A Simple Index for Representing the Discrepancy between Simulations of Physiological Pharmacokinetic Models and Experimental Data

1995 ◽  
Vol 11 (4) ◽  
pp. 413-421 ◽  
Author(s):  
Kannan Krishnan ◽  
Sami Haddad ◽  
Michael Pelekis
Keyword(s):  
Experimental Data ◽  
Root Mean Square ◽  
Pbpk Model ◽  
Quantitative Measure ◽  
Sampling Point ◽  
Mean Square ◽  
Data Set ◽  
Model Simulations ◽  
Pbpk Models ◽  
Experimental Values

The objective of this study was to develop an index that would provide a quantitative measure of the degree of discrepancy between simulations of physiologically based pharmacokinetic (PBPK) models and experimental data. The approach we developed involves the calculation of the root mean square of the error (representing the difference between the individual simulated and experimental values for each sampling point in a time course curve), and dividing it by the root mean square of the experimental values. The resulting numerical values of discrepancy measures for several data sets (each corresponding to an end point) obtained in a single experimental study are then combined on the basis of a weighting proportional to the number of data points contained in each data set. Such consolidated discrepancy indices obtained from several experiments (e.g., exposure scenarios, doses, routes, species) are averaged to get an overall discrepancy index, referred to as the PBPK index. This empirical index reflects the overall, weighted average percent difference between the a priori PBPK model simulations and experimental data. The proposed methodology is illustrated using previously published experimental and simulated data on dichloromethane pharmacokinetics in humans. The application of this kind of a "quantitative" method should help remove the ambiguity in communicating the degree of concordance or discrepancy between PBPK model simulations and experimental data.

scholarly journals Observed and estimated leaf appearance of landrace and improved maize cultivars

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Josana Andreia Langner ◽  
Nereu Augusto Streck ◽  
Angelica Durigon ◽  
Stefanía Dalmolin da Silva ◽  
Isabel Lago ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Sowing Date ◽  
Mean Square ◽  
Data Set ◽  
Growing Seasons ◽  
Maize Cultivars ◽  
Maize Varieties ◽  
Leaf Appearance

ABSTRACT: The objective of this study was to compare the simulations of leaf appearance of landrace and improved maize cultivars using the CSM-CERES-Maize (linear) and the Wang and Engel models (nonlinear). The coefficients of the models were calibrated using a data set of total leaf number collected in the 11/04/2013 sowing date for the landrace varieties ‘Cinquentinha’ and ‘Bico de Ouro’ and the simple hybrid ‘AS 1573PRO’. For the ‘BRS Planalto’ variety, model coefficients were estimated with data from 12/13/2014 sowing date. Evaluation of the models was with independent data sets collected during the growing seasons of 2013/2014 (Experiment 1) and 2014/2015 (Experiment 2) in Santa Maria, RS, Brazil. Total number of leaves for both landrace and improved maize varieties was better estimated with the Wang and Engel model, with a root mean square error of 1.0 leaf, while estimations with the CSM-CERES-Maize model had a root mean square error of 1.5 leaf.

scholarly journals Corn Yield Prediction With Ensemble CNN-DNN

2021 ◽  
Vol 12 ◽  
Author(s):  
Mohsen Shahhosseini ◽  
Guiping Hu ◽  
Saeed Khaki ◽  
Sotirios V. Archontoulis
Keyword(s):  
Root Mean Square ◽  
Predictive Performance ◽  
Ensemble Method ◽  
Corn Belt ◽  
Corn Yield ◽  
Yield Prediction ◽  
Mean Square ◽  
Data Set ◽  
The Us ◽  
Spatio Temporal

We investigate the predictive performance of two novel CNN-DNN machine learning ensemble models in predicting county-level corn yields across the US Corn Belt (12 states). The developed data set is a combination of management, environment, and historical corn yields from 1980 to 2019. Two scenarios for ensemble creation are considered: homogenous and heterogenous ensembles. In homogenous ensembles, the base CNN-DNN models are all the same, but they are generated with a bagging procedure to ensure they exhibit a certain level of diversity. Heterogenous ensembles are created from different base CNN-DNN models which share the same architecture but have different hyperparameters. Three types of ensemble creation methods were used to create several ensembles for either of the scenarios: Basic Ensemble Method (BEM), Generalized Ensemble Method (GEM), and stacked generalized ensembles. Results indicated that both designed ensemble types (heterogenous and homogenous) outperform the ensembles created from five individual ML models (linear regression, LASSO, random forest, XGBoost, and LightGBM). Furthermore, by introducing improvements over the heterogenous ensembles, the homogenous ensembles provide the most accurate yield predictions across US Corn Belt states. This model could make 2019 yield predictions with a root mean square error of 866 kg/ha, equivalent to 8.5% relative root mean square and could successfully explain about 77% of the spatio-temporal variation in the corn grain yields. The significant predictive power of this model can be leveraged for designing a reliable tool for corn yield prediction which will in turn assist agronomic decision makers.

