MATH 774: Topics in Statistics (Fall 2005)

Instructor: Michael Nussbaum, Malott Hall 441, 255 3403, nussbaum@math.cornell.edu

Meeting Time & Room

4 credits. Prerequisites: Basic mathematical statistics (MATH 674 or equivalent) and measure theoretic probability (MATH 671).

Textbook: Wasserman, L., All of Statistics, Springer Verlag, 2004.

Other reference books: The Elements of Statistical Learning (Data Mining, Inference and Prediction ) by T. Hastie, R. Tibshirani, J. H. Friedman, Springer, 2001; Monte Carlo Statistical Methods by C. Robert and G. Casella, Springer, 1999.

Abstract: The course is intended as a continuation of MATH 674. Topics to be covered include classification, support vector machines, kernelization, neural networks, pattern recognition and simulation. We will initially follow the textbook by Wasserman to recap and continue classification and related topics from 674. Then statistical simulation will be introduced together with a summary of Markov chain Monte Carlo. The textbook will serve to give a very condensed review of these topics and of the prerequisites from stochastic processes. We will then switch to the two reference books for a deeper acquaintance with the topics Statistical learning and/or Simulation. It can be decided during the course, according to interest, whether to focus more on one of these topics

Further references:

  1. Vapnik, V. , Statistical Learning Theory, Wiley, 1998. A large treatise, mathematically rigorous, much different in style from Hastie et al. which focuses on application, and is not proof oriented.
  2. Vapnik, V., The Nature of Statistical Learning Theory, 2nd ed, Springer 1999. An abstract of the treatise above without proofs and with much background discussion.
  3. Devroye, L, Gyorfi, L., Lugosi, G., A Probabilistic Theory of Pattern Recognition, Spriner 1997. Mathematically rigorous as well, with different emphasis.
  4. Winkler, G., Image Analysis, Random Fields and Dynamic Monte Carlo Methods: A Mathematical Introduction. Springer 1995. An alternative to Robert and Casella for Markov chain Monte Carlo, excellent clear style.

Last modified: June 3, 2005