Stochastic systems courses: Difference between revisions
| Line 53: | Line 53: | ||
<span id=ACM116 /> | <span id=ACM116 /> | ||
'''ACM/EE 116 | '''ACM/EE 116. Introduction to Stochastic Processes and Modeling.''' 9 units (3-0-6); first term. Prerequisite: Ma 2 ab or instructor’s permission.Introduction to fundamental ideas and techniques of stochastic analysis and modeling. Random variables, expectation and conditional expectation, joint distributions, covariance, moment generating function, central limit theorem, weak and strong laws of large numbers, discrete time stochastic processes, stationarity, power spectral densities and the Wiener-Khinchine theorem, Gaussian processes, Poisson processes, Brownian motion. The course develops applications in selected areas such as signal processing (Wiener filter), information theory, genetics, queuing and waiting line theory, and finance. | ||
<span id=ACM118 /> | |||
'''ACM/ESE 118. Methods in Applied Statistics and Data Analysis.''' 9 units (3-0-6); first term. Prerequisite: Ma 2 or another introductory course in probability and statistics. Introduction to fundamental ideas and techniques of statistical modeling, with an emphasis on conceptual understanding and on the analysis of real data sets. Multiple regression: estimation, inference, model selection, model checking. Regularization of ill-posed and rank-deficient regression problems. Cross-validation. Principal component analysis. Discriminant analysis. Resampling methods and the bootstrap. | |||
<span id=ACM216 /> | <span id=ACM216 /> | ||
'''ACM 216 | '''ACM 216. Markov Chains, Discrete Stochastic Processes and Applications.''' 9 units (3-0-6); second term. Prerequisite: ACM/EE 116 or equivalent. Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bounds. | ||
Revision as of 00:19, 25 January 2009
This page collects some information about stochastic systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on the current stochastic systems sequence (ACM/EE 116, ACM 216, ACM 217/EE 164).
History
Overview of current course sequence
Additional stochastic systems courses at Caltech
The following table lists all of the courses that I was able to find that have been taught in the last five years.
| Course | enroll | 2008-09 | 2007-08 | 2006-07 | 2005-06 |
| ACM/EE 116 - Introduction to Stochastic Processes and Modeling | 30-50 | Owhadi | Owhadi | Owhadi | Owhadi |
| ACM 216 - Markov Chains | 15-20 | Owhadi | Owhadi | Candes | Owhadi |
| ACM 217 - Advanced Topics in Stochastic Analysis | 2-12 | Owhadi | Von Handel | Hassibi | N/O |
| ACM 257 - Special Topics in Financial Mathematics | 20 | N/O | Hill | N/O | N/O |
Courses on statistics
Course on random processes
Discipline-specific courses
Course listings
The course listings below are from the Caltech catalog, mainly to serve as a reference for the rest of the information on this page.
ACM/EE 116. Introduction to Stochastic Processes and Modeling. 9 units (3-0-6); first term. Prerequisite: Ma 2 ab or instructor’s permission.Introduction to fundamental ideas and techniques of stochastic analysis and modeling. Random variables, expectation and conditional expectation, joint distributions, covariance, moment generating function, central limit theorem, weak and strong laws of large numbers, discrete time stochastic processes, stationarity, power spectral densities and the Wiener-Khinchine theorem, Gaussian processes, Poisson processes, Brownian motion. The course develops applications in selected areas such as signal processing (Wiener filter), information theory, genetics, queuing and waiting line theory, and finance.
ACM/ESE 118. Methods in Applied Statistics and Data Analysis. 9 units (3-0-6); first term. Prerequisite: Ma 2 or another introductory course in probability and statistics. Introduction to fundamental ideas and techniques of statistical modeling, with an emphasis on conceptual understanding and on the analysis of real data sets. Multiple regression: estimation, inference, model selection, model checking. Regularization of ill-posed and rank-deficient regression problems. Cross-validation. Principal component analysis. Discriminant analysis. Resampling methods and the bootstrap.
ACM 216. Markov Chains, Discrete Stochastic Processes and Applications. 9 units (3-0-6); second term. Prerequisite: ACM/EE 116 or equivalent. Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bounds.
