Linear and nonlinear regression

Chapters 1 and 2 cover the geometry of linear and nonlinear least squares and QR decomposition:

Bates, D. and D. Watts, 1988, Nonlinear Regression Analysis and its Applications, Wiley (on reserves in the SFU library)

G.A.F. Seber, 2003, Nonlinear Regression, Wiley-Interscience (on reserves in the SFU library)

MATLAB

Online book to help you learn Matlab www.scribd.com/doc/8961437/Learn-Matlab-70

This book describes Matlab basics for statisticians and includes the computational statistics software package:

W.L. Martinez and A.R. Martinez, 2008 Computational Statistics Handbook with Matlab (available online through the library web site and on reserves) see also the MCMC software section below

MCMC

This is usually the first paper that I give someone if they ask me about MCMC:

Liu, J (1999), Markov Chain Monte Carlo and Related Topics, Proceedings of the IX General Assembly, p451

Convergence diagnostics like Raftery-Lewis, Geweke and Gelman-Rubin are described here:

Cowles, M. K., and Carlin, B., P. (1996), Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review, Journal of the American Statistical Association, 91, 883-904.

Population MCMC (including Parallel Tempering) description and details in a review paper:

Jasra, A., Stephens, D. and Holmes, C. (2007), On Population-based Simulation for Static Inference, Stat Comput, 17, 263-279

W.S. Kendall, F. Liang, J.-S. Wang (Eds.) 2005, Markov chain Monte Carlo: innovations and applications (available online through the library and on reserves)

Liang F, Liu, Chuanhai, Carroll RJ. (2007) Stochastic Approximation in Monte Carlo Computing. Journal of the American Statistical Association 102(477), 305-20.

MCMC Software in Matlab

A Matlab version of the popular R software CODA: along with documentation for the Raftery-Lewis and Geweke MCMC diagnostics

The Computational Statistics Handbook with Matlab also offers the computational statistics software library from the webpage of the book

Functional Data Analysis

webpage with software in R and Matlab. Also look for the software manual (with the software) and the examples tab from the main-page. The examples offer some extra background to supplement what we've been doing in class. I'd suggest this as the first place to go for more resources

In the week 3 day 1 and 2 classes we covered parts of the first 5 chapters of the Functional Data Analysis (book) by Ramsay and Silverman, available online through the SFU library site. We will also cover parts of chapters 14, 17, 18 and 19. Clearly we are giving this material only superficial treatment so that we can focus on dynamical systems.

There is also a book Applied Functional Data Analysis also online through the SFU library site. This book is very applied and focuses on using the methods through a lot of examples.

M. Varziri, K. McAuley, and P. McLellan Parameter Estimation in Continuous-Time Dynamic Models in the Presence of Unmeasured States and Nonstationary Disturbances Ind. Eng. Chem. Res. 2008, 47 (2), 380-393

Ramsay, J. O., Hooker, G., Campbell, D. and Cao, J. (2007). Parameter estimation for differential equations: A generalized smoothing approach (with discussion). Journal of the Royal Statistical Society, Series B. 69, 741-796

General Advanced Statistics

This book has some info on basis expansions, kernel smoothing, MCMC and more. For our purposes it is not in depth but it is one of the most popular advanced statistics texts:

Hastie, T., Tibshirani, R. and J. Friedman (2009) Elements of Statistical Learning: Data Mining, Inference, and Prediction 2nd ed. (available online through the library)

The best selling Bayesian text. Includes minimal sections on fancy MCMC methods but an excellent Bayesian text. Chapter 20 is about non-linear models and section 20.3 provides an in-depth example of an ODE system:

Gelman, A., Carlin, J., Stern, H. and D. Rubin (2004) Bayesian Data Analysis (unfortunately not on reserves or online from the library but some pages are available through google books)

Filtering

An Introduction to the Kalman Filter a light introduction by Welch and Bishop.

Some discussion about filtering methods:

J.R. Raol, G. Girija & J. Singh, 2004, Modelling and Parameter Estimation of Dynamic Systems, iee control series. (on reserves in the SFU library)

Learning the Kalman Filter a Matlab m file function for the basic Kalman filter with a lot of comments

Kalman Filter Tutorial a Matlab m file tutorial for the Extended Kalman Filter

Learning the Extended Kalman Filter a Matlab m file function with many comments.

Inference for Nonlinear Dynamical Systems by Ionides et al. in PNAS December 2006, Vol 103, No 49 p18438-18443 See also the supporting material from the web page of Ed Ionides

A Sequential Monte Carlo Approach for Marine Ecological Prediction by Dowd in Environmetrics, Dec 2005, Vol 17, Iss 5 p435-455