scholarly journals Improvement of model evaluation by incorporating prediction and measurement uncertainty

2017 ◽  
Author(s):  
Lei Chen ◽  
Shuang Li ◽  
Yucen Zhong ◽  
Zhenyao Shen

Abstract. Numerous research studies have been conducted to assess uncertainty in hydrological and nonpoint source pollution predictions, but few studies have considered both prediction and measurement uncertainty in the model evaluation process. In this study, the Cumulative Distribution Function Approach (CDFA) and the Monte Carlo Approach (MCA) were used to develop two new approaches for model evaluation within an uncertainty framework. For the CDFA, a new distance between the cumulative distribution functions of the predicted data and the measured data was established, whereas the MCA was proposed to address conditions with dispersed data points. These new approaches were then applied in combination with the Soil and Water Assessment Tool in the Three Gorges Region, China. Based on the results, these two new approaches provided more accurate goodness-of-fit indicators for model evaluation compared to traditional methods. The model performance worsened when the error range became larger, and the choice of probability density functions (PDFs) affected model performance, especially for non-point source (NPS) predictions. The case study showed that if the measured error is small and if the distribution can be specified, the CDFA and MCA could be extended to other model applications within an uncertain condition.

2018 ◽  
Vol 22 (8) ◽  
pp. 4145-4154 ◽  
Author(s):  
Lei Chen ◽  
Shuang Li ◽  
Yucen Zhong ◽  
Zhenyao Shen

Abstract. Numerous studies have been conducted to assess uncertainty in hydrological and non-point source pollution predictions, but few studies have considered both prediction and measurement uncertainty in the model evaluation process. In this study, the cumulative distribution function approach (CDFA) and the Monte Carlo approach (MCA) were developed as two new approaches for model evaluation within an uncertainty condition. For the CDFA, a new distance between the cumulative distribution functions of the predicted data and the measured data was established in the model evaluation process, whereas the MCA was proposed to address conditions with dispersed data points. These new approaches were then applied in combination with the Soil and Water Assessment Tool in the Three Gorges Region, China. Based on the results, these two new approaches provided more accurate goodness-of-fit indicators for model evaluation compared to traditional methods. The model performance worsened when the error range became larger, and the choice of probability density functions (PDFs) affected model performance, especially for non-point source (NPS) predictions. The case study showed that if the measured error is small and if the distribution can be specified, the CDFA and MCA could be extended to other model evaluations within an uncertainty framework and even be used to calibrate and validate hydrological and NPS pollution (H/NPS) models.


Blood ◽  
2021 ◽  
Vol 138 (Supplement 1) ◽  
pp. 104-104
Author(s):  
Frauke Bellos ◽  
Kim Pawelka ◽  
Elena Fortina ◽  
Manusnan Suriyalaksh ◽  
Sven Maschek ◽  
...  

