17.8XX Math Prefresher I The Math Prefesher is designed to introduce and review core mathematics and probability prerequisites that you will need to be successful in the quantitative methods courses in the Political Science department and elsewhere at MIT. In an intense one-week course, we will cover key concepts from calculus, linear algebra, probability theory, and an introduction to statistical computing. The learning will proceed through lectures, hands-on exercises, and homework. The aim of the course is to give you an opportunity to practice some of the mathematics you may have previously learned and to introduce you to areas that may be new to you so that you will be ready to enter classes that presume prior familiarity with these concepts, such as 17.800 Quantitative Research Methods I. Syllabus. 17.8XX Math Prefresher II The math camp will prepare students to take Quant III and Quant IV as well as other advance classes in political methodology. The goal of the class will be to remind students of basic and intermediate mathematical concepts that are useful for Quant III and Quant IV and increase both mathematical fluency and problem solving ability. I will also try to give some programming tools that you may find useful when solving problem sets of Quant III. The prerequisites include Quant I and Quant II. Syllabus. 17.800 Quantitative Research Methods I: Regression Graduate level introduction to statistical methods for political science and public policy research, with a focus on linear regression. Teaches students how to apply multiple regression models as used in much of political science and public policy research. Also covers fundamentals of probability and sampling theory. Syllabus. 17.802 Quantitative Research Methods II: Causal Inference Survey of advanced empirical tools for political science and public policy research with a focus on statistical methods for causal inference, i.e. methods designed to address research questions that concern the impact of some potential cause (e.g., an intervention, a change in institutions, economic conditions, or policies) on some outcome (e.g., vote choice, income, election results, levels of violence). Covers a variety of causal inference designs, including experiments, matching, regression, panel methods, difference-in-differences, synthetic control methods, instrumental variable estimation, regression discontinuity designs, quantile regressions, and bounds. Syllabus. 17.804: Quantitative Research Methods III: Generalized Linear Models and Extensions This course is the third course in the quantitative research methods sequence at the MIT political science department. Building on the first two courses of the sequence (17.800 and 17.802), this class covers advanced statistical tools for empirical analysis in modern political science. Our focus in this course will be on techniques for model-based inference, including various regression models for cross-section data (e.g., binary outcome models, discrete choice models, sample selection models, event count models, survival outcome models, etc.) as well as grouped data (e.g., mixed effects models and hierarchical models). This complements the methods for design-based inference primarily covered in the previous course of the sequence. This course also covers basics of the fundamental statistical principles underlying these models (e.g., maximum likelihood theory, theory of generalized linear models, Bayesian statistics) as well as a variety of estimation techniques (e.g., numerical optimization, bootstrap, Markov chain Monte Carlo). The ultimate goal of this course is to provide students with adequate methodological skills for conducting cutting-edge empirical research in their own fields of substantive interest. Syllabus. 17.806: Quantitative Research Methods IV: Advanced Topics This course is the fourth and final course in the quantitative methods sequence at the MIT political science department. The course covers various advanced topics in applied statistics, including those that have only recently been developed in the methodological literature and are yet to be widely applied in political science. The topics for this year are organized into three broad areas: (1) research computing, where we introduce various techniques for automated data collection, visualization, and analysis of massive datasets; (2) statistical learning, where we provide an overview of machine learning algorithms for predictive and descriptive inference; and (3) finite mixture models (e.g., Latent Dirichlet allocation for text analysis), as well as a variety of estimation techniques such as EM Algorithm and Variational Inference. Syllabus.