Model Validation of Functional Responses Across Experimental Regions Using Functional Regression Extensions to the CORA Objective Rating System

As we continue to model more complex systems, the validation of dynamical responses has come to the forefront of modeling and simulation. One form of dynamic response is when the output is a function of time. The proper evaluation of functional data over an array of desired input parameters is critical to achieving a robust validation assessment of a simulation model. We extend the correlation analysis (CORA) objective rating system to validate functional data across experimental regions. Functional regression analysis is used to generate surrogate estimations of the system response functions at points within the region where experimental observations are absent. These CORA scores provide a measure of disagreement at each desired parameter configuration. An overall score for model validity is achieved using a weighted linear combination of the individual CORA scores. Finally, an improved CORA size scoring metric is introduced.

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A general framework for functional regression modelling

Statistical Modelling ◽

10.1177/1471082x16681317 ◽

2017 ◽

Vol 17 (1-2) ◽

pp. 1-35 ◽

Cited By ~ 32

Author(s):

Sonja Greven ◽

Fabian Scheipl

Keyword(s):

Functional Data ◽

Regression Models ◽

Generalized Additive Models ◽

Large Body ◽

Imaging Study ◽

Additive Models ◽

Gradient Boosting ◽

Functional Regression ◽

Functional Responses ◽

Additive Mixed Models

Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for ‘generalized’ functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases—particularly splines and functional principal components—and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost , respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

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Establishment of a Medication Acuity Scoring Tool at a Tertiary Pediatric Teaching Hospital: A 2-Phase Process

Journal of Pharmacy Practice ◽

10.1177/0897190018795261 ◽

2018 ◽

Vol 33 (2) ◽

pp. 164-172

Author(s):

Kailynn DeRonde ◽

Claire Palmer ◽

Jane Gralla ◽

Kevin Poel

Keyword(s):

Phase I ◽

Clinical Experience ◽

Phase Ii ◽

Rating System ◽

Intrarater Reliability ◽

Safety Standards ◽

Objective Rating ◽

The Individual ◽

Scoring Tool ◽

Phase Process

Background: Currently, there is no validated objective rating system to address the acuity of medication orders that pharmacists review. Objective: The objective was to assess the acuity of a given medication through creating and validating an acuity scoring tool. Methods: Phase I included the development of the medication acuity scoring tool (MAST) from national safety standards and clinical experience. A survey was administered to pharmacists nationwide to establish a consensus on the individual components of the tool and their associated weighted scores. Phase II was designed to assess MAST's predictive validity by comparing a medication acuity rating generated by MAST to a rating assigned based upon clinical experience of experts. Additionally, in phase II, interrater and intrarater reliability of MAST was evaluated. Results: In phase I, most of MAST’s components and their associated scores achieved >75% agreement for inclusion in the final tool. In phase II, without MAST, approximately 50% of pharmacist-assigned acuity ratings were statistically consistent with tool-generated acuity ratings, and there was fair agreement between respondents (k=0.31). With the use of MAST, agreement in acuity ratings improved to substantial (k=0.69), and intrarater reliability was almost perfect (k=0.88). Conclusion: MAST is a validated rating system that captures the acuity of medications.

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Regression Modeling for Computer Model Validation With Functional Responses

Volume 1: 34th Design Automation Conference, Parts A and B ◽

10.1115/detc2008-49662 ◽

2008 ◽

Author(s):

Xuyuan Liu ◽

Kwok-Leung Tsui ◽

Wei Chen

Keyword(s):

Computer Model ◽

Functional Data ◽

Single Step ◽

Functional Regression ◽

Computationally Efficient ◽

Functional Responses ◽

Physical Experiments ◽

Step Procedure ◽

Combining Data ◽

Bias Function

Statistical analysis of functional responses based on functional data from both computer and physical experiments has gained increasing attention due to the dynamic nature of many engineering systems. However, the complexity and huge amount of functional data bring many difficulties to apply traditional or existing methodologies. The objective of the present study is twofold: (1) prediction of functional responses based on functional data and (2) prediction of bias function for validation of a computer model that predicts functional responses. In this paper, we first develop a functional regression model with linear basis functions to analyze functional data. Then combining data from both computer and physical experiments, we use the functional analysis modeling to predict the bias function which is crucial for validating a computer model. The proposed method, following the classical nonparametric regression framework, uses a single step procedure which is easily implemented and computationally efficient. Through an application example of motor engine analysis to predict acceleration performance and gear shift events, we demonstrate our approach and compare it to using the Gaussian process modeling approach.

