scholarly journals Confidence Intervals for Stochastic Arithmetic

2021 ◽  
Vol 47 (2) ◽  
pp. 1-33
Author(s):  
Devan Sohier ◽  
Pablo De Oliveira Castro ◽  
François Févotte ◽  
Bruno Lathuilière ◽  
Eric Petit ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Uncertainty Quantification ◽  
Case Studies ◽  
Confidence Intervals ◽  
Scientific Computing ◽  
Floating Point ◽  
Stochastic Arithmetic ◽  
Quantity Of Interest ◽  
Normally Distributed

Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results. In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and code_aster.

scholarly journals PENERAPAN METODE BOOTSTRAP RESIDUAL DALAM MENGATASI BIAS PADA PENDUGA PARAMETER ANALISIS REGRESI

2014 ◽  
Vol 3 (4) ◽  
pp. 130
Author(s):  
NI MADE METTA ASTARI ◽  
NI LUH PUTU SUCIPTAWATI ◽  
I KOMANG GDE SUKARSA
Keyword(s):  
Regression Analysis ◽  
Statistical Analysis ◽  
Confidence Intervals ◽  
Bootstrap Method ◽  
Least Square ◽  
Prediction Tool ◽  
Analysis Method ◽  
Ordinary Least Square ◽  
Independent Variable ◽  
Parameter Estimators

Statistical analysis which aims to analyze a linear relationship between the independent variable and the dependent variable is known as regression analysis. To estimate parameters in a regression analysis method commonly used is the Ordinary Least Square (OLS). But the assumption is often violated in the OLS, the assumption of normality due to one outlier. As a result of the presence of outliers is parameter estimators produced by the OLS will be biased. Bootstrap Residual is a bootstrap method that is applied to the residual resampling process. The results showed that the residual bootstrap method is only able to overcome the bias on the number of outliers 5% with 99% confidence intervals. The resulting parameters estimators approach the residual bootstrap values ??OLS initial allegations were also able to show that the bootstrap is an accurate prediction tool.

scholarly journals Statistical analysis of cytogenetic data

2021 ◽  
Vol 28 ◽  
pp. 146-150
Author(s):  
L. A. Atramentova
Keyword(s):  
Data Structure ◽  
Statistical Analysis ◽  
Confidence Interval ◽  
Statistical Method ◽  
Confidence Intervals ◽  
Study Design ◽  
Cytogenetic Study ◽  
Data Set ◽  
Statistical Errors ◽  
Cytogenetic Data

Using the data obtained in a cytogenetic study as an example, we consider the typical errors that are made when performing statistical analysis. Widespread but flawed statistical analysis inevitably produces biased results and increases the likelihood of incorrect scientific conclusions. Errors occur due to not taking into account the study design and the structure of the analyzed data. The article shows how the numerical imbalance of the data set leads to a bias in the result. Using a dataset as an example, it explains how to balance the complex. It shows the advantage of presenting sample indicators with confidence intervals instead of statistical errors. Attention is drawn to the need to take into account the size of the analyzed shares when choosing a statistical method. It shows how the same data set can be analyzed in different ways depending on the purpose of the study. The algorithm of correct statistical analysis and the form of the tabular presentation of the results are described. Keywords: data structure, numerically unbalanced complex, confidence interval.

Case studies of predictive uncertainty quantification for geothermal models

Geothermics ◽  
2021 ◽  
Vol 97 ◽  
pp. 102263
Author(s):  
Jericho Omagbon ◽  
John Doherty ◽  
Angus Yeh ◽  
Racquel Colina ◽  
John O'Sullivan ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Case Studies ◽  
Predictive Uncertainty

Metal Adsorption in Biomass: Fundamentals and Application

2020 ◽  
Vol 25 ◽  
pp. 154-167
Author(s):  
M.F.C. Silva Canuto ◽  
J. Morais Ferreira ◽  
S.W.C. Araújo Silva ◽  
Líbia de Sousa Conrado ◽  
Odelsia Leonor Sánchez Alsina ◽  
...  
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Statistical Analysis ◽  
Confidence Intervals ◽  
Flow Rate ◽  
Fixed Bed ◽  
Metal Adsorption ◽  
Metallic Ions ◽  
Initial Concentration ◽  
System Temperature ◽  
Superficial Area

In this chapter the adsorption fundamentals using biomass as adsorbents in the removal of metallic ions are presented. The research as shows the importance of many factors that affects the adsorption, such as the biomass superficial area, system temperature, pH, initial concentration of the metal, biomass amount and status (living or dead). The study was directed at the approach of two applications using Saccharomyces cerevisiae yeast in the adsorption of Cd2+ metal ions. In the first application it is discussed the influence of the pH of the medium and the biomass status (living or dead) in the adsorption of Cd2+, in batch. In the second application, it was studied the adsorption of Cd2+metallic ions through the Saccharomyces cerevisiae yeast immobilized in chitosan, in fixed bed, where the influence inlet mass flow rate and the initial effluent concentration on the adsorption capacity and percentage of Cd2+ ions removal are evaluated.The studies realized are supported by statistical analysis with 95% confidence intervals.

scholarly journals Floating-point profiling of ACTS using Verrou

2019 ◽  
Vol 214 ◽  
pp. 05025
Author(s):  
Hadrien Grasland ◽  
François Févotte ◽  
Bruno Lathuilière ◽  
David Chamont
Keyword(s):  
Iterative Methods ◽  
Numerical Stability ◽  
Scientific Computing ◽  
Floating Point ◽  
Track Reconstruction ◽  
Dual Purpose ◽  
Dynamic Instrumentation

Floating-point computations play a central role in scientific computing. Achieving high numerical stability in these computations affects not just correctness, but also computing efficiency, by accelerating the convergence of iterative methods and expanding the available choices of precision. The ACTS project aims at establishing an experiment-agnostic track reconstruction toolkit. It originates from the ATLAS Run2 tracking software and has already received strong adoption by FCC-hh. It is also being evaluated for possible use by the CLICdp and Belle 2 experiments. In this study, Verrou, a Valgrind-based tool for dynamic instrumentation of floating-point computations, was applied to the ACTS codebase for the dual purpose of evaluating its numerical stability and investigating possible avenues for use of reduced-precision arithmetic.

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