scholarly journals Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
H. Thomas Banks ◽  
Jared Catenacci ◽  
Shuhua Hu
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Measurement Errors ◽  
Model Misspecification ◽  
Building Blocks ◽  
Estimation Methods ◽  
Numerical Examples ◽  
Variance Estimate ◽  
Model Discrepancy

AbstractNormalized differences of several adjacent observations, referred to as pseudo-measurement errors in this paper, are used in so-called difference-based estimation methods as building blocks for the variance estimate of measurement errors. Numerical results demonstrate that pseudo-measurement errors can be used to serve the role of measurement errors. Based on this information, we propose the use of pseudo-measurement errors to determine an appropriate statistical model and then to subsequently investigate whether there is a mathematical model misspecification or error. We also propose to use the information provided by pseudo-measurement errors to quantify uncertainty in parameter estimation by bootstrapping methods. A number of numerical examples are given to illustrate the effectiveness of these proposed methods.

Role of extravascular protein in capillary-tissue fluid exchange

1978 ◽  
Vol 234 (1) ◽  
pp. H52-H58
Author(s):  
E. P. Salathe ◽  
R. Venkataraman
Keyword(s):  
Mathematical Model ◽  
Perturbation Theory ◽  
Osmotic Pressure ◽  
Analytic Solutions ◽  
Tissue Fluid ◽  
Fluid Exchange ◽  
Numerical Examples ◽  
Pathological Conditions ◽  
And Diffusion

A mathematical model of capillary-tissue fluid exchange is presented. The effect of variation in plasma and interstitial osmotic pressure that occurs as a result of convection and diffusion of protein is examined. Analytic solutions to the resulting equations are obtained by using the methods of perturbation theory. It is found that fluid exchange can significantly alter the pericapillary interstitial osmotic pressure, reducing both filtration and reabsorption. Variation in plasma osmotic pressure is important only for certain pathological conditions in which excessive filtration occurs. Specific numerical examples are presented which show quantitatively the extent of these effects for various normal and pathological conditions of physiological interest.

Estimation of lateral-directional aerodynamic derivatives from flight data using conventional and neural based methods

2014 ◽  
Vol 118 (1210) ◽  
pp. 1453-1479 ◽  
Author(s):  
R. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
A Priori ◽  
Estimation Methods ◽  
Control Input ◽  
Feed Forward Neural Network ◽  
Additional Advantage ◽  
Flight Data ◽  
Aerodynamic Derivatives ◽  
Different Types

Abstract The paper presents the estimation of lateral-directional aerodynamic derivatives (parameters) using conventional and neural based methods from real flight data of Hansa-3 aircraft. The conventional methods such as least squares (LS) and maximum likelihood (ML) require an a priori postulation of mathematical model to estimate the parameters. Whereas the neural-based method such as Neural-Gauss-Newton (NGN) is an algorithm that utilises feed forward neural network and Gauss-Newton optimisation to estimate the parameters and does not require any a priori postulation of mathematical model or solution of equations of motion. In the paper, the LS, ML and NGN methods are applied to lateral-directional flight data in order to estimate parameters. The results obtained in terms of lateral-directional aerodynamic derivatives are reasonably accurate to establish LS, ML and NGN as parameter estimation methods along with NGN method having an additional advantage of non-requirement of a priori mathematical model. The paper also highlights the effect of different types of control inputs on parameter estimation. For this, three types of control inputs were used to generate real flight data. The ailerons and rudder were deflected in the first, the ailerons were deflected while keeping rudder at trim condition in the second and the rudder was deflected while keeping ailerons at trim condition in the third type of control input to generate the real flight data. The paper presents the effect of three different types of control inputs in terms of aerodynamic parameters estimated through conventional and neural based methods using flight data generated through these inputs.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

The Role of the City in Merovingian Francia

2020 ◽  
pp. 581-610
Author(s):  
S. T. Loseby
Keyword(s):  
Roman Empire ◽  
Urban Communities ◽  
Late Antiquity ◽  
Building Blocks ◽  
Urban Network ◽  
City Councils ◽  
Royal Courts ◽  
Range Of Functions ◽  
Fierce Competition

