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AKTU Statistical Computing (BCS051) Syllabus PDF – B.Tech 3rd Year
Statistical Computing BCS051
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Official AKTU syllabus of Statistical Computing (BCS051) for B.Tech 3rd Year – 3 credits, L-T-P 3-0-0. Read the unit-wise course content, course outcomes, evaluation pattern and recommended books online, or download the PDF.
Syllabus — Statistical Computing
Download PDFBCS051 · 3 credits · L-T-P 3-0-0
Course Outcomes
At the end of course , the student will be able to:
| CO 1 | Understand and apply the probability distributions, random number generation and density estimations to perform analysis of various kinds of data | K2, K , K 4 6 |
| CO 2 | Understand and manipulate data, design and perform simple Monte Carlo experiments, and be able to use resampling methods | K , K 5 6 |
| CO 3 | Perform statistical analysis on variety of data | K , K 2 5 |
| CO 4 | Perform appropriate statistical tests using R and visualize the outcome | K , K 2 4 |
| CO 5 | Discuss the results obtained from their analyses after creating customized graphical and numerical summaries | K , K 2 3 |
Course Content
L-T-P: 3-0-0
| Unit | Topic | Proposed Lecture |
|---|---|---|
| I | Descriptive Statistics: Diagrammatic representation of data, measures of central tendency, measures of dispersion, measures of skewness and kurtosis, correlation, inference procedure for correlation coefficient, bivariate correlation, multiple correlations, linear regression and its inference procedure, multiple regression. Probability: Measures of probability, conditional probability, independent event, Bayes’ theorem, random variable, discrete and continuous probability distributions, expectation and variance, markov inequality, chebyshev’s inequality, central limit theorem. | 08 |
| II | Inferential Statistics: Sampling & Confidence Interval, Inference & Significance. Estimation and Hypothesis Testing, Goodness of fit, Test of Independence, Permutations and Randomization Test, t-test/z-test (one sample, independent, paired), ANOVA, chi-square. Linear Methods for Regression Analysis: multiple regression analysis, orthogonalization by Householder transformations (QR); singular value decomposition (SVD); linear dimension reduction using principal component analysis (PCA). | 08 |
| III | Pseudo-Random Numbers: Random number generation, Inverse-transform, acceptance-rejection, transformations, multivariate probability calculations. Monte Carlo Integration: Simulation and Monte Carlo integration, variance reduction, Monte Carlo hypothesis testing, antithetic variables/control variates, importance sampling, stratified sampling Markov chain Monte Carlo (McMC): Markov chains; Metropolis-Hastings algorithm; Gibbs sampling; convergence | 08 |
| IV | Resampling Methods: Cross-validation, Bootstrapping, Jackknife resampling, percentile confidence intervals, permutation tests Density Estimation: Univariate density estimation, kernel smoothing, multivariate density estimation Numerical Methods: Root finding; more on numerical integration; numerical maximization/minimization; constrained and unconstrained optimization; EM (Expectation- Maximization) algorithm; simplex algorithm | 08 |
| V | Introduction to R programming: History of R programming, starting and ending R, R as a scientific calculator , handling package, workspace, inspecting variables, operators and expressions inR, data objects and types, vectors, matrices and arrays, lists and data frames, built-in and user-defined functions , strings and factors, flow control and loops, advanced looping, date and times. | 08 |
Computer Science and Information Technology, IT (V & VI semester) Using R for statistical analysis: Importing data files, exporting data, outputting results, exporting graphs, graphics in R, interactively adding information of plot, performing data analysis tasks.
R commands for descriptive statistics, data aggregation, representation of multivariate data, code factorization and optimization, statistical libraries in R.
Reference Books
- S.C. Gupta & V.K. Kapoor, “Fundamentals of Mathematical Statistics”, Sultan Chand & Sons
- Sheldon M. Ross, “Introduction to Probability and Statistics for Engineers and Scientists”, Academic Press.
- Dudewicz, E.J., Mishra, S.N., “Modern Mathematical Statistics”, Willy
- Purohit S. G., Gore S. D., Deshmukh S. K., “Statistics using R, Narosa
- Rizzo, M. L., “Statistical Computing with R”, Boca Raton, FL: Chapman & Hall/CRC Press
- Normal Maltoff, The Art of R programming, William
- Dalgaard, Peter, “Introductory statistics with R”, Springer Science & Business Media
- M. D. Ugarte, A. F. Militino, A. T. Arnholt, “Probability and Statistics with R”, CRC Press
- Kundu, D. and Basu, A., “Statistical computing – existing methods and recent developments”, Narosa
- Gentle, James E., Härdle, Wolfgang Karl, Mori, Yuich, “Handbook of Computational Statistics”, Springer
- Givens and Hoeting, “Computational Statistics”, Wiley Series in Prob. and Statistics
- Michael J. Crawley “The R Book”, John Wiley and Sons.
- Richard Cotton, “Learning R”, O’Reilly
- Brain S. Everitt, “A Handbook of Statistical Analysis Using R”, Second Edition, LLC
- Randall E. Schumacker, “Learning Statistics Using R”, Sage.
- Jared P. Lander, “R for Everyone” Addison Wesley.
- Monahan, J.F., “Numerical methods of statistics”, Cambridge University Press.
- Robert, C. and Casella, G., “Introducing Monte Carlo Methods with R”, Springer Verlag, New York. Computer Science and Information Technology, IT (V & VI semester)
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