Estimation Of Model Parameters Research Articles

Budyko-based past and future disaggregation of climate and catchment effects on streamflow changes

ABSTRACT Budyko-based approaches are widely used to separate climate and catchment effects on streamflow changes. Considering the potential changes in streamflow, such separation is essential for future water resources management. In this study, we propose a method that allows for continuous disaggregation of climate and catchment impacts from the past to the future. We utilize a generalized linear model to represent catchment parameters based on climate and catchment features. Subsequently, we determine the future positions of the catchment in the Budyko-state space. This framework is applied to four Model Parameter Estimation Experiment (MOPEX) catchments with varying aridity indices in the USA. The results indicate that, in the recent historical period (1971–2011), climate change has contributed to increased streamflow in three catchments compared to the baseline (1948–1970) period. However, future projections indicate a mixed pattern of contributions in two of these catchments due to increased potential evapotranspiration, resulting in decreased streamflow.

Structural and practical identifiability of contrast transport models for DCE-MRI.

Contrast transport models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

An optimization-free Fisher information driven approach for online design of experiments

Developing mathematical models used to elucidate reaction kinetics plays a crucial role in the design, control, and optimization of chemical processes. One of the most challenging tasks in kinetic model identification is the precise estimation of unknown kinetic model parameters. This challenge can be effectively addressed through the application of Model-Based Design of Experiments (MBDoE) techniques, which enable the design of experiments facilitating precise model parameter estimation with minimal runs and analytical resources. Nevertheless, MBDoE techniques rely on an optimization procedure that is susceptible to parametric uncertainty, making the design procedure computationally intensive and prone to issues of local optimality. MBDoE techniques are also employed in online procedures to expedite the identification of kinetic models in autonomous platforms. As a result, ensuring rapid convergence becomes imperative to mitigate numerical issues during operational processes. In this paper a Fisher Information Matrix Driven (FIMD) approach is introduced to tackle these challenges. The methodology integrates a sampling-based experimental design approach with experiment ranking based on FIM to select the most informative experiment at each iteration. The effectiveness of the proposed design methodology is examined and discussed via two different case studies of increasing complexity: a fed-batch reactor in which the fermentation of baker’s yeast is carried out and a nucleophilic aromatic substitution in a flow reactor system.

Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors

This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a combination of inverse probability weighting (IPW) and mean imputation is utilized to mitigate the bias caused by missing data. Under several mild conditions, it is demonstrated that the proposed estimators are consistent and possess oracle properties. The efficacy of the proposed parameter estimation process is assessed through Monte Carlo simulation studies. Finally, the applicability of the proposed method is further substantiated using the Boston Housing Dataset.

A unified framework for prediction of liver steatosis dynamics in response to different diet and drug interventions

Background & AimsNon-alcoholic fatty liver disease (NAFLD) is a common metabolic disorder, characterized by the accumulation of excess fat in the liver, and is a driving factor for various severe liver diseases. These multi-factorial and multi-timescale changes are observed in different clinical studies, but these studies have not been integrated into a unified framework. In this study, we aim to present such a unified framework in the form of a dynamic mathematical model. MethodsFor model training and validation, we collected data for dietary or drug-induced interventions aimed at reducing or increasing liver fat. The model was formulated using ordinary differential equations (ODEs) and the mathematical analysis, model simulation, model formulation and the model parameter estimation were all performed in MATLAB ResultsOur mathematical model describes accumulation of fat in the liver and predicts changes in lipid fluxes induced by both dietary and drug interventions. The model is validated using data from a wide range of drug and dietary intervention studies and can predict both short-term (days) and long-term (weeks) changes in liver fat. Importantly, the model computes the contribution of each individual lipid flux to the total liver fat dynamics. Furthermore, the model can be combined with an established bodyweight model, to simulate even longer scenarios (years), also including the effects of insulin resistance and body weight. To help prepare for corresponding eHealth applications, we also present a way to visualize the simulated changes, using dynamically changing lipid droplets, seen in images of liver biopsies. ConclusionIn conclusion, we believe that the minimal model presented herein might be a useful tool for future applications, and to further integrate and understand data regarding changes in dietary and drug induced changes in ectopic TAG in the liver. With further development and validation, the minimal model could be used as a disease progression model for steatosis.

