Parameter Identifiability Issues Research Articles

Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding

Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research.

A simple modeling framework for prediction in the human glucose-insulin system.

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

Nonlinear identifiability analysis of Multiphase Porous Electrode Theory-based battery models: A Lithium Iron Phosphate case study

Porous electrode theory (PET) is widely used to model battery dynamics by describing electrochemical kinetics and transport in solid particles and electrolyte. Standard PET models rely on black-box descriptions of the thermodynamics of active materials, typically obtained by fitting an open-circuit potential which does not allow for a consistent description of phase-separating materials. Multiphase PET (MPET) was recently developed to describe batteries using white- or gray-box descriptions of the thermodynamics with additional parameters that need to be estimated from experimental data. This work analyzes the identifiability of parameters in the MPET model, including the standard kinetics and diffusion parameters, as well as MPET-specific parameters for the free energy of active materials. Based on synthetic discharge data, both linearized and nonlinear identifiability analyses are performed for an MPET model of a commercial Lithium Iron Phosphate/Graphite battery, which identify which model parameters are not identifiable and which are identifiable only with large uncertainty. The identifiable parameters control phase separation, reaction kinetics, and electrolyte transport, but not solid diffusion, consistent with rate limitation by intercalation reactions at low rates and by electrolyte diffusion at high rates. The article also proposes approaches for reducing parameter identifiability issues.

A model-based calibration approach for structural fault diagnosis using piezoelectric impedance measurements and a finite element model

The electromechanical coupling property of piezoelectric transducers gives rise to a promising class of structural fault diagnosis methods often referred to collectively as impedance-based approaches. One active line of research in the related literature is the development of data-driven methods that can leverage the available experimental impedance measurements to accurately pinpoint the location and severity of structural faults. In this article, we offer a new perspective to the problem by casting the impedance-based fault diagnosis into a statistical calibration formulation, which has gained a wide popularity in the industrial statistics community in the past two decades. Specifically, we decide to estimate the values of the fault attributes (e.g. location and severity) that achieve the closest match between the outputs from a finite element model and those experimentally solicited from the host structure. We further propose to couple this statistical formulation with a pre-screening procedure to reduce the calibration search space and mitigate parameter identifiability issues. In addition to the merit of capably diagnosing structural faults, the proposed approach extends various useful concepts from the statistical calibration literature to the structural health monitoring applications, such as the construction of surrogate models for modeling and predicting impedance changes, the explicit use of a bias function to correct for inherent inadequacies in finite element models, as well as the ability to produce continuous probability distributions for quantifying a fault’s severity. These additional benefits substantially enhance both the fault diagnosis capability and computational efficiency. We demonstrate the effectiveness of the proposed approach using two simulated and two experimental case studies from the literature.

Assessment of regional inter-basin groundwater flow using both simple and highly parameterized optimization schemes

The need for regional-scale integrated hydrological models for the purpose of water resource management is increasing. Distributed physically based coupled surface-subsurface models are usually complex and contain a large amount of spatio-temporal information that leads to a relatively long forward runtime. One of the main challenges with regard to regional-scale inverse modeling relates to parameterization and how to adequately exploit the information embedded in the existing observational data while avoiding parameter identifiability issues. This study examined and compared the calibration of a “highly parameterized” model with a “classical” unit-based parameterization scheme in which the dominant geological features were assumed to be known. The physically based coupled surface-subsurface model MIKE SHE was used for conducting the study of five river basins (4,900 km2) in central Jutland in Denmark, characterized by heterogeneous geology and a considerable amount of groundwater flux across topographical catchment boundaries. The results indicated that introducing more flexibility in the parameter estimation process through a regularized approach significantly improved the model performance, in particular head and water balance errors. The highly parameterized calibration results additionally provided very useful insights into the model deficiencies in terms of conceptual model structure and incorrectly imposed boundary conditions. Furthermore, the results from data-worth analysis indicated that the highly parameterized model has more effectively utilized the information in the dataset compared to a traditional unit-based calibration approach.

Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models

BackgroundMathematical modeling is now frequently used in outbreak investigations to understand underlying mechanisms of infectious disease dynamics, assess patterns in epidemiological data, and forecast the trajectory of epidemics. However, the successful application of mathematical models to guide public health interventions lies in the ability to reliably estimate model parameters and their corresponding uncertainty. Here, we present and illustrate a simple computational method for assessing parameter identifiability in compartmental epidemic models.MethodsWe describe a parametric bootstrap approach to generate simulated data from dynamical systems to quantify parameter uncertainty and identifiability. We calculate confidence intervals and mean squared error of estimated parameter distributions to assess parameter identifiability. To demonstrate this approach, we begin with a low-complexity SEIR model and work through examples of increasingly more complex compartmental models that correspond with applications to pandemic influenza, Ebola, and Zika.ResultsOverall, parameter identifiability issues are more likely to arise with more complex models (based on number of equations/states and parameters). As the number of parameters being jointly estimated increases, the uncertainty surrounding estimated parameters tends to increase, on average, as well. We found that, in most cases, R0 is often robust to parameter identifiability issues affecting individual parameters in the model. Despite large confidence intervals and higher mean squared error of other individual model parameters, R0 can still be estimated with precision and accuracy.ConclusionsBecause public health policies can be influenced by results of mathematical modeling studies, it is important to conduct parameter identifiability analyses prior to fitting the models to available data and to report parameter estimates with quantified uncertainty. The method described is helpful in these regards and enhances the essential toolkit for conducting model-based inferences using compartmental dynamic models.