scholarly journals The application of data mining techniques for the regionalisation of hydrological variables

2002 ◽  
Vol 6 (4) ◽  
pp. 685-694 ◽  
Author(s):  
M. J. Hall ◽  
A. W. Minns ◽  
A. K. M. Ashrafuzzaman
Keyword(s):  
Data Mining ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Root Mean Square ◽  
Data Sets ◽  
Mean Square ◽  
Data Set ◽  
South West ◽  
Catchment Areas ◽  
Hydrological Variables

Abstract. Flood quantile estimation for ungauged catchment areas continues to be a routine problem faced by the practising Engineering Hydrologist, yet the hydrometric networks in many countries are reducing rather than expanding. The result is an increasing reliance on methods for regionalising hydrological variables. Among the most widely applied techniques is the Method of Residuals, an iterative method of classifying catchment areas by their geographical proximity based upon the application of Multiple Linear Regression Analysis (MLRA). Alternative classification techniques, such as cluster analysis, have also been applied but not on a routine basis. However, hydrological regionalisation can also be regarded as a problem in data mining — a search for useful knowledge and models embedded within large data sets. In particular, Artificial Neural Networks (ANNs) can be applied both to classify catchments according to their geomorphological and climatic characteristics and to relate flow quantiles to those characteristics. This approach has been applied to three data sets from the south-west of England and Wales; to England, Wales and Scotland (EWS); and to the islands of Java and Sumatra in Indonesia. The results demonstrated that hydrologically plausible clusters can be obtained under contrasting conditions of climate. The four classes of catchment found in the EWS data set were found to be compatible with the three classes identified in the earlier study of a smaller data set from south-west England and Wales. Relationships for the parameters of the at-site distribution of annual floods can be developed that are superior to those based upon MLRA in terms of root mean square errors of validation data sets. Indeed, the results from Java and Sumatra demonstrate a clear advantage in reduced root mean square error of the dependent flow variable through recognising the presence of three classes of catchment. Wider evaluation of this methodology is recommended. Keywords: regionalisation, floods, catchment characteristics, data mining, artificial neural networks

Quantifying the Robustness of a Broth-Based Escherichia coli O157:H7 Growth Model in Ground Beef†

2005 ◽  
Vol 68 (11) ◽  
pp. 2301-2309 ◽  
Author(s):  
DANILO T. CAMPOS ◽  
BRADLEY P. MARKS ◽  
MARK R. POWELL ◽  
MARK L. TAMPLIN
Keyword(s):  
Escherichia Coli ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Growth Model ◽  
Standard Error ◽  
Ground Beef ◽  
Escherichia Coli O157 ◽  
Mean Square ◽  
Data Set

The robustness of a microbial growth model must be assessed before the model can be applied to new food matrices; therefore, a methodology for quantifying robustness was developed. A robustness index (RI) was computed as the ratio of the standard error of prediction to the standard error of calibration for a given model, where the standard error of calibration was defined as the root mean square error of the growth model against the data (log CFU per gram versus time) used to parameterize the model and the standard error of prediction was defined as the root mean square error of the model against an independent data set. This technique was used to evaluate the robustness of a broth-based model for aerobic growth of Escherichia coli O157:H7 (in the U.S Department of Agriculture Agricultural Research Service Pathogen Modeling Program) in predicting growth in ground beef under different conditions. Comparison against previously published data (132 data sets with 1,178 total data points) from experiments in ground beef at various experimental conditions (4.8 to 45°C and pH 5.5 to 5.9) yielded RI values ranging from 0.11 to 2.99. The estimated overall RI was 1.13. At temperatures between 15 and 40°C, the RI was close to and smaller than 1, indicating that the growth model is relatively robust in that temperature range. However, the RI also was related (P < 0.05) to temperature. By quantifying the predictive accuracy relative to the expected accuracy, the RI could be a useful tool for comparing various models under different conditions.

scholarly journals Error propagation approach for estimating root mean square error of the reference evapotranspiration when estimated with alternative data

2019 ◽  
Vol 50 (3) ◽  
pp. 120-126
Author(s):  
Homayoon Ganji ◽  
Takamitsu Kajisa
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Error Propagation ◽  
Reference Evapotranspiration ◽  
Mean Square ◽  
Severe Restriction ◽  
Data Set ◽  
Model Improvement ◽  
Using Data

