Information
About Castro Urdiales
Scope of the course
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The ECAS 2013 session will give a general overview of the methodological and practical aspects of Functional Data Analysis (FDA) with recent advances. Functional data analysis is a branch of statistics that analyzes data providing information about curves, surfaces or anything else varying over a continuum. The continuum is often time, but may also be spatial location, wavelength, probability, etc. The data may be so accurate that error can be ignored, may be subject to substantial measurement error, or even have a complex indirect relationship to the curve that they define. Models for functional data and methods for their analysis may resemble those for conventional multivariate data, including linear and nonlinear regression models, principal components analysis, and many others. But the possibility of using derivative information greatly extends the power of these methods, and also leads to purely functional models such as those defined by differential equations. Most recent developments will be considered too, and their practical approach will receive attention using the R software. For example, measurements of the heights of children over a wide range of ages have an error level so small as to be ignorable for many purposes, but daily records of precipitation at a weather station are so variable as to require careful and sophisticated analyses in order to extract something like a mean precipitation curve. These curves are often smooth in functional data analysis. In particular, functional data analyses often make use of the information in the slopes and curvatures of curves, as reflected in their derivatives. Plots of first and second derivatives as functions of t, or plots of second derivative values as functions of first derivative values, may reveal important aspects of the processes generating the data. As a consequence, curve estimation methods designed to yield good derivative estimates can play a critical role in functional data analysis. The analysis of complex data types that is an extension of Functional Data Analysis where one considers methods to analyze data samples of complex objects. Modern science is generating a need to understand, and statistically analyze, populations of increasingly complex types. The potential audience of this ECAS Session are PhD students, substantive researches, methodologists in Mathematics and Computer Science (Bioinformatics, Biostatistics, Epidemiologist), as well as statisticians with interests in FDA. It is assumed that the participants benefit of a good background in statistics up to and including multivariate analysis, and have been exposed to matrix algebra. Participants will learn modeling real data – eventually on their own WIFI compatible laptop - but no previous acquaintance with one of the currently available software packages in FDA is required. Topics
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