Statistical Analysis of Functional Data

2010 ◽  
pp. 417-425 ◽  
Author(s):  
F. Ferraty ◽  
P. Sarda ◽  
P. Vieu
Keyword(s):  
Statistical Analysis ◽  
Functional Data

scholarly journals Advanced Statistical Analysis of 3D Kinect Data: Mimetic Muscle Rehabilitation Following Head and Neck Surgeries Causing Facial Paresis

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 103
Author(s):  
Jan Kohout ◽  
Ludmila Verešpejová ◽  
Pavel Kříž ◽  
Lenka Červená ◽  
Karel Štícha ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Functional Data ◽  
Muscle Function ◽  
Evaluation Process ◽  
Multiple Logistic Regression ◽  
Facial Paresis ◽  
Kinect Camera ◽  
3D Camera ◽  
Mimetic Muscles ◽  
Data Analytic

An advanced statistical analysis of patients’ faces after specific surgical procedures that temporarily negatively affect the patient’s mimetic muscles is presented. For effective planning of rehabilitation, which typically lasts several months, it is crucial to correctly evaluate the improvement of the mimetic muscle function. The current way of describing the development of rehabilitation depends on the subjective opinion and expertise of the clinician and is not very precise concerning when the most common classification (House–Brackmann scale) is used. Our system is based on a stereovision Kinect camera and an advanced mathematical approach that objectively quantifies the mimetic muscle function independently of the clinician’s opinion. To effectively deal with the complexity of the 3D camera input data and uncertainty of the evaluation process, we designed a three-stage data-analytic procedure combining the calculation of indicators determined by clinicians with advanced statistical methods including functional data analysis and ordinal (multiple) logistic regression. We worked with a dataset of 93 distinct patients and 122 sets of measurements. In comparison to the classification with the House–Brackmann scale the developed system is able to automatically monitor reinnervation of mimetic muscles giving us opportunity to discriminate even small improvements during the course of rehabilitation.

Variation and Evolution of Function-Valued Traits

2018 ◽  
Vol 49 (1) ◽  
pp. 139-164 ◽  
Author(s):  
Richard Gomulkiewicz ◽  
Joel G. Kingsolver ◽  
Patrick A. Carter ◽  
Nancy Heckman
Keyword(s):  
Statistical Analysis ◽  
Conceptual Understanding ◽  
Functional Data ◽  
Evolutionary Dynamics ◽  
Natural Populations ◽  
Worked Examples ◽  
Heritable Variation ◽  
Continuous Index

Function-valued traits—phenotypes whose expression depends on a continuous index (such as age, temperature, or space)—occur throughout biology and, like any trait, it is important to understand how they vary and evolve. Although methods for analyzing variation and evolution of function-valued traits are well developed, they have been underutilized by evolutionists, especially those who study natural populations. We seek to summarize advances in the study of function-valued traits and to make their analyses more approachable and accessible to biologists who could benefit greatly from their use. To that end, we explain how curve thinking benefits conceptual understanding and statistical analysis of functional data. We provide a detailed guide to the most flexible and statistically powerful methods and include worked examples (with R code) as supplemental material. We review ways to characterize variation in function-valued traits and analyze consequences for evolution, including constraint. We also discuss how selection on function-valued traits can be estimated and combined with estimates of heritable variation to project evolutionary dynamics.

Statistical analysis of classification

1966 ◽  
Vol 24 ◽  
pp. 188-189
Author(s):  
T. J. Deeming
Keyword(s):  
Multivariate Analysis ◽  
Statistical Analysis ◽  
Classification Scheme ◽  
Analytical Procedure ◽  
Narrow Band ◽  
Scientific Research ◽  
Maximum Amount ◽  
Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

Quantitative parallel EELS spectrum imaging developed as a new tool in AEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1202-1203
Author(s):  
Gianluigi Botton ◽  
Gilles L'espérance
Keyword(s):  
Statistical Analysis ◽  
Spatial Resolution ◽  
Personal Computer ◽  
Systematic Study ◽  
Present Author ◽  
Chemical Elements ◽  
Detection Limits ◽  
Research Groups ◽  
Quantitative Performance ◽  
Spectrum Imaging

As interest for parallel EELS spectrum imaging grows in laboratories equipped with commercial spectrometers, different approaches were used in recent years by a few research groups in the development of the technique of spectrum imaging as reported in the literature. Either by controlling, with a personal computer both the microsope and the spectrometer or using more powerful workstations interfaced to conventional multichannel analysers with commercially available programs to control the microscope and the spectrometer, spectrum images can now be obtained. Work on the limits of the technique, in terms of the quantitative performance was reported, however, by the present author where a systematic study of artifacts detection limits, statistical errors as a function of desired spatial resolution and range of chemical elements to be studied in a map was carried out The aim of the present paper is to show an application of quantitative parallel EELS spectrum imaging where statistical analysis is performed at each pixel and interpretation is carried out using criteria established from the statistical analysis and variations in composition are analyzed with the help of information retreived from t/γ maps so that artifacts are avoided.

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