Estimation of reference evapotranspiration (ET0) with the Food and Agricultural Organisation (FAO) Penman-Monteith model requires temperature, relative humidity, solar radiation, and wind speed data. The lack of availability of the complete data set at some meteorological stations is a severe restriction for the application of this model. To overcome this problem, ET0 can be calculated using alternative data, which can be obtained via procedures proposed in FAO paper No.56. To confirm the validity of reference evapotranspiration calculated using alternative data (ET0(Alt)), the root mean square error (RMSE) needs to be estimated; lower values of RMSE indicate better validity. However, RMSE does not explain the mechanism of error formation in a model equation; explaining the mechanism of error formation is useful for future model improvement. Furthermore, for calculating RMSE, ET0 calculations based on both complete and alternative data are necessary. An error propagation approach was introduced in this study both for estimating RMSE and for explaining the mechanism of error formation by using data from a 30-year period from 48 different locations in Japan. From the results, RMSE was confirmed to be proportional to the value produced by the error propagation approach (ΔET0). Therefore, the error propagation approach is applicable to estimating the RMSE of ET0(Alt) in the range of 12%. Furthermore, the error of ET0(Alt) is not only related to the variables’ uncertainty but also to the combination of the variables in the equation.

scholarly journals Which method is more accurate? or errors have error bars

2017 ◽  
Author(s):  
Jan H Jensen
Keyword(s):  
Root Mean Square ◽  
Mean Square ◽  
Data Set ◽  
Error Bars ◽  
The Difference ◽  
Mean Square Errors

This document is my attempt at distilling some of the information in two papers published by Anthony Nicholls (J. Comput. Aided Mol. Des. 2014, 28, 887; ibid 2016, 30, 103). Anthony also very kindly provided some new equations, not found in the papers, in response to my questions. The paper describes how one determines whether the difference in accuracy of two methods in predicting some properties for the same data set is statistically significant using root-mean-square errors, mean absolute errors, mean errors, and Pearsons r values.

Quantitative measure of the isospin splitting of the effective nucleon mass

2021 ◽  
Author(s):  
S. Haddad
Keyword(s):  
Root Mean Square ◽  
Asymmetry Parameter ◽  
Quantitative Measure ◽  
Nuclear Interaction ◽  
Mass Splitting ◽  
Nucleon Mass ◽  
Mean Square ◽  
Coupling Channel ◽  
Isospin Splitting ◽  
The Asymmetry

The effective nucleon mass splits into two components, one for the proton and another for the neutron, in the case of adding the isovector coupling channel of the nuclear interaction, while being the same in the case of considering only the isoscalar coupling. A quantitative measure of the splitting is defined by the root mean square (RMS) value of the effective nucleon mass splitting and applied to the effective nucleon mass splitting in lead and tin isotopes. The isospin splitting of the effective nucleon mass is found to increase almost linearly with the asymmetry parameter.

Numerical investigation of transonic buffet on supercritical airfoil considering uncertainties in wind tunnel testing

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040083
Author(s):  
Hong-Yu Zhu ◽  
Gang Wang ◽  
Yi Liu ◽  
Ze-Kun Zhou
Keyword(s):  
Experimental Data ◽  
Wind Tunnel ◽  
Pressure Distribution ◽  
Root Mean Square ◽  
Numerical Results ◽  
Uncertain Parameters ◽  
Mean Square ◽  
Supercritical Airfoil ◽  
Mean Pressure ◽  
Transonic Buffet

To improve the predictive ability of computational fluid dynamics (CFD) on the transonic buffet phenomenon, NASA SC(2)-0714 supercritical airfoil is numerically investigated by noninstructive probabilistic collocation method for uncertainty quantification. Distributions of uncertain parameters are established according to the NASA wind tunnel report. The effects of the uncertainties on lift, drag, mean pressure and root-mean square pressure are discussed. To represent the stochastic solution, the mean and standard deviation of variation of flow quantities such as lift and drag coefficients are computed. Furthermore, mean pressure distribution and root-mean square pressure distribution from the upper surface are displayed with uncertainty bounds containing 95% of all possible values. It is shown that the most sensitive part of flow to uncertain parameters is near the shock wave motion region. Comparing uncertainty bounds with experimental data, numerical results are reliable to predict the reduced frequency and mean pressure distribution. However, for root-mean square pressure distribution, numerical results are higher than the experimental data in the trailing edge region.

Sign in / Sign up

Export Citation Format

Share Document