Error propagation with R-matrix model fitting

2003 ◽  
Vol 46 (3) ◽  
pp. 225 ◽  
Author(s):  
Zhenpeng CHEN
Keyword(s):  
Matrix Model ◽  
Error Propagation ◽  
Model Fitting ◽  
R Matrix

Big-Bang reaction rates within the R-matrix model

2005 ◽  
Vol 758 ◽  
pp. 783-786 ◽  
Author(s):  
P. Descouvemont ◽  
A. Adahchour ◽  
C. Angulo ◽  
A. Coc ◽  
E. Vangioni-Flam
Keyword(s):  
Matrix Model ◽  
Reaction Rates ◽  
Big Bang ◽  
R Matrix

scholarly journals Bias-free model fitting of correlated data in interferometry

2021 ◽  
Vol 38 ◽  
Author(s):  
Régis Lachaume
Keyword(s):  
Covariance Matrix ◽  
Nuclear Physics ◽  
Error Propagation ◽  
Model Fitting ◽  
Correlated Data ◽  
High Spectral Resolution ◽  
Model Parameters ◽  
Correlated Errors ◽  
Long Baseline ◽  
Significant Bias

Abstract In optical and infrared long-baseline interferometry, data often display significant correlated errors because of uncertain multiplicative factors such as the instrumental transfer function or the pixel-to-visibility matrix. In the context of model fitting, this situation often leads to a significant bias in the model parameters. In the most severe cases, this can can result in a fit lying outside of the range of measurement values. This is known in nuclear physics as Peelle’s Pertinent Puzzle. I show how this arises in the context of interferometry and determine that the relative bias is of the order of the square root of the correlated component of the relative uncertainty times the number of measurements. It impacts preferentially large datasets, such as those obtained in medium to high spectral resolution. I then give a conceptually simple and computationally cheap way to avoid the issue: model the data without covariances, estimate the covariance matrix by error propagation using the modelled data instead of the actual data, and perform the model fitting using the covariance matrix. I also show that a more imprecise but also unbiased result can be obtained from ignoring correlations in the model fitting.

Three Conceptual Impediments to Developing Scale Theory for Formative Scales

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 156-164 ◽  
Author(s):  
Keith A. Markus
Keyword(s):  
Scale Development ◽  
Item Analysis ◽  
Model Fitting ◽  
Item Bias ◽  
Validity Evidence ◽  
Scale Theory ◽  
Underlying Theory ◽  
Standard Scale ◽  
Item Scores

Abstract. Bollen and colleagues have advocated the use of formative scales despite the fact that formative scales lack an adequate underlying theory to guide development or validation such as that which underlies reflective scales. Three conceptual impediments impede the development of such theory: the redefinition of measurement restricted to the context of model fitting, the inscrutable notion of conceptual unity, and a systematic conflation of item scores with attributes. Setting aside these impediments opens the door to progress in developing the needed theory to support formative scale use. A broader perspective facilitates consideration of standard scale development concerns as applied to formative scales including scale development, item analysis, reliability, and item bias. While formative scales require a different pattern of emphasis, all five of the traditional sources of validity evidence apply to formative scales. Responsible use of formative scales requires greater attention to developing the requisite underlying theory.

Statistical Model Fitting: A State-of-the-Art Review

1978 ◽  
Vol 23 (11) ◽  
pp. 937-938
Author(s):  
JAMES R. KLUEGEL
Keyword(s):  
Statistical Model ◽  
State Of The Art ◽  
Model Fitting

Toward a relational matrix model of avatar-mediated interactions.

2019 ◽  
Vol 8 (3) ◽  
pp. 287-295 ◽  
Author(s):  
Jaime Banks ◽  
Caleb T. Carr
Keyword(s):  
Matrix Model

An approach for comparative quantification of myocardial blood flow (0-15-H2O-PET), perfusion (Tc-99m-tetrofosmin-SPECT), and metabolism (F 18-FDG-PET)

2001 ◽  
Vol 40 (05) ◽  
pp. 164-171 ◽  
Author(s):  
B. Nowak ◽  
H.-J. Kaiser ◽  
S. Block ◽  
K.-C. Koch ◽  
J. vom Dahl ◽  
...  
Keyword(s):  
Blood Flow ◽  
Myocardial Blood Flow ◽  
Fdg Pet ◽  
Model Fitting ◽  
Compartment Model ◽  
Left Ventricular ◽  
Short Axis ◽  
New Approach ◽  
Single Compartment Model ◽  
Tissue Fraction

Summary Aim: In the present study a new approach has been developed for comparative quantification of absolute myocardial blood flow (MBF), myocardial perfusion, and myocardial metabolism in short-axis slices. Methods: 42 patients with severe CAD, referred for myocardial viability diagnostics, were studied consecutively with 0-15-H2O PET (H2O-PET) (twice), Tc-99m-Tetrofosmin 5PECT (TT-SPECT) and F-18-FDG PET (FDG-PET). All dato sets were reconstructed using attenuation correction and reoriented into short axis slices. Each heart was divided into three representative slices (base, rnidventricular, apex) and 18 ROIs were defined on the FDG PET images and transferred to the corresponding H2O-PET and TT-SPECT slices. TT-SPECT and FDG-PET data were normalized to the ROI showing maximum perfusion. MBF was calculated for all left-ventricular ROIs using a single-compartment-model fitting the dynamic H2O-PET studies. Microsphere equivalent MBF (MBF_micr) was calculated by multiplying MBF and tissue-fraction, a parameter which was obtained by fitting the dynamic H2O-PET studies. To reduce influence of viability only well perfused areas (>70% TT-SPECT) were used for comparative quantification. Results: First and second mean global MBF values were 0.85 ml × min-1 × g-1 and 0.84 ml × min-1 × g1, respectively, with a repeatability coefficient of 0.30 ml ÷ min-1 × gl. After sectorization mean MBF_micr was between 0.58 ml × min1 ÷ ml"1 and 0.68 ml × min-1 × ml"1 in well perfused areas. Corresponding TT-SPECT values ranged from 83 % to 91 %, and FDG-PET values from 91 % to 103%. All procedures yielded higher values for the lateral than the septal regions. Conclusion: Comparative quantification of MBF, MBF_micr, TT-SPECT perfusion and FDG-PET metabolism can be done with the introduced method in short axis slices. The obtained values agree well with experimentally validated values of MBF and MBF_micr.

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