scholarly journals A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 2996
Author(s):  
Hao Li ◽  
Enze Zhang
Keyword(s):  
Parameter Estimation ◽  
Confidence Interval ◽  
Prior Knowledge ◽  
Sampling Design ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Uniform Sampling ◽  
Sampling Points ◽  
Non Uniform Sampling

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

Interpretation of Simulation Studies for Efficient Estimation of Population Pharmacokinetic Parameters

1993 ◽  
Vol 27 (9) ◽  
pp. 1034-1039 ◽  
Author(s):  
Ene I. Ette ◽  
Andrew W. Kelman ◽  
Catherine A. Howie ◽  
Brian Whiting
Keyword(s):  
Parameter Estimation ◽  
Efficient Estimation ◽  
Experimental Unit ◽  
Pharmacokinetic Parameters ◽  
Population Pharmacokinetic ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Good Precision ◽  
Simulation Studies ◽  
Individual Parameter

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (Φ) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The Φ approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the Φ for individual parameter estimation and the overall Φ for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.

scholarly journals Fault Detection in Wastewater Treatment Systems Using Multiparametric Programming

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 231 ◽  
Author(s):  
Ernie Che Mid ◽  
Vivek Dua
Keyword(s):  
Wastewater Treatment ◽  
Parameter Estimation ◽  
Fault Detection ◽  
Normal Operation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Multiparametric Programming ◽  
Nonlinear Algebraic Equations ◽  
Wastewater Treatment Systems

In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, ; concentration of organic matter, ; concentration of dissolved oxygen, ; and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

scholarly journals An Overcomplete Approach to Fitting Drift-Diffusion Decision Models to Trial-By-Trial Data

2021 ◽  
Vol 4 ◽  
Author(s):  
Q. Feltgen ◽  
J. Daunizeau
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Reaction Times ◽  
Mechanistic Explanation ◽  
Added Value ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Drift Diffusion ◽  
Neural Noise ◽  
Computational Bottleneck

Drift-diffusion models or DDMs are becoming a standard in the field of computational neuroscience. They extend models from signal detection theory by proposing a simple mechanistic explanation for the observed relationship between decision outcomes and reaction times (RT). In brief, they assume that decisions are triggered once the accumulated evidence in favor of a particular alternative option has reached a predefined threshold. Fitting a DDM to empirical data then allows one to interpret observed group or condition differences in terms of a change in the underlying model parameters. However, current approaches only yield reliable parameter estimates in specific situations (c.f. fixed drift rates vs drift rates varying over trials). In addition, they become computationally unfeasible when more general DDM variants are considered (e.g., with collapsing bounds). In this note, we propose a fast and efficient approach to parameter estimation that relies on fitting a “self-consistency” equation that RT fulfill under the DDM. This effectively bypasses the computational bottleneck of standard DDM parameter estimation approaches, at the cost of estimating the trial-specific neural noise variables that perturb the underlying evidence accumulation process. For the purpose of behavioral data analysis, these act as nuisance variables and render the model “overcomplete,” which is finessed using a variational Bayesian system identification scheme. However, for the purpose of neural data analysis, estimates of neural noise perturbation terms are a desirable (and unique) feature of the approach. Using numerical simulations, we show that this “overcomplete” approach matches the performance of current parameter estimation approaches for simple DDM variants, and outperforms them for more complex DDM variants. Finally, we demonstrate the added-value of the approach, when applied to a recent value-based decision making experiment.

scholarly journals Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment

2017 ◽  
Author(s):  
Yu-Han Kao ◽  
Marisa C. Eisenberg
Keyword(s):  
Parameter Estimation ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Environmental Drivers ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Basic Reproduction Number

AbstractBackgroundMathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many of these studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset.Methodology/Principle FindingsIdentifiability methods allow us to examine whether model parameters can be estimated uniquely—a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquitoborne disease, using 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, which can lead to incorrect predictions of the effects of interventions. However, in spite of unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field.ConclusionsWhile we only consider the simplest case for the model, without explicit environmental drivers, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions, and particularly highlights the importance of combining experimental, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.Author SummaryMathematical models have seen increasing use in understanding transmission processes, developing interventions, and predicting disease incidence and prevalence. Vector-borne diseases in particular present both a challenge and an opportunity for modeling, due to the complex interactions between host and vector species. A key step in many of these studies is connecting transmission models with data to infer parameters and make useful predictions, which requires careful consideration of identifiability and uncertainty of the model parameters. Whether due to intrinsic limitations of the model structure, or practical limitations of the data collected, is common that many different parameter values may yield the same or very similar fits to the data, making it impossible to successfully estimate the parameters. This issue of parameter unidentifiability can have broad implications for our ability to draw conclusions from mechanistic models—in some cases making it difficult or impossible to generate specific predictions, forecasts, or parameter estimates from a given model and data. Here, we evaluate these questions for a commonly-used model of vectorborne disease, examining how parameter uncertainty and unidentifiability can affect intervention predictions, estimation of the basic reproduction number, and other public health conclusions drawn from the model.

