Projects
Project 1 [Due 1/28/2021]
Project 2 [Due 2/25/2021] - This project is optional, but I encourage your to attempt a solution before it is discussed in class.
Final project topics [Instructions.pdf]
Sparse FPCA
Bayesian FPCA
Curve Registration and Alignment Issues
Structured Functional Data, e.g. longitudinal functional, spatial functional, multivariate functional, …
Clustering Functional Data
Classification using Functional Predictors
Schedule of Lectures
(1/05) Introduction to Functional Data - Elements of Multivariate Analysis [Lecture.1.pdf - Recording]
(1/07) Mixed Effects Models [Lecture2.pdf - Recording]
(1/12) Basis Expansion and Smoothing [Lecture3.pdf - Lecture3.Rmd - Recording]
(1/14) Cross Validation and Mixed Effects Representations [Lecture4.pdf - Lecture4.Rmd - Recording]
(1/19) Mathematical Foundations [Lecture5.pdf - Recording]
(1/21) Estimation of the Mean and Covariance Functions [Lecture6.pdf - Lecture6.Rmd - Recording]
(1/26) Functional Principal Components Analysis [Lecture7.pdf - Lecture7.Rmd]
(1/28) fPCA for Sparse Data (Project 1 due) [Lecture8.pdf - Lecture8.Rmd - Recording]
(2/02) Discussion 1 (Project 1) [R_notebook - Recording]
(2/04) Class Cancelled
(2/09) Discussion 2 (Examples in fPCA) [R_notebook - Recording]
(2/11) Scalar on Function Regression [Lecture9.pdf - Recording]
(2/16) Functional Response Models [Lecture10.pdf - Recording]
(2/19) Discussion3: Functional Regression [R_notebook - Recording]
(2/23) Generalized Functional Regression and Inference for Functional Effects [Lecture11.pdf - Recording]
(2/25) Multivariate Functional Data [Lecture12.pdf - Lecture12.Rmd - Recording](Project 2 due)
(3/02) Longitudinal and Multidimensional Functional Data [Lecture13.pdf - Recording]
(3/04) Discussion of Project 2 [R_nootebook]
(3/09) Bayesian Analysis of Functional Data [Lecture13.pdf - Recording]
(3/11) Students Presentation
Coursework
60%: Two take-home projects
40%: Final project [Due March 19]
Reading List
Kokoszka P. and Reimherr M. Introduction to Functional Data Analysis. CRC Press. [IFDA]
Hsing T. and Eubank R. Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. Wiley.
Manuscripts
Xiao L, Li, Y, Ruppert D. (2013) Fast bivariate P-splines: the sandwich smoother. JRSS-B.
Xiao L, Zipunnikov V, Ruppert D, Crainiceanu C. (2016). Fast covariance estimation for high-dimensional functional data. Statistics and Computing.
Yao F, Muller HG, Wang JL. (2005) Functional data analysis for sparse longitudinal data. JASA.
Goldsmith et al. (2011) Penalized Functional Regression. JCGS.
Scheipl et al. (2015) Functional Additive Mixed Models. JCGS.
Suarez and Goshal, (2014) Bayesian Estimation of Principal Components for Functional Data. Bayesian Analysis.
Montagna et Al. (2012) Bayesian Latent Factor Regression for Functional and Longitudinal Data. Biometrics.
Happ C and Greven S (2018) Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains. JASA
Chen, K., Delicado, P., Müller, H.G. (2017). Modeling function-valued stochastic processes, with applications to fertility dynamics. J. Royal Statistical Society B.