Full Homogenized Macroscale Model and Pseudo-2-Dimensional Model for Lithium-Ion Battery Dynamics: Comparative Analysis, Experimental Verification and Sensitivity Analysis

Control-oriented models based on electrochemistry have conventionally been evaluated and designed from the Doyle-Fuller-Newman (DFN) macroscale model. However, the DFN model is susceptible in predicting battery response under certain operating conditions since it is an approximate representation of pore-scale dynamics. This work shows the limitations of the DFN model in predicting voltage response at high temperatures of cell operation. A full homogenized macroscale (FHM) model, developed in previous research, is shown to overcome these limitations. Results indicate that the predictability of the DFN model deteriorates when trying to predict the voltage response at low state of charge for high temperature of operation under 1 C-rate discharge. The influence of parameters on the model states and output is investigated as a means to address parameter identifiability issues, for which, we formulate and resolve sensitivity functions for the partial differential equations (PDEs) of the FHM model. Results show that parameter identifiability is dependent on the battery state of charge.

Parameter sensitivity analysis for biochemical reaction networks.

Biochemical reaction networks describe the chemical interactions occurring between molecular populations inside the living cell. These networks can be very noisy and complex and they often involve many variables and even more parameters. Parameter sensitivity analysis that studies the effects of parameter changes to the behaviour of biochemical networks can be a powerful tool in unravelling their key parameters and interactions. It can also be very useful in designing experiments that study these networks and in addressing parameter identifiability issues. This article develops a general methodology for analysing the sensitivity of probability distributions of stochastic processes describing the time-evolution of biochemical reaction networks to changes in their parameter values. We derive the coefficients that efficiently summarise the sensitivity of the probability distribution of the network to each parameter and discuss their properties. The methodology is scalable to large and complex stochastic reaction networks involving many parameters and can be applied to oscillatory networks. We use the two-dimensional Brusselator system as an illustrative example and apply our approach to the analysis of the Drosophila circadian clock. We investigate the impact of using stochastic over deterministic models and provide an analysis that can support key decisions for experimental design, such as the choice of variables and time-points to be observed.

Uncertainty analysis of the CPA and a quadrupolar CPA equation of state – With emphasis on CO2

The parameters of thermodynamic models, such as the cubic plus association (CPA) equation of state, are subject to uncertainties due to measurement errors in the experimental data that the models are correlated to. More importantly as the number of adjustable parameters increase, the parameter estimation problem becomes more complicated due to parameter identifiability issues. In this work the uncertainties in the pure compound parameters of CO2 are investigated using several different CPA approaches, including a new quadrupolar CPA. The uncertainties are estimated using both least squares estimation and the bootstrap method for parameter estimation. The uncertainties in the parameters estimated from the bootstrap method are propagated to physical property and vapor liquid equilibrium predictions using Monte Carlo simulations.The results indicate that both the pure compound parameter uncertainty and the propagated uncertainty are negligible for the modeling approaches which employ three adjustable parameters. For modeling approaches with more than three adjustable parameters, however, there may be significant uncertainties in the pure compound parameters, as well as a high degree of correlation between the adjustable parameters. This results in significant propagated errors for certain output properties. To reduce the uncertainty in the adjustable model parameters the heat of vaporization was included as additional correlation data. This resulted in parameter distributions which followed a normal distribution more closely, however, the correlation between the adjustable parameters remained high. Overall the results indicate, that it is important to report parameter uncertainties together with their correlation matrix when a model is developed, so that better informed decisions can be made, for instance about which model extension, or association scheme should be employed.

A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property Models—An Application to the Heat of Combustion

A rigorous methodology is developed that addresses numerical and statistical issues when developing group contribution (GC) based property models such as regression methods, optimization algorithms, performance statistics, outlier treatment, parameter identifiability, and uncertainty of the prediction. The methodology is evaluated through development of a GC method for the prediction of the heat of combustion (ΔHco) for pure components. The results showed that robust regression lead to best performance statistics for parameter estimation. The bootstrap method is found to be a valid alternative to calculate parameter estimation errors when underlying distribution of residuals is unknown. Many parameters (first, second, third order group contributions) are found unidentifiable from the typically available data, with large estimation error bounds and significant correlation. Due to this poor parameter identifiability issues, reporting of the 95% confidence intervals of the predicted property values should be...

