Reference EntryDOI
Functional Data Analysis
Reads0
Chats0
TLDR
The article considers general issues such as characteristics of functional data, uses of derivatives in functional modelling, estimation of phase variation by the alignment or registration of curve features, the nature of error, and so forth.Abstract:
When either data or the models for them involve functions, and when only weak assumptions about these functions such as smoothness are permitted, familiar statistical methods must be modified and new approaches developed in order to take advantage of this smoothness. The first part of the article considers some general issues such as characteristics of functional data, uses of derivatives in functional modelling, estimation of phase variation by the alignment or registration of curve features, the nature of error, and so forth. The second section describes functional versions of traditional methods such principal components analysis and linear modelling, and also mentions purely functional approaches that involve working with and estimating differential equations in the functional data analysis process.read more
Citations
More filters
Journal ArticleDOI
Principal component analysis: a review and recent developments
TL;DR: The basic ideas of PCA are introduced, discussing what it can and cannot do, and some variants of the technique have been developed that are tailored to various different data types and structures.
Journal ArticleDOI
Inverse problems: A Bayesian perspective
TL;DR: The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Journal ArticleDOI
Gaussian predictive process models for large spatial data sets
TL;DR: This work achieves the flexibility to accommodate non‐stationary, non‐Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets in the form of a computational template encompassing these diverse settings.
Journal ArticleDOI
Health behavior models in the age of mobile interventions: are our theories up to the task?
William T. Riley,Daniel E. Rivera,Audie A. Atienza,Wendy Nilsen,Susannah Allison,Robin J. Mermelstein +5 more
TL;DR: Current theories appear inadequate to inform mobile intervention development as these interventions become more interactive and adaptive, and Dynamic feedback system theories of health behavior can be developed utilizing longitudinal data from mobile devices and control systems engineering models.
Journal ArticleDOI
Attention to eyes is present but in decline in 2–6-month-old infants later diagnosed with autism
Warren Jones,Ami Klin +1 more
TL;DR: It is shown in a prospective longitudinal study that infants later diagnosed with autism spectrum disorders (ASDs) exhibit mean decline in eye fixation from 2 to 6 months of age, a pattern not observed in infants who do not develop ASD.
References
More filters
Book ChapterDOI
Functional Data Analysis
TL;DR: In this article, the authors introduce the concept of functional data analysis (FDA) to describe the smoothness of the process of generating functional data from a set of observed curves and images.
Journal ArticleDOI
Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields
TL;DR: In this paper, the expected Euler characteristic of excursion sets of stationary Gaussian random fields has been derived by Adler and Hasofer (1976) and Adler (1981), and applied to some 3D images of cerebral blood flow from a study on pain perception.