This is a course in the intermediate and advanced foundations of statistical inference in the context of applied research. Assuming some prior exposure to probability and statistics, this course will first cover topics such as the principles of estimation and hypothesis testing, and the general and generalized linear models, including scientific computation. This course thoroughly explores the frequentist approach to inference. The student will be expected to understand the mathematical theory, implement related statistical algorithms in statistical programming language such as R, and interpret models and parameters in the context of applied statistical analysis of real data.