Addressing parameter identifiability by model-based experimentation

Mathematical description of biological processes such as gene regulatory networks or signalling pathways by dynamic models utilising ordinary differential equations faces challenges if the model parameters like rate constants are estimated from incomplete and noisy experimental data. Typically, biological networks are only partially observed. Only a fraction of the modelled molecular species is measurable directly. This can result in structurally non-identifiable model parameters. Furthermore, practical non-identifiability can arise from limited amount and quality of experimental data. In the challenge of growing model complexity on one side, and experimental limitations on the other side, both types of non-identifiability arise frequently in systems biological applications often prohibiting reliable prediction of system dynamics. On theoretical grounds this article summarises how and why both types of non-identifiability arise. It exemplifies pitfalls where models do not yield reliable predictions of system dynamics because of non-identifiabilities. Subsequently, several approaches for identifiability analysis proposed in the literature are discussed. The aim is to provide an overview of applicable methods for detecting parameter identifiability issues. Once non-identifiability is detected, it can be resolved either by experimental design, measuring additional data under suitable conditions; or by model reduction, tailoring the size of the model to the information content provided by the experimental data. Both strategies enhance model predictability and will be elucidated by an example application. [Includes supplementary material].

A practical protocol for calibration of nutrient removal wastewater treatment models

Activated sludge models can be very useful for designing and managing wastewater treatment plants (WWTPs). However, as with every model, they need to be calibrated for correct and reliable application. Activated sludge model calibration is still a crucial point that needs appropriate guidance. Indeed, although calibration protocols have been developed, the model calibration still represents the main bottleneck to modelling. This paper presents a procedure for the calibration of an activated sludge model based on a comprehensive sensitivity analysis and a novel step-wise Monte Carlo-based calibration of the subset of influential parameters. In the proposed procedure the complex calibration issue is tackled both by making a prior screening of the most influential model parameters and by simplifying the problem of finding the optimal parameter set by splitting the estimation task into steps. The key point of the proposed step-wise procedure is that calibration is undertaken for sub-groups of variables instead of solving a complex multi-objective function. Moreover, even with this step-wise approach parameter identifiability issues may occur, but this is dealt with by using the general likelihood uncertainty estimation (GLUE) method, that so far has rarely been used in the field of wastewater modelling. An example from a real case study illustrates the effectiveness of the proposed methodology. Particularly, a model was built for the simulation of the nutrient removal in a Bardenpho scheme plant. The model was successfully and efficiently calibrated to a large WWTP in Sicily.

Spatiotemporal topological kriging of runoff time series

This paper proposes a geostatistical method for estimating runoff time series in ungauged catchments. The method conceptualizes catchments as space‐time filters and exploits the space‐time correlations of runoff along the stream network topology. We hence term the method topological kriging or top kriging. It accounts for hydrodynamic and geomorphologic dispersion as well as routing and estimates runoff as a weighted average of the observed runoff in neighboring catchments. Top kriging is tested by cross validation on 10 years of hourly runoff data from 376 catchments in Austria and separately for a subset of these data, the Innviertel region. The median Nash‐Sutcliffe efficiency of hourly runoff in the Innviertel region is 0.87 but decreases to 0.75 for the entire data set. For a subset of 208 catchments, the median efficiency of daily runoff estimated by top kriging is 0.87 as compared to 0.67 for estimates of a deterministic runoff model that uses regionalized model parameters. The much better performance of top kriging is because it avoids rainfall data errors and avoids the parameter identifiability issues of traditional runoff models. The analyses indicate that the kriging variance can be used for identifying catchments with potentially poor estimates. The Innviertel region is used to examine the kriging weights for nested and nonnested catchments and to compare various variants of top kriging. The spatial kriging variant generally performs better than the more complex spatiotemporal kriging and spatiotemporal cokriging variants. It is argued that top kriging may be preferable to deterministic runoff models for estimating runoff time series in ungauged catchments, provided stream gauge density is high and there is no need to account for causal rainfall‐runoff processes. Potential applications include the estimation of flow duration curves in a region and near–real time mapping of runoff.

Quasi-ML period estimation from incomplete timing data

Given a noisy sequence of (possibly shifted) integer multiples of a certain period, it is often of interest to accurately estimate the period. With known integer regressors, the problem is classical linear regression. In many applications, however, the regressors are unknown integers, and only loose bounds on the period are available. Examples include hop period and timing estimation, wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band; Pulse Repetition Interval (PRI) analysis; and passive rotating-beam radio scanning. We study several pertinent period estimators. Our emphasis is on a Quasi-Maximum Likelihood approach developed herein and an earlier method based on the Fourier Transform of a Dirac delta train representation of the data. Surprisingly, both are capable of attaining the clairvoyant Crame/spl acute/r-Rao Bound at moderate signal-to-noise ratios (SNRs), even for short (e.g., 10) samples. We carefully address parameter identifiability issues and corroborate our findings with extensive simulations.