friedman R. 2001.The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer.

Kennedy WJ and Gentle JE. 1980. Statistical Computing. Marcel Dekker.

Miller RG Jr. 1986.Beyond ANOVA, Basics of Applied Statistics.John Wiley.

Rajaraman V. 1993.Computer Oriented Numerical Methods. Prentice-Hall.

Ross S. 2000. Introduction to Probability Models.Academic Press.

Ryan BF and Joiner BL. 1994.MINITAB Handbook.3rd Ed. Duxbury Press.

Simonoff JS. 1996. Smoothing Methods in Statistics. Springer.

Snell EJ. 1987. Applied Statistics: A Handbook of BMDP Analyses. Chapman & Hall.

Thisted RA. 1988. Elements of Statistical Computing. Chapman & Hall.

Venables WN and Ripley BD. 1999.Modern Applied Statistics With S-Plus. 3rd Ed. Springer.

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