scholarly journals Data-Driven Model Updating of an Offshore Wind Jacket Substructure

2021 ◽  
Author(s):  
Dawid Augustyn ◽  
Martin Dalgaard Ulriksen
Keyword(s):  
Parameter Estimation ◽  
Model Updating ◽  
Offshore Wind ◽  
Modal Parameters ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Modal Parameter ◽  
In Situ Data ◽  
Non Linear ◽  
Updating Procedure

The present paper provides a model updating application study concerning the jacket substructure of an o?shore wind turbine. Theupdating is resolved in a sensitivity-based parameter estimation setting, where a cost function expressing the discrepancy betweenexperimentally obtained modal parameters and model-predicted ones is minimized. The modal parameters of the physical systemare estimated through stochastic subspace identification (SSI) applied to vibration data captured for idling and operational states ofthe turbine. From a theoretical outset, the identification approach relies on the system being linear and time-invariant (LTI) and theinput white noise random processes; criteria which are violated in this application due to sources such as operational variability, theturbine controller, and non-linear damping. Consequently, particular attention is given to assess the feasibility of extracting modalparameters through SSI under the prevailing conditions and subsequently using these parameters for model updating. On this basis,it is deemed necessary to disregard the operational turbine states—which severely promote non-linear and time-variant structuralbehaviour and, as such, imprecise parameter estimation results—and conduct the model updating based on modal parametersextracted solely from the idling state. The uncertainties associated with the modal parameter estimates and the model parameters tobe updated are outlined and included in the updating procedure using weighting matrices in the sensitivity-based formulation. Byconducting the model updating based on in-situ data harvested from the jacket substructure during idling conditions, the maximumeigenfrequency deviation between the experimental estimates and the model-predicted ones is reduced from 30% to 1%.

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.

scholarly journals Constraining Land Surface and Atmospheric Parameters of a Locally Coupled Model Using Observational Data

2005 ◽  
Vol 6 (2) ◽  
pp. 156-172 ◽  
Author(s):  
Yuqiong Liu ◽  
Hoshin V. Gupta ◽  
Soroosh Sorooshian ◽  
Luis A. Bastidas ◽  
William J. Shuttleworth
Keyword(s):  
Parameter Estimation ◽  
Observational Data ◽  
Land Surface ◽  
Climate Model ◽  
Model Performance ◽  
Computational Time ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Atmospheric Parameters ◽  
Estimation Process

Abstract In coupled land surface–atmosphere modeling, the possibility and benefits of constraining model parameters using observational data bear investigation. Using the locally coupled NCAR Single-column Community Climate Model (NCAR SCCM), this study demonstrates some feasible, effective approaches to constrain parameter estimates for coupled land–atmosphere models and explores the effects of including both land surface and atmospheric parameters and fluxes/variables in the parameter estimation process, as well as the value of conducting the process in a stepwise manner. The results indicate that the use of both land surface and atmospheric flux variables to construct error criteria can lead to better-constrained parameter sets. The model with “optimal” parameters generally performs better than when a priori parameters are used, especially when some atmospheric parameters are included in the parameter estimation process. The overall conclusion is that, to achieve balanced, reasonable model performance on all variables, it is desirable to optimize both land surface and atmospheric parameters and use both land surface and atmospheric fluxes/variables for error criteria in the optimization process. The results also show that, for a coupled land–atmosphere model, there are potential advantages to using a stepwise procedure in which the land surface parameters are first identified in offline mode, after which the atmospheric parameters are determined in coupled mode. This stepwise scheme appears to provide comparable solutions to a fully coupled approach, but with considerably reduced computational time. The trade-off in the ability of a model to satisfactorily simulate different processes simultaneously, as observed in most multicriteria studies, is most evident for sensible heat and precipitation in this study for the NCAR SCCM.

Sign in / Sign up

Export Citation Format

Share Document