Abstract Background: Artificial intelligence (AI) has steadily been entering the field supporting diagnostic workup of hematological neoplasms. Its application in flow cytometry (FC) so far mostly included visualization steps with the potential disadvantage of data reduction. Aim: To implement AI models based on raw matrix data for diagnosing main entities of hematologic neoplasms by FC. Methods: For examination of acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), myelodysplastic syndromes (MDS), multiple myeloma (MM) and mature T- and B-cell neoplasms (T-NHL, B-NHL), six machine learning (ML) models were trained on the respective dataset consisting of uniformly analyzed samples (Navios and Cytoflex cytometers, Kaluza analysis software, Beckman Coulter, Miami, FL) resulting in ".fcs" or ".lmd" files, after being classified and diagnosed by human experts. In total 36,662 cases were included, in detail 3,961 for AML model (3,120 AML, 841 no AML), 2,931 for T-NHL (204 T-NHL, 40 NK-cell neoplasm [NK], 2,687 no NHL), 766 for ALL (364 c-ALL/Pre-B-ALL, 95 Pro-B-ALL, 55 cortical T-ALL, 34 Pre-T-ALL, 11 Pro-T-ALL, 3 mature T-ALL, 15 ETP-ALL, 189 no ALL), 7,503 for MM (1,297 MM, 1,261 consistent with MM (<10% plasma cells by FC), 3,613 consistent with monoclonal gammopathy of undetermined significance (MGUS), 1,332 no MM/MGUS), 9,664 for B-NHL (440 hairy cell leukemia (HCL), 3,771 chronic lymphocytic leukemia (CLL), 3,062 CD5-negative NHL, 1,318 CD5-positive NHL, 1,073 no NHL) and 11,837 for MDS (5,206 consistent with MDS, 6,631 no MDS). For each model, feature engineering (FE) techniques were applied. These included division of values by their maximal values, multiplication by 1024, standardization, arcsinh transformation and one- (for all models) or two- (for T-NHL and ALL) dimensional distribution of marker values using empirical cumulative distribution functions (cdfs), with the number of bins set to two for two-dimensional histograms and between 16 and 128 for one-dimensional histograms optimized for each model. Further expert-based features were applied (for T-NHL, ALL, MM, MDS) including setting positive/negative thresholds on marker values, focusing on cell populations of interest by applying clustering techniques, considering percentages of certain cell types and calculating features to capture their specific properties (e.g. distribution of markers of the subpopulations). For MM, B-NHL and MDS we also calculated covariance between key markers. Taken together, 345 features were applied for AML, 772 features for T-NHL, 339 for ALL, 1,800 for MM, 3,275 for MDS and 3,145 for B-NHL. Following ML models were used: XGBoost, weighted SVC and LinearSVC, hierarchical model (four XGBoost with SMOTE models), AutoGluon (using weighted L2 ensemble of XGBoost, LightGBMXT and CatBoost). For MDS an approach similar to manual gating strategies was implemented dividing cells into five partitions combining predictions for each partition to a final result. Model performance was assessed with stratified five-fold cross validation (training/test set 80/20% of data) repeated 10 times. Test recall (R), precision (P) and prediction probabilities (PP) were recorded. Results: Application of the ML models (see figure 1) detected AML vs no AML with average R (aR) of 99.8% and average P (aP) of 99.9% when considering cases with PP ≥0.9 covering 82% of all cases analyzed for AML. For T-NHL we saw aR of 87% and aP 86.7% for detection of NK, T-NHL and no NHL, respectively. In general PP for NK were low and thus prohibited application of a high PP threshold which would have excluded many cases. With a PP threshold of 0.9 (82% of cases) ALL model resulted in prediction of classes Pro-B-ALL, T-ALL non-cortical, c-ALL, cortical T-ALL and no ALL with aR 91.7% and aP 92.5%. MM model separated consistent with MGUS from consistent with MM and no MM (PP=0.9, 66% of cases) with aR 97.7 % and aP 93.5 %. For MDS aR was 85.6% and aP 84.7% with PP=0.9 (74% of samples). Applying PP of 0.9 (51% of cases) B-NHL model classified CD5 negative, CD5 positive, CLL, HCL and no NHL with aR 84.6% and aP 91.5%. Conclusions: Training AI models for FC using raw matrix data is feasible and yields striking R and P values for various models when restricting to cases with high PP. Besides further improving all models future work will focus on identification of additional sub-entities and application of transfer learning to achieve universal applicability to any FC data. Figure 1 Figure 1. Disclosures Haferlach: MLL Munich Leukemia Laboratory: Other: Part ownership. Haferlach: MLL Munich Leukemia Laboratory: Other: Part ownership. Kern: MLL Munich Leukemia Laboratory: Other: Part ownership.


2015 ◽  
Vol 45 (3) ◽  
pp. 353-363 ◽  
Author(s):  
Jari Vauhkonen ◽  
Lauri Mehtätalo

Undetected trees and inaccuracies in the predicted allometric relationships of tree stem attributes seriously constrain single-tree remote sensing of seminatural forests. A new approach to compensate for these error sources was developed by applying a histogram matching technique to map the transformation between the cumulative distribution functions of crown radii extracted from airborne laser scanning (ALS) data and field-measured stem diameters (dbh, outside bark measured at 1.3 m aboveground). The ALS-based crown data were corrected for the censoring effect caused by overlapping tree crowns, assuming that the forest is an outcome of a homogeneous, marked Poisson process with independent marks of the crown radii. The transformation between the cumulative distribution functions was described by a polynomial regression model. The approach was tested for the prediction of plot-level stem number (N), quadratic mean diameter (DQM), and basal area (G) in a managed boreal forest. Of the 40 plots studied, a total of 18 plots met the assumptions of the Poisson process and independent marks. In these plots, the predicted N, DQM, and G had best-case root mean squared errors of 299 stems·ha−1 (27.6%), 2.1 cm (13.1%), and 2.9 m2·ha−1 (13.0%), respectively, and the null hypothesis that the mean difference between the measured and predicted values was 0 was not rejected (p > 0.05). Considerably less accurate results were obtained for the plots that did not meet the assumptions. However, the goodness-of-fit of the predicted diameter distribution was especially improved compared with the single-tree remote sensing prediction, and observations realistically obtainable with ALS data showed potential to further localize the predictions. Remarkably, predictions of N showing no evidence against zero bias were derived solely based on the ALS data for the plots meeting the assumptions made, and limited training data are proposed to be adequate for predicting the stem diameter distribution, DQM, and G. Although this study was based on ALS data, we discuss the possibility of using other remotely sensed data as well. Taken together with the low requirements for field reference data, the presented approach provides interesting practical possibilities that are not typically proposed in the forest remote sensing literature.


