DA 241 Statistical Foundations for Data Science

Course Description

This course is an introduction to statistical ideas and tools, underlying the foundations of data science. The course is broadly divided into 5 modules:

• Module 1 Descriptive Statistics
• Module 2 Probability & Random variables
• Module 3 Estimation & Inference
• Module 4 Statistical Modeling
• Module 5 Statistical Computing

Course Syllabus

Elements of descriptive statistics, averages, dispersion, skewness, quantiles; graphical displays, pie charts, bar charts, histograms, scatter plots, box plots, steam and leaf plots.

Probability spaces, conditional probability, independence; Random variables, distribution functions, probability mass and density functions, functions of random variables, standard univariate discrete and continuous distributions; Mathematical expectations, moments, moment generating functions, inequalities; Multidimensional random variables, joint, marginal and conditional distributions, conditional expectations, independence, covariance, correlation, standard multivariate distributions, functions of multidimensional random variables; Forms of convergence, law of large numbers, central limit theorem.

Sampling distributions; Point estimation - estimators, minimum variance unbiased estimation, maximum likelihood estimation, method of moments estimation, Cramer -Rao inequality, consistency; Interval estimation; Testing of hypotheses - tests and critical regions, Neymann-Pearson lemma, uniformly most powerful tests, likelihood ratio tests.

Linear regression, ANOVA, discriminant analysis.

Computing techniques, cross-validation, bootstrap re-sampling.

Course Logistics

• This semester the first half of the course was taught by Dr. Amulya Kumar Mahato. We will start the next half after the mid-semeser examination week.
• Schedule: Slot C, 10:00 am - 10:55 am Monday, 11:00 am - 11:55 am Tuesday, 9:00 am - 9:55 am Friday
• Venue: 5201, Core 5.

Course Evaluation

There will be 3 quizzes and an end-semester examination with the following weightage:

• Quizzes: 15%
• Attendance: 5%
• End semester exam: 30%

Some references (not an exhaustive list)

• Hogg, R.V., McKean, J. and Craig, A.T., Introduction to mathematical statistics, 7th edition, Pearson Education, 2012.
• Rice, J.A., Mathematical statistics and data analysis. 3rd edition, Cengage Learning, 2006
• Wasserman, L., All of statistics: a concise course in statistical inference, Volume 26, New York Springer, 2004
• Rohatgi, V.K. and Saleh, A.M.E., An introduction to probability and statistics, 3rd edition, John Wiley & Sons, 2015.
• DeGroot, M.H. and Schervish, M.J., Probability and statistics, 4th edition, Pearson Education, 2010.

Topics Covered during the weeks