Statistics is the discipline that concerns the process of learning about the world through the analysis of data. The mathematical foundation of Statistics lies in the theory of Probability, the extension of logical reasoning to situations involving uncertainty -- a setting that includes most of the difficult and interesting questions in life.  Probability and Statistical Inference are subjects of keen intellectual interest in their own right, as well as being among the most applicable of mathematical areas. In addition to quantifying uncertainty and providing a basis for sound inferences and decisions, Statistics is key to the scientific method, and applications of Statistics pervade the natural and social sciences. The discipline is still actively developing and growing, with advances continually occurring in the theory, methodology, and applications.

The major

The major in Statistics is intended to equip students with the fundamental concepts, ideas and methodologies of Statistics, as well as quantitative thinking and analysis skills can be employed in practice in a flexible way.

In addition to the core theory of Probability and Statistics, areas of emphasis for practical statistical analysis include a variety of computational techniques, methods of visualizing and exploring data, methods of seeking and establishing structure and trends in data, and a mode of questioning and reasoning that quantifies uncertainty.

The curriculum for the major is a synthesis of theory, methods, and applications. It contains a set of required and elective courses covering the fundamental concepts, theory, and methods in Statistics and Probability as well as their applied aspects. Systematic development of Probability and statistical inference involves rigorous mathematical treatment, and working with data requires at least basic computing skills. Therefore, the prerequisites consist of mathematical preparation, and a course in computing is required in the major.

FAQs regarding the Statistics major at Yale

Specific requirements

• two courses in the theory and applications of Probability: Probability Theory (Stat 241a) and Stochastic Processes (Stat 251b)
• two courses emphasizing the theory of statistical inference: Theory of Statistics (Stat 242b) and Linear Models (Stat 312a)
• two courses in the methods and practice of data analysis, chosen from the four options Introductory Data Analysis (Stat 230b), Data Analysis (Stat 361a), Multivariate Statistics for Social Sciences (Stat 363b), and Case Studies (Stat 625a ).

Beyond the above, the BA degree requires 3 more Statistics courses. Two of these 3 courses are electives. The third course is the Senior Seminar and Project (Stat 490a), taken in the fall of the senior year. In Stat 490a, the students will work on a research project, present and share their progress with each other during the seminar meetings, and write a final report. For students who have become very interested in the topic of their senior project and wish to continue working on it further, it could be possible to continue the project as an independent study with the supervision of a faculty member in the spring. The BS adds additional depth by requiring one additional Statistics elective and one course in mathematical analysis.

Elective courses

For elective courses, in addition to the options indicated in the data analysis section of the major requirements (the last bulleted item above), further undergraduate courses that we usually offer every year include:

• Advanced Probability (Stat 300b)
• Information Theory (Stat 364b)
• Data Mining and Machine Learning (Stat 365b)

• Survey Sampling (BIS 538b)
• Fundamentals of Clinical Trials (BIS 540a)
• Applied Regression Analysis (BIS 623b)
• Categorical Data Analysis (BIS 625b)
• Longitudinal Data Analysis (BIS 628b)
• Applied Survival Analysis (BIS 630b)
• Theory of Survival Analysis and Its Application (BIS 643a)
• Nonparametric Statistical Methods and Their Applications (BIS 646a)