2015 ◽  
Vol 10 (2) ◽  
pp. 17
Author(s):  
Sandra G. Garcia Galiano ◽  
Juan Diego Giraldo Osorio ◽  
Patricia Olmos Gimenez

<p>Improving the knowledge about the impacts of climate change on extreme drought events at basin scale, is important for decision makers in order to develop drought contingency plans which are the leading edge of adaptive management strategy. Considering high-resolution grids of observed daily rainfall and information provided by latest-generation Regional Climate Models (RCMs), the changes in the spatio-temporal patterns of extreme droughts in peninsular Spain are assessed. The non-stationarity character of time series, due to climate and anthropogenic changes, is represented by probabilistic models considering the time evolution of probability density function (PDF) parameters fitted to annual maximum lengths of dry spells time series. By a PDF ensemble from 17 RCMs, the spatio-temporal variability exhibited by the RCMs is represented. Scoring of models is based in the goodness-of-fit to CDFs (cumulative distribution functions) of observed annual maximum dry spells lengths. The reliability and skills of RCMs are assessed, for building the PDF ensemble, at grid site for the study area. Therefore, by adjusting PDF to series of annual maximum dry spells lengths, applying GAMLSS and bootstrapping techniques, the assessment of regional changes and trends associated to high returns periods (<em>Tr</em> = 25 and 50 yr.) is assessed. In general, an intensification of drought events for 2050 horizon, in contrast with 1990, is expected. By increasing return periods, the length of the annual maximum dry spells rises, albeit with a smaller number of areas with significant differences. The areas prone to extreme droughts in mainland Spain are identified.</p>


Author(s):  
Russell Cheng

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.


2020 ◽  
Vol 15 (4) ◽  
pp. 351-361
Author(s):  
Liwei Huang ◽  
Arkady Shemyakin

Skewed t-copulas recently became popular as a modeling tool of non-linear dependence in statistics. In this paper we consider three different versions of skewed t-copulas introduced by Demarta and McNeill; Smith, Gan and Kohn; and Azzalini and Capitanio. Each of these versions represents a generalization of the symmetric t-copula model, allowing for a different treatment of lower and upper tails. Each of them has certain advantages in mathematical construction, inferential tools and interpretability. Our objective is to apply models based on different types of skewed t-copulas to the same financial and insurance applications. We consider comovements of stock index returns and times-to-failure of related vehicle parts under the warranty period. In both cases the treatment of both lower and upper tails of the joint distributions is of a special importance. Skewed t-copula model performance is compared to the benchmark cases of Gaussian and symmetric Student t-copulas. Instruments of comparison include information criteria, goodness-of-fit and tail dependence. A special attention is paid to methods of estimation of copula parameters. Some technical problems with the implementation of maximum likelihood method and the method of moments suggest the use of Bayesian estimation. We discuss the accuracy and computational efficiency of Bayesian estimation versus MLE. Metropolis-Hastings algorithm with block updates was suggested to deal with the problem of intractability of conditionals.


2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.


2021 ◽  
Vol 13 (6) ◽  
pp. 1096
Author(s):  
Soi Ahn ◽  
Sung-Rae Chung ◽  
Hyun-Jong Oh ◽  
Chu-Yong Chung

This study aimed to generate a near real time composite of aerosol optical depth (AOD) to improve predictive model ability and provide current conditions of aerosol spatial distribution and transportation across Northeast Asia. AOD, a proxy for aerosol loading, is estimated remotely by various spaceborne imaging sensors capturing visible and infrared spectra. Nevertheless, differences in satellite-based retrieval algorithms, spatiotemporal resolution, sampling, radiometric calibration, and cloud-screening procedures create significant variability among AOD products. Satellite products, however, can be complementary in terms of their accuracy and spatiotemporal comprehensiveness. Thus, composite AOD products were derived for Northeast Asia based on data from four sensors: Advanced Himawari Imager (AHI), Geostationary Ocean Color Imager (GOCI), Moderate Infrared Spectroradiometer (MODIS), and Visible Infrared Imaging Radiometer Suite (VIIRS). Cumulative distribution functions were employed to estimate error statistics using measurements from the Aerosol Robotic Network (AERONET). In order to apply the AERONET point-specific error, coefficients of each satellite were calculated using inverse distance weighting. Finally, the root mean square error (RMSE) for each satellite AOD product was calculated based on the inverse composite weighting (ICW). Hourly AOD composites were generated (00:00–09:00 UTC, 2017) using the regression equation derived from the comparison of the composite AOD error statistics to AERONET measurements, and the results showed that the correlation coefficient and RMSE values of composite were close to those of the low earth orbit satellite products (MODIS and VIIRS). The methodology and the resulting dataset derived here are relevant for the demonstrated successful merging of multi-sensor retrievals to produce long-term satellite-based climate data records.


Author(s):  
Rama Subba Reddy Gorla

Heat transfer from a nuclear fuel rod bumper support was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rates due to the thermodynamic random variables. These results can be used to identify quickly the most critical design variables in order to optimize the design and to make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in heat transfer and to the identification of both the most critical measurements and the parameters.


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