This course introduces basic probability theory, statistical methods, and computational algorithms to perform mathematically rigorous data analysis. The course starts with basic foundational concepts of random variables, histograms, and various plots (PMF, PDF, and CDF).
Students learn various popular discrete and continuous distributions like Bernoulli, Binomial, Poisson, Gaussian, Exponential, Pareto, log-normal, etc., both mathematically and from an applicative perspective. Students learn various measures like mean, median, percentiles, quantiles, variance, and interquartile range. Students learn the pros and cons of each metric and understand when and how to use them in practice.
Students will learn conditional probability and Bayes theorem in the applied context of real-world problems in medicine and healthcare. The module teaches the foundations of non-parametric statistics and applies them to solve problems using computational tools. Students learn various methods to determine correlations rigorously in data. This is followed by the applied and mathematical understanding of the statistics underlying control-treatment (A/B) experiments and hypothesis testing. The module engages computation tools in modern statics like Bootstrapping, Monte-Carlo methods, RANSAC, etc.