Functional Data Analysis
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1 Functional Data Analysis Venue: Tuesday/Thursday 1:25-2:40 WN 145 Lecturer: Giles Hooker Office Hours: Wednesday 2-4 Comstock 1186 Ph: gjh27
2 Texts and Resources Ramsay and Silverman, 2007, "Functional Data Analysis", Springer Other Books: Eubank, 1996, "Nonparametric Regression and Spline Smoothing" Wahba, 1990, "Spline Models for Observational Data" Ferraty and Vieu, 2006, "Nonparametric Functional Data Analysis" Berlinet and Thomas-Agnan, 2004, "Reproducing Kernel Hilbert Spaces in Probability and Statistics"
3 Background Expectations Prerequisites: BTRY 601, 602 and ORIE 670 Really: Basic probability, theoretical statistics, linear algebra, multivariate calculus, programming. Helpful: Multivariate statistics, functional analysis, differential equations.
4 Software Matlab: fdam toolbox ( FDA toolbox also available for R/S-Plus I do not assume familiarity with Matlab, but some knowledge of programming may be helpful.
5 Assessment 3 assignments (15% each) In class discussion (15%) Brumback and Rice, 1998, "Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves", JASA, with discussion. Cuevas, Febrero and Fraiman, 2004, "An ANOVA Test for Functional Data", CSDA. Class project (40%) See Lecture 3
6 What is Functional Data? Measures of position of nib of a pen when writing "fda". 20 replications, measurements taken at 200 hertz.
7 Characteristics Data are measurements of smooth processes over time We usually do not want to make parametric assumptions about those processes. Often have multiple measurements of the same process We are interested in describing the variation of processes. Frequently, collected data have high resolution and low noise. Can be applied to any estimate of a smooth process.
8 Data may be measured more noisily Average daily precipitation in Vancouver, BC
9 Data may exhibit multiple modes of variation Nondurable goods index. Monthly readings
10 A More Complicated Scenario Data are low noise but low-resolution Measured at unequal intervals We know that the curves must be monotone
11 Salient Features May Be Rates of Change
12 Variation Is Not Always Vertical
13 And also: binary data count data density estimation bivariate/multivariate data
14 What is Functional Data Analysis? Analysis of data that are viewed as smooth curves Modes of variation between curves Discrimination between curves Using curves to predict other quantities (and vice versa) Making use of derivatives as data
15 Smoothing How, when, how much, properties:
16 Analysis of Multiple Curves Modes of variation First and second principle components of handwriting data.
17 Inference About Treatement Boys vs Girls
18 Relate Curves To Other Quantities Scalars predicted from curves: Also: curves from scalars, curves from curves, multiple regression.
19 Relationships Between Derivatives
20 Course Outline Introduction: Matlab, FDA Toolbox, Vizualisation, Projects Smoothing: Series estimators, splines, kernel estimates, computation Functional Data Analysis: Functional analysis, modes of variation, functional linear models Analysis of Derivatives: Differential equations, principle differential analysis, interpretation Constrained Smoothing: Positive, monotone smoothing; density estimation, registration. Requests and Suggestions
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