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

• Schedule: Slot B, 9:00 am - 9:55 am Monday, 10:00 am - 10:55 am Tuesday, 11:00 am - 11:55 am Wednesday
• Venue: 5103, Core 5.

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