PV Panel Model Parameter Estimation by Using Particle Swarm Optimization and Artificial Neural Network.

Photovoltaic (PV) panels are one of the popular green energy resources and PV panel parameter estimations are one of the popular research topics in PV panel technology. The PV panel parameters could be used for PV panel health monitoring and fault diagnosis. Recently, a PV panel parameters estimation method based in neural network and numerical current predictor methods has been developed. However, in order to further improve the estimation accuracies, a new approach of PV panel parameter estimation is proposed in this paper. The output current and voltage dynamic responses of a PV panel are measured, and the time series of the I-V vectors will be used as input to an artificial neural network (ANN)-based PV model parameter range classifier (MPRC). The MPRC is trained using an I-V dataset with large variations in PV model parameters. The results of MPRC are used to preset the initial particles' population for a particle swarm optimization (PSO) algorithm. The PSO algorithm is used to estimate the PV panel parameters and the results could be used for PV panel health monitoring and the derivation of maximum power point tracking (MMPT). Simulations results based on an experimental I-V dataset and an I-V dataset generated by simulation show that the proposed algorithms can achieve up to 3.5% accuracy and the speed of convergence was significantly improved as compared to a purely PSO approach.

Weighted likelihood transfer learning for high-dimensional generalized linear models

To simultaneously improve parameter estimation and variable selection for a target model by the auxiliary information from source models, a weighted likelihood transfer learning (WL-TL), together with a l 1 -penalty, is proposed for high-dimensional generalized linear models. To implement the transfer learning, the relevant techniques, including iterative algorithm and the choice of weight, are suggested. The methodology is computational simple, without need for the bias-correction used in the existing literature of parameter-transfer learning. The theoretical properties such as the quadratic error bound of the parameter estimator and the estimation consistency are established. A specific weight selection method based on the Bayesian decision theory has been proposed and studied. Comprehensive simulation experiments and real data analyzes are conducted to further illustrate the performance of the new method.

Online Muscle Activation Onset Detection Using Likelihood of Conditional Heteroskedasticity of Electromyography Signals.

The real-time, accurate detection of muscle activation onset (MAO) is significant for EMG-triggered control strategies in embedded applications like prostheses and exoskeletons. This paper investigates sEMG signals using the generalized autoregressive conditional heteroskedasticity (GARCH) model, focusing on variance. A novel feature, the likelihood of conditional heteroskedasticity (LCH) extracted from the maximum likelihood estimation of GARCH parameters, is proposed. This feature effectively distinguishes signal from noise based on heteroskedasticity, allowing for the detection of MAO through the LCH feature and a basic threshold classifier. For online calculation, the model parameter estimation is simplified, enabling direct calculation of the LCH value using fixed parameters. The proposed method was validated on two open-source datasets and demonstrated superior performance over existing methods. The mean absolute error of onset detection, compared with visual detection results, is approximately 65 ms under online conditions, showcasing high accuracy, universality, and noise insensitivity. The results indicate that the proposed method using the LCH feature from the GARCH model is highly effective for real-time detection of muscle activation onset in sEMG signals. This novel approach shows great potential and possibility for real-world applications, reflecting its superior performance in accuracy, universality, and insensitivity to noise.

A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the time-invariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.

Estimation of virus transport parameters in both unsaturated-saturated zone using numerical simulation and flower pollination algorithm

To develop a virus transport model considering both the unsaturated and saturated zone, it is essential to consider separate parameters for both the zone. This is because the virus fate and transport process depends on the degree of saturation. As such, this paper introduces a parameter estimation model that simultaneously identifies virus transport parameters in an unconfined aquifer for both the unsaturated and saturated zones. The proposed model utilizes a linked simulation-optimization technique to minimize errors between observed and simulated virus concentrations. The simulation model used in this study is termed as “variable detachment model,” this is because the simulation component of this approach incorporates varying adsorption rates, which are influenced by the degree of saturation. This study also highlights the complexities involved in parameter estimation for virus transport models, such as non-uniqueness, instability, and non-identifiability. These challenges arise when multiple parameter combinations can produce similar model predictions, leading to difficulty in determining the actual parameter values. To address these challenges, a meta-heuristic optimization algorithm, Flower Pollination Algorithm (FPA), is used, effectively solving such non-convex problems. The model could estimate all the parameters accurately except the inactivation rates of viruses. Later when the global sensitivity analysis was carried out to understand the relative importance of each parameter, inactivation rates were found to be less influential to the model output. Thus, FPA based parameter estimation model can be used as an alternative for estimating the virus transport parameters in groundwater aquifers.

