Doctoral students working in the Engineering Statistics and Machine Learning Laboratory (ESAMLab) focus their research mainly in the development of new methodologies, as opposed to simple application of existing methods. This requires a solid foundation in the underlying science, namely, Statistics, and a strong degree of mathematical maturity. Therefore, prior to starting their research, Ph.D. students in the lab are expected to complete successfully the following coursework at PSU or elsewhere:
- STAT 513 and STAT 514
- IE 583 (Response Surface Methods) or IE 584 (Time Series Control), depending on area of interest;
- IE 521 (Nonlinear Programming) or CSE 555 (Numerical Optimization), or IE 597 (Convex Optimization)
- STAT 557/558 (Machine Learning/Data Mining).
- Other STAT graduate courses, depending on the area of interest: STAT 551/552(Linear Models), STAT 515 (Stochastic Processes and Monte Carlo Methods).
Mathematical maturity is necessary at the level of say MATH 401 to MATH 404, and MATH 435-436. A very useful and non measure-theoretic course is STAT 553 (Asymptotic tools). A very useful and measure-theoretic course is MATH 503 (Functional Analysis). Some recent work in the lab requires notions from Math courses in Differential Geometry, Partial Differential Equations and their numerical solution via Finite Element Methods, and Basic Combinatorial Topology.
Ph.D. students working in the ESAMLab typically end up obtaining a Ph.D. dual degree in IE & OR with a minor in Statistics or a Ph.D. dual degree in Statistics and OR. Other students get minors in Mathematics or Computer Science.
If you are a student with interest in the research opportunities at the ESAMLab, please contact Dr. Castillo at exd13@psu.edu.