A DYNAMIC-STOCHASTIC PRINCIPLE OF MATHEMATICAL SIMULATION

2021 ◽  
Author(s):  
Yu. A. Gusman ◽  
◽  
Yu. A. Pichugin ◽  
Keyword(s):  
Probability Distribution ◽  
Mathematical Simulation ◽  
Predictive Models ◽  
Stochastic Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Mathematical Apparatus ◽  
Model Parameter ◽  
Stochastic Nature ◽  
Dynamic Stochastic

The paper considers the dynamic-stochastic approach to the construction and use of predictive models, which is based on the stochastic nature of model parameter estimates. A mathematical apparatus for generating perturbations of model parameters in accordance with their probability distribution is proposed.

Optimized blood sampling protocols and sequential design of kinetic experiments

1981 ◽  
Vol 240 (5) ◽  
pp. R259-R265 ◽  
Author(s):  
J. J. DiStefano
Keyword(s):  
Endocrine System ◽  
Primary Objective ◽  
Blood Sampling ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reverse T3 ◽  
Model Parameter ◽  
Maximum Accuracy ◽  
Sampling Protocols

Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

scholarly journals An application of the ensemble Kalman filter in epidemiological modelling

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256227
Author(s):  
Rajnesh Lal ◽  
Weidong Huang ◽  
Zhenquan Li
Keyword(s):  
Parameter Estimation ◽  
Model Simulation ◽  
Synthetic Data ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Parameter ◽  
Reliable Model ◽  
Reported Data ◽  
Parameter Estimation Methods

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter’s performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.

A normalized regression based regional model for generating flows at ungauged basins

2013 ◽  
Vol 68 (1) ◽  
pp. 99-108
Author(s):  
Borislava Blagojević ◽  
Jasna Plavšić
Keyword(s):  
Input Data ◽  
Absolute Error ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Efficiency Coefficient ◽  
Ungauged Basins ◽  
Model Parameter ◽  
Proposed Model ◽  
Two Parameter

Revision of existing methodologies for generating monthly-flow series at ungauged basins based on multivariate nonlinear correlation has led to a simple two-parameter model. While the existing methodology used hydrological, meteorological and geomorphologic input data, the proposed model requires hydrological and geomorphologic input data only. The proposed methodology requires formation of separate pools of donor catchments for model parameter estimates. The proposed two-parameter model and improvement in the sphere of homogeneous region identification were verified using 195 runoff data sets from hydrologic stations in Serbia in the 1961–2005 period, divided into three non-overlapping 15-year periods. Nash-Sutcliffe's model efficiency coefficient (NSE) was used to assess the: (1) quality of proposed model with identified model parameters; (2) quality of a nonlinear multivariate equation for standard normal variables estimation with identified model parameters; (3) quality of proposed model with model parameter estimates. Generated time-series statistics and nonlinear multivariate equation quality are also evaluated. Five model calibration and validation results are shown. Generated flow series variation coefficient is the best replicated statistics with relative absolute error less than 10%.

Simultaneous Determination of Skeletal Model Parameter Values, Motions, and Controls From Noisy Measurement Data

2008 ◽  
Author(s):  
Michael G. Fattey ◽  
Benjamin J. Fregly
Keyword(s):  
Inverse Dynamics ◽  
Optimal Parameter ◽  
Measurement Data ◽  
Biomechanical Model ◽  
Optimization Techniques ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Parameter ◽  
Multi Level ◽  
Cadaver Studies

Accurate model parameter value and motion determination is important for obtaining reliable results from inverse dynamics analyses of gait. If the model parameters do not properly match their true values, the predicted motions and loads may lose their clinical significance [1]. Typical approaches to biomechanical model parameter estimation have included the use of scaling rules based on cadaver studies [2] and the use of multi-level optimization routines [3,4]. However, scaling rules do not provide optimal parameter estimates, and multi-level optimization techniques are computationally expensive.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Multi-day flow forecasting using the Kalman filter

1991 ◽  
Vol 18 (2) ◽  
pp. 320-327 ◽  
Author(s):  
Murray A. Fitch ◽  
Edward A. McBean
Keyword(s):  
Kalman Filter ◽  
Prediction Model ◽  
Linear Prediction ◽  
Measured Data ◽  
System Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Forecasting Performance ◽  
Optimal Forecasting ◽  
Linear Prediction Model

A model is developed for the prediction of river flows resulting from combined snowmelt and precipitation. The model employs a Kalman filter to reflect uncertainty both in the measured data and in the system model parameters. The forecasting algorithm is used to develop multi-day forecasts for the Sturgeon River, Ontario. The algorithm is shown to develop good 1-day and 2-day ahead forecasts, but the linear prediction model is found inadequate for longer-term forecasts. Good initial parameter estimates are shown to be essential for optimal forecasting performance. Key words: Kalman filter, streamflow forecast, multi-day, streamflow, Sturgeon River, MISP algorithm.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

Conditioning Model Ensembles to Various Observed Data (Field and Regional Level) by Applying Machine-Learning-Augmented Workflows to a Mature Field with 70 Years of Production History

2021 ◽  
pp. 1-18
Author(s):  
Gisela Vanegas ◽  
John Nejedlik ◽  
Pascale Neff ◽  
Torsten Clemens
Keyword(s):  
Machine Learning ◽  
Oil Recovery ◽  
Numerical Models ◽  
Operating Conditions ◽  
Model Parameters ◽  
Large Set ◽  
Model Parameter ◽  
Production History ◽  
Hydrocarbon Fields ◽  
Parameter Distributions

Summary Forecasting production from hydrocarbon fields is challenging because of the large number of uncertain model parameters and the multitude of observed data that are measured. The large number of model parameters leads to uncertainty in the production forecast from hydrocarbon fields. Changing operating conditions [e.g., implementation of improved oil recovery or enhanced oil recovery (EOR)] results in model parameters becoming sensitive in the forecast that were not sensitive during the production history. Hence, simulation approaches need to be able to address uncertainty in model parameters as well as conditioning numerical models to a multitude of different observed data. Sampling from distributions of various geological and dynamic parameters allows for the generation of an ensemble of numerical models that could be falsified using principal-component analysis (PCA) for different observed data. If the numerical models are not falsified, machine-learning (ML) approaches can be used to generate a large set of parameter combinations that can be conditioned to the different observed data. The data conditioning is followed by a final step ensuring that parameter interactions are covered. The methodology was applied to a sandstone oil reservoir with more than 70 years of production history containing dozens of wells. The resulting ensemble of numerical models is conditioned to all observed data. Furthermore, the resulting posterior-model parameter distributions are only modified from the prior-model parameter distributions if the observed data are informative for the model parameters. Hence, changes in operating conditions can be forecast under uncertainty, which is essential if nonsensitive parameters in the history are sensitive in the forecast.

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