Parameter estimation and global sensitivity analysis of a bacterial-plasmid model with impulsive drug treatment

In this paper, a mathematical model is developed to study bacterial resistance caused by plasmids and mutations in the presence of the impulsive drug treatment. Firstly, the stability of the bacterial-plasmid extinction periodic solution is proved by Floquet theory and the permanence of system is presented while some conditions are satisfied. Secondly, the nontrivial periodic solution bifurcated from the bacterial-plasmid extinction periodic solution is obtained in view of the four-dimensional impulsive control of bifurcation method. Good fitting results are given by the Mean Absolute Percentage Error method for four different cases of bacterial media. Further, the global sensitivity of R0 is analyzed by the Partial Rank Correlation Coefficient method, and the parameters that have important influence on the system are determined. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.

Bottom-up parameterization of enzyme rate constants: Reconciling inconsistent data

Kinetic models of metabolism are promising platforms for studying complex metabolic systems and designing production strains. Given the availability of enzyme kinetic data from historical experiments and machine learning estimation tools, a straightforward modeling approach is to assemble kinetic data enzyme by enzyme until a desired scale is reached. However, this type of ‘bottom up’ parameterization of kinetic models has been difficult due to a number of issues including gaps in kinetic parameters, the complexity of enzyme mechanisms, inconsistencies between parameters obtained from different sources, and in vitro-in vivo differences. Here, we present a computational workflow for the robust estimation of kinetic parameters for detailed mass action enzyme models while taking into account parameter uncertainty. The resulting software package, termed MASSef (the Mass Action Stoichiometry Simulation Enzyme Fitting package), can handle standard ‘macroscopic’ kinetic parameters, including Km, kcat, Ki, Keq, and nh, as well as diverse reaction mechanisms defined in terms of mass action reactions and ‘microscopic’ rate constants. We provide three enzyme case studies demonstrating that this approach can identify and reconcile inconsistent data either within in vitro experiments or between in vitro and in vivo enzyme function. We further demonstrate how parameterized enzyme modules can be used to assemble pathway-scale kinetic models consistent with in vivo behavior. This work builds on the legacy of knowledge on kinetic behavior of enzymes by enabling robust parameterization of enzyme kinetic models at scale utilizing the abundance of historical literature data and machine learning parameter estimates.

Fitting metabolic models to dissolved oxygen data: The estuarine Bayesian single‐station estimation method

AbstractContinuous measurements of dissolved oxygen (DO) are useful for quantifying ecosystem metabolism, which is critical for understanding estuarine biogeochemistry and ecology, but current methods applied to these data may lead to estimates that are physically impossible and poorly constrained errors. Here, we present a new approach for estimating estuarine metabolism: Estuarine BAyesian Single‐station Estimation (EBASE). EBASE applies a Bayesian framework to a simple process‐based model and DO observations, allowing the estimation of critical model parameters, specifically light efficiency and respiration, as informed by a set of prior distributions. EBASE improves upon the stream‐based model from which it was derived by accommodating missing DO data and allowing the user to set the time period over which parameters are estimated. We demonstrate that EBASE can recover known metabolic parameters from a synthetic time series, even in the presence of noise (e.g., due to tidal advection) and when prior distributions are uninformed. Optimization periods of 7 and 30 d are more preferable than 1 d. A comparison with the more‐conventional method of Odum reveals the ability of EBASE to avoid unphysical results (such as negative photosynthesis and respiration) and improves when the DO data are detided. EBASE is available using open‐source software (R) and can be readily applied to multiple years of long‐term monitoring data that are available in many estuaries. Overall, EBASE provides an accessible method to parameterize a simple metabolic model appropriate for estuarine systems and will provide additional understanding of processes that influence ecosystem status and condition.

DIMOND: DIffusion Model OptimizatioN with Deep Learning.