The Merovingians inherited an urban network from the Roman Empire that remained substantially intact. Although Gallic cities had long been declining in extent and sophistication, during late antiquity their landscapes were adapted to contemporary priorities through the provision of walls and churches, and their politics was transformed by the emergence of bishops as leaders of urban communities. When the upper tiers of imperial administration disappeared, this equipped the vast majority of cities to survive as the basic building blocks of Merovingian kingdoms that were initially conceived as aggregations of city–territories. In ruling through their cities, the Merovingians expanded upon existing mechanisms for the extraction of taxes and services, while relying on centrally appointed bishops and counts rather than city councils for the projection of their authority. This generated fierce competition between kings for control of cities and among local elites for positions of power within them. In the later Merovingian period, however, the significance of cities diminished as stable territorial kingdoms emerged, political practice was centralized around the royal courts, and the Roman administrative legacy finally disintegrated. But the cities remained preeminent religious centers, and, with the beginnings of economic revival, continued to perform a range of functions unmatched by other categories of settlement.

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

scholarly journals Characterizing the building blocks of Problematic Use of the Internet (PUI): The role of obsessional impulses and impulsivity traits among Italian young adults

2021 ◽  
Vol 106 ◽  
pp. 152225
Author(s):  
Francesco Di Carlo ◽  
Mauro Pettorruso ◽  
Maria Chiara Alessi ◽  
Elena Picutti ◽  
Rebecca Collevecchio ◽  
...  
Keyword(s):  
Young Adults ◽  
Building Blocks ◽  
The Internet ◽  
Problematic Use ◽  
Use Of The Internet

Adoption of improved cassava varieties in Nigeria: Insights from DNA fingerprinting versus self-reporting varietal identification approaches

2021 ◽  
pp. 003072702199003
Author(s):  
Patience Ifeyinwa Opata ◽  
Oguejiofor Joseph Okorie ◽  
Juliana Chinasa Iwuchukwu ◽  
Chukwuma Otum Ume ◽  
Oyakhilomen Oyinbo
Keyword(s):  
Measurement Errors ◽  
Empirical Studies ◽  
Sub Saharan Africa ◽  
Limited Attention ◽  
Adoption Studies ◽  
Hidden Hunger ◽  
Varietal Identification ◽  
Sub Saharan ◽  
Cassava Varieties

Much of the empirical studies on crop varietal adoption in Sub-Saharan Africa relied on self-reported adoption in farm-household surveys, which is prone to measurement errors. In addition, farmers’ perceptions of consumption-related varietal traits in adoption studies has received limited attention compared with production-related traits. Using DNA-based and self-reported adoption measures, we analyze the adoption of improved cassava varieties (ICVs) with a focus on the extent of varietal misidentification, the sensitivity of the drivers of adoption to varietal misidentification and the role of farmers’ perceptions of biofortification trait in adoption decisions. We find that the adoption rate of ICVs is relatively high using both DNA-based and self-reported adoption measures, but there is notable misclassification in varietal adoption. We find that the mismatch in DNA-based and self-reported adoption measures leads to some variation in the factors that influence the likelihood and intensity of adoption of ICVs. This suggests that appropriate varietal identification helps in better understanding of the drivers of adoption. In addition, we find that despite the observed varietal misclassification, farmers’ perceptions of biofortification trait is significantly correlated with the probability and intensity of adoption of ICVs using both DNA-based and self-reported varietal identification. This suggests that inclusion of biofortification trait in cassava matters for both the likelihood and extent of adoption of ICVs. The latter lends credence to the emerging policy interests in breeding programs for biofortified crops to address hidden hunger in Nigeria.

scholarly journals Distance-Based Estimation Methods for Models for Discrete and Mixed-Scale Data

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 107
Author(s):  
Elisavet M. Sofikitou ◽  
Ray Liu ◽  
Huipei Wang ◽  
Marianthi Markatou
Keyword(s):  
Data Model ◽  
Null Hypothesis ◽  
Model Misspecification ◽  
Asymptotic Properties ◽  
Estimation Methods ◽  
Measurement Scale ◽  
Interval Scale ◽  
Pearson Residuals ◽  
Using Data ◽  
Scale Data

Pearson residuals aid the task of identifying model misspecification because they compare the estimated, using data, model with the model assumed under the null hypothesis. We present different formulations of the Pearson residual system that account for the measurement scale of the data and study their properties. We further concentrate on the case of mixed-scale data, that is, data measured in both categorical and interval scale. We study the asymptotic properties and the robustness of minimum disparity estimators obtained in the case of mixed-scale data and exemplify the performance of the methods via simulation.

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