Uncertainty analysis of arbitrary probability distribution based on Stieltjes Process

2017 ◽  
Author(s):  
Gang Zhang ◽  
Jinjun Bai ◽  
Lixin Wang ◽  
Xiyuan Peng
Keyword(s):  
Probability Distribution ◽  
Uncertainty Analysis

scholarly journals Impact of probability distribution on the uncertainty of resistance measurement

2019 ◽  
Vol 28 ◽  
pp. 01038 ◽  
Author(s):  
Stanisław Szczesny ◽  
Anna Golijanek-Jędrzejczyk ◽  
Dariusz Świsulski
Keyword(s):  
Probability Distribution ◽  
Uncertainty Analysis ◽  
Measurement Uncertainty ◽  
Probability Distributions ◽  
Resistance Measurement ◽  
Measuring Instruments ◽  
Triangular Distribution ◽  
Expanded Uncertainty ◽  
Uncertainty Measurement

The paper presents studies on the influence of probability distributions on the expanded uncertainty of the resistance measurement. Choosing the correct probability distribution is very important to estimate of measurement uncertainty. The paper presents the results of analysis of the resistance measurement uncertainty using the technical method of resistance: 100 GW. The analysis of the uncertainty measurement of resistance was carried out repeatedly, each time assuming a different probability distribution of measuring instruments (normal, quadratic, U and triangular distribution).The results of the research presented in the article show that the influence of the assumed probability distributions on the result of the measurement uncertainty analysis is significant and results discrepancies can reach up to 40%.

scholarly journals Uncertainty Analysis for Data-Driven Chance-Constrained Optimization

2020 ◽  
Vol 12 (6) ◽  
pp. 2450
Author(s):  
Bartolomeus Häussling Löwgren ◽  
Joris Weigert ◽  
Erik Esche ◽  
Jens-Uwe Repke
Keyword(s):  
Probability Distribution ◽  
Uncertainty Analysis ◽  
Constrained Optimization ◽  
Process Model ◽  
Data Driven ◽  
Distribution Model ◽  
Chance Constraint ◽  
Distribution Models ◽  
Complex Models ◽  
Increase In Accuracy

In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.

Factors Affecting Model Sensitivity and Uncertainty: Application to an Irrigation Scheduler

2017 ◽  
Vol 60 (3) ◽  
pp. 803-812
Author(s):  
Anna C. Linhoss ◽  
Mary Love Tagert ◽  
Hazel Buka ◽  
Gretchen Sassenrath
Keyword(s):  
Sensitivity Analysis ◽  
Probability Distribution ◽  
Uncertainty Analysis ◽  
Objective Function ◽  
Model Uncertainty ◽  
Irrigation Scheduling ◽  
Model Complexity ◽  
Objective Functions ◽  
Important Input ◽  
Sensitivity And Uncertainty Analysis

Abstract. This work describes the global sensitivity and uncertainty analysis of the Mississippi Irrigation Scheduling Tool (MIST) using the Sobol’ method. An often overlooked but driving factor in any sensitivity and uncertainty analysis is the selection of the prior probability distribution functions (PDFs) that are used to describe parameter and input uncertainty. These prior PDFs have a direct impact on the total model uncertainty as well as the ranking of importance of model inputs and parameters. Furthermore, an uncertainty and sensitivity analysis generally focuses on a single objective function for analysis, but model outputs are often analyzed and summarized using a variety of objective functions. Therefore, it is important to include this variety of objective functions in any sensitivity and uncertainty analysis. In this article, we show how the choice of prior PDFs and objective functions impacts the ranking of important parameters and inputs in the MIST model. For example, under the “first day to irrigate” objective function, precipitation was the most important input when using informed prior PDFs, but precipitation ranked as the tenth most important input when using uninformed prior PDFs. Similarly, when using the uninformed prior PDFs, the curve number was the second most important input for the water balance objective function but only the eighth most important when assessing the “first day to irrigate” objective function. Furthermore, in the MIST model, increasing model complexity through the addition of algorithms, inputs, and parameters increases model uncertainty. Finally, in this particular application using the data described, the crop coefficient and precipitation were the most important parameters or inputs, while the initial abstraction and minimum temperature were the least important parameters or inputs. These results provide theoretical insights into sensitivity and uncertainty analysis studies as well as context-specific implications for strategic enhancement of the MIST model. Keywords: Crop water use, Evapotranspiration, Irrigation scheduling, Objective function, Probability distribution function, Sensitivity analysis, Uncertainty analysis.

scholarly journals Uncertainty analysis of the rate of change of quantile due to global warming using uncertainty analysis of non-stationary frequency model of peak-over-threshold series

2020 ◽  
Author(s):  
Okjeong Lee ◽  
Jeonghyeon Choi ◽  
Jeongeun Won ◽  
Sangdan Kim
Keyword(s):  
Probability Distribution ◽  
Uncertainty Analysis ◽  
Frequency Analysis ◽  
Time Series Data ◽  
Rate Of Change ◽  
Point Of View ◽  
Series Data ◽  
Stationary Model ◽  
Peak Over Threshold ◽  
Quantile Estimates

Abstract. Several methods have been proposed to analyze the frequency of non-stationary anomalies. The applicability of the non-stationary frequency analysis has been mainly evaluated based on the agreement between the time series data and the applied probability distribution. However, since the parameters of the estimated probability distribution contain a lot of uncertainty, the uncertainty in the correspondence between samples and probability distribution is inevitably large. In this study, an extreme rainfall frequency analysis is performed that fits the Peak-over-threshold series to the covariate-based non-stationary Generalized Pareto distribution. By quantitatively evaluating the uncertainty of daily rainfall quantile estimates at Busan and Seoul sites of the Korea Meteorological Administration using the Bayesian approach, we tried to evaluate the applicability of the non-stationary frequency analysis with a focus on uncertainty. From the point of view of the agreement between the time series data and the applied probability distribution, the non-stationary model was found to be slightly better. When comparing the performance of the stationary and non-stationary model from the uncertainty point of view, the uncertainty of the non-stationary model was greater than that of the stationary model since the non-stationary model included variability arising from covariates. However, it was found that if the appropriate covariate corresponding to the quantile was selected (that is, if the variability of the covariate was eliminated), the reliability of the non-stationary model could be higher than that of the stationary model. Given the covariate, it was confirmed that the uncertainty reduction in quantile estimates for the increase in sample size is more pronounced in the non-stationary model. In addition, how to use the dew point-based non-stationary frequency analysis when integrating information on global temperature rise is described. Finally, it is proposed how to quantify the uncertainty of the rate of change in the future quantile due to global warming using the rainfall quantile ensemble obtained in the uncertainty analysis process.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

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