This course covers the probabilistic foundations of inference in data science. Key topics include frequentist and Bayesian decision-making, maximum likelihood estimation, statistical inference and hypothesis testing, false discovery rate control with ROC analysis, Bayesian hierarchical models, rejection and Gibbs sampling, robust methods like bootstrap confidence intervals and permutation based hypothesis tests, nonparametric methods like kernel density estimation and k-nearest neighbors, machine learning fundamentals including decision trees and ensemble methods, equip students with essential skills for data-driven decision-making.