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Wildfires Vegetation Recovery through Satellite Remote Sensing and Functional Data Analysis

Mathematics ◽

10.3390/math9111305 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1305

Author(s):

Feliu Serra-Burriel ◽

Pedro Delicado ◽

Fernando M. Cucchietti

Keyword(s):

Remote Sensing ◽

Data Analysis ◽

Functional Data Analysis ◽

Functional Data ◽

Vegetation Index ◽

Vegetation Recovery ◽

Functional Responses ◽

Elapsed Time ◽

Synthetic Controls ◽

Available Information

In recent years, wildfires have caused havoc across the world, which are especially aggravated in certain regions due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following years. We aim to explain the dynamics of wildfires’ effects on a vegetation index (previously estimated by causal inference through synthetic controls) from pre-wildfire available information (mainly proceeding from satellites). For this purpose, we use regression models from Functional Data Analysis, where wildfire effects are considered functional responses, depending on elapsed time after each wildfire, while pre-wildfire information acts as scalar covariates. Our main findings show that vegetation recovery after wildfires is a slow process, affected by many pre-wildfire conditions, among which the richness and diversity of vegetation is one of the best predictors for the recovery.

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Recombination within the HLA-D region. Correlation of molecular genotyping with functional data.

Journal of Experimental Medicine ◽

10.1084/jem.160.1.222 ◽

1984 ◽

Vol 160 (1) ◽

pp. 222-238 ◽

Cited By ~ 16

Author(s):

M A Robinson ◽

E O Long ◽

A H Johnson ◽

R J Hartzman ◽

B Mach ◽

...

Keyword(s):

Functional Data ◽

Southern Blot Analysis ◽

Hla Typing ◽

Subtle Difference ◽

Molecular Genotyping ◽

Recombinant Haplotype ◽

Allelic Differences ◽

D Region ◽

The Individual ◽

Hla Haplotypes

Molecular genotyping of the HLA-D/DR region in a family correlated with serologic and cellular typing data. It was further possible to predict a subtle difference in SB region-related functions from such molecular studies. A family that included an individual who inherited an HLA haplotype with a paternal recombination between HLA-B and the HLA-D/DR region was identified by classic HLA typing techniques. Segregation of HLA-D/DR region genes in this family was studied by Southern blot analysis using cDNA probes for DR alpha, DR beta, DC alpha, DC beta, and SB beta. Restriction enzyme fragment polymorphisms observed for every gene tested were in concordance with assigned HLA haplotypes (including the individual known to have inherited a paternal recombinant haplotype) with one exception: two HLA identical siblings were observed to have different SB beta restriction fragment patterns. Further testing revealed that one individual inherited a maternal HLA haplotype recombinant between the HLA-D/DR region and SB beta. Although both maternal SB alleles typed as SB4, allelic differences could be detected cellularly by primed lymphocytes and by the differential expression of a class II cell surface antigen using monoclonal antibody. Therefore, predicted and nonpredicted recombinant haplotypes were detected in a family by molecular genotyping.

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Circadian system response to night work in relation to the individual circadian phase position

International Archives of Occupational and Environmental Health ◽

10.1007/bf00378145 ◽

1979 ◽

Vol 43 (2) ◽

pp. 73-83 ◽

Cited By ~ 51

Author(s):

G. Hildebrandt ◽

I. Stratmann

Keyword(s):

Circadian System ◽

Night Work ◽

System Response ◽

Circadian Phase ◽

The Individual

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Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

Journal of Vibration and Acoustics ◽

10.1115/1.2893859 ◽

1998 ◽

Vol 120 (2) ◽

pp. 509-516 ◽

Cited By ~ 5

Author(s):

J. A. Morgan ◽

C. Pierre ◽

G. M. Hulbert

Keyword(s):

Frequency Response ◽

Coupled System ◽

Companion Paper ◽

Component Mode Synthesis ◽

Response Functions ◽

Frequency Response Functions ◽

Measured Frequency ◽

Measured Frequency Response ◽

Coupled Beams ◽

The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

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Kernel Regression Estimation for Functional Data

10.1093/oxfordhb/9780199568444.013.4 ◽

2018 ◽

Author(s):

Frédéric Ferraty ◽

Philippe Vieu

Keyword(s):

Kernel Methods ◽

Functional Data ◽

Linear Functional ◽

Kernel Smoothing ◽

Kernel Regression ◽

Functional Regression ◽

Regression Estimation ◽

Asymptotic Results ◽

Kernel Regression Estimation ◽

The Impact

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.

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Dynamic Analysis of Ball Bearings Due to Clearance Effect

Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2009-87147 ◽

2009 ◽

Author(s):

S. H. Upadhyay ◽

S. C. Jain ◽

S. P. Harsha

Keyword(s):

Chaotic Behavior ◽

Equations Of Motion ◽

Peak Frequency ◽

System Response ◽

Ball Bearings ◽

Outer Race ◽

Lagrange’S Equation ◽

Rolling Elements ◽

Machine Systems ◽

The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

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