Introduction to Computational Methods in Biostatistics (FALL 2014)

  • Instructor
  • Donatello Telesca
  • Office location: PUB HLT 21-254B
  • Office Hours: TR (2:30PM - 3:30PM)  or by appointment  
  • dtelesca at ucla dot edu

Meeting Times
  • Lecture          TR  1:00PM - 2:50PM   PUB HLT  41235

Syllabus

Lectures
  • (10/02) Introduction to R + Linear Regression + Matrix Manipulations - Sweep and Cholesky (Lange Ch.6 - 7)
  • (10/07) Gram-Schmidt's QR decomposition - Eigenanalysis and Singular Value Decomposition (Lange Ch. 8-9)
  • (10/09) Ridge Regression and Bayesian Analysis of Linear Models + Rudiments of Optimization (Lange Ch 9, 11)
  • (10/14) Newton's method and Fisher scoring (Lange ch14, GH ch 2).
  • (10/16) L1 Regularization, LARS and Gradient Descent (Lange Ch 16 + Efron et. al, 2004) - Project 1 Due 
  • (10/21) MM and EM algorithms (GH Ch 4 - Lange Ch 12-13)
  • (10/23) More applications of MM-EM - Examples: Adaptive Lasso, Linear and Logistic Regression. (Lange Ch 12)
  • (10/28) Optimization Lab (Logistic Regression via Fisher and MM) + Hidden Markov Models. (Bayesian Core, Ch. 7) 
  • (10/30) Introduction to Numerical Integration and Quadrature (GH Ch 5)
  • (11/04) Class Cancelled 
  • (11/06) Gaussian Quadrature + Laplace Approximations - Approximation of Marginal Likelihoods (GH Ch 5 +  Lange Ch 4)
  • (11/11) Veterans Day Holiday (no class)
  • (11/13) Intro to Monte Carlo - Generation of Random Variates - AR - ARS - [Lange Ch 22] Project 2 Due
  • (11/18) Monte Carlo Metods - Variance Reduction [GH + Lange]
  • (11/20) Review of Bayesian Inference [See. Hoff Textbook + Notes]
  • (11/25) Introduction to Markov Chain Monte Carlo
  • (11/27) Thanksgiving Holiday (no class)
  • (12/02) Directed Acyclic Graphs, Hierarchical Models and Bayesian Computation [Hoff +Bayesian Core]
  • (12/04) Mixture Models, Auxiliary Variables and Varying Dimensional Problems. [Bayesian Core]
  • (12/09) Statistics Seminar Lecture on Model Selection (2:00 PM - 4216 Young Hall)
  • (12/11) Project 3 Due

Coursework
  • 3 take home projects  -  each counting for 1/3 of your final grade

Reading List
Books:
  • (Required) G. H. Givens and J. A. Hoeting. Computational Statistics, Wiley. [Good introduction to most problems]
  • (Optional) K. Lange. Numerical Analysis for Statisticians. Springer. [More rigorous introduction to numerical analysis]
  • (Optional) P. Dalgaard. Introductory Statistics with R. Springer. [Useful if you are new to R or programming]
  • (Optional) Wicham H. Advanced R. [In progress, but already a wonderful reference for more advanced R programming. Available at: http://adv-r.had.co.nz]

Manuscripts and additional Books:
  • Efron B, Hastie T, Johnstone I and Tibshirani R. 2004. Least Angle Regression. Annals of Statistics, 32 (2), 407-499.
  • The Bayesian Core, Marin and Robert, Springer (Available online as an electronic text form the ucla library).
  • A First Course in Bayesian Statistical Methods. Hoff, P., Springer (Available online as an electronic text from the ucla library).
  • Linear Algebra and Matrix Analysis for Statistics. Banerjee S. and Roy A. CRC Press.
  • An Introduction to Statistical Learning (with applications in R). Gareth J., Witten D, Hastie T, Tibshirani R. Springer.
  • Machine Learning. A Probabilistic Perspective. Murphy K. MIT Press
  • Introducing Monte Carlo Methods with R. Robert C.P. and Casella G. Springer 
(Please visit the site regularly for updates)

Computing
Computing for Biostat 213 will be based on the R programming language (http://cran.r-project.org/).
Instructions will be given in class on how to set up your computational platform.