Diffusion magnetic resonance imaging is an important tool for mapping tissue microstructure and structural connectivity non-invasively in the in vivo human brain. Numerous diffusion signal models are proposed to quantify microstructural properties. Nonetheless, accurate estimation of model parameters is computationally expensive and impeded by image noise. Supervised deep learning-based estimation approaches exhibit efficiency and superior performance but require additional training data and may be not generalizable. A new DIffusion Model OptimizatioN framework using physics-informed and self-supervised Deep learning entitled "DIMOND" is proposed to address this problem. DIMOND employs a neural network to map input image data to model parameters and optimizes the network by minimizing the difference between the input acquired data and synthetic data generated via the diffusion model parametrized by network outputs. DIMOND produces accurate diffusion tensor imaging results and is generalizable across subjects and datasets. Moreover, DIMOND outperforms conventional methods for fitting sophisticated microstructural models including the kurtosis and NODDI model. Importantly, DIMOND reduces NODDI model fitting time from hours to minutes, or seconds by leveraging transfer learning. In summary, the self-supervised manner, high efficacy, and efficiency of DIMOND increase the practical feasibility and adoption of microstructure and connectivity mapping in clinical and neuroscientific applications.

Self-Diagnostic and Self-Compensation Methods for Resistive Displacement Sensors Tailored for In-Field Implementation.

This paper presents a suitably general model for resistive displacement sensors where the model parameters depend on the current sensor conditions, thereby capturing wearout and failure, and proposes a novel fault detection method that can be seamlessly applied during sensor operation, providing self-diagnostic capabilities. On the basis of the estimation of model parameters, an innovative self-compensation method is derived to increase the accuracy of sensors subject to progressive wearout. The proposed model and methods have been validated by both numerical simulations and experimental tests on two real resistive displacement sensors, placed in undamaged and faulty conditions, respectively. The fault detection method has shown an accuracy of 97.2%. The position estimation error is < ±0.2% of the full-scale span for the undamaged sensor, while the self-compensation method successfully reduces the position estimation error from ±15% to approximately ±2% of the full-scale span for the faulty sensor.

Quasi‐Likelihood Estimation in Volatility Models for Semi‐Continuous Time Series

Time series containing non‐negligible portion of possibly dependent zeros, whereas the remaining observations are positive, are considered. They are regarded as GARCH processes consisting of non‐negative values. Our first aim lies in estimation of the omnibus model parameters taking into account the semi‐continuous distribution. The hurdle distribution together with dependent zeros cause that the classical GARCH estimation techniques fail. Two different quasi‐likelihood approaches are employed. Both estimators are proved to be strongly consistent and asymptotically normal. The second goal consists in the proposed predictions with bootstrap add‐ons. The considered class of models can be reformulated as multiplicative error models. The empirical properties are illustrated in a simulation study, which demonstrates computational efficiency of the employed methods. The developed techniques are presented through an actuarial problem concerning insurance claims.

A neural network paradigm for modeling psychometric data and estimating IRT model parameters: Cross estimation network.

This paper presents a novel approach known as the cross estimation network (CEN) for fitting the datasets obtained from psychological or educational tests and estimating the parameters of item response theory (IRT) models. The CEN is comprised of two subnetworks: the person network (PN) and the item network (IN). The PN processes the response pattern of individual respondent and generates an estimate of the underlying ability, while the IN takes in the response pattern of individual item and outputs the estimates of the item parameters. Four simulation studies and an empirical study were comprehensively and rigorously conducted to investigate the performance of CEN on parameter estimation of the two-parameter logistic model under various testing scenarios. Results showed that CEN effectively fit the training data and produced accurate estimates of both person and item parameters. The trained PN and IN adhered to AI principles and acted as intelligent agents, delivering commendable evaluations for even unseen patterns of new respondents and items.

EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters.

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

Sobolev Calibration of Imperfect Computer Models

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic normality and semiparametric efficiency. We also demonstrate an interesting property that the Sobolev calibration can bridge the gap between two influential methods: L 2 calibration and Kennedy and O’Hagan’s calibration. In addition to exploring the deterministic physical experiments, we theoretically justify that our method can transfer to the case when the physical process is indeed a Gaussian process, which follows the original idea of Kennedy and O’Hagan’s. Numerical simulations as well as a real-world example illustrate the competitive performance of the proposed method.

Efficient parameter extraction of photovoltaic models with a novel enhanced prairie dog optimization algorithm

The growing demand for solar energy conversion underscores the need for precise parameter extraction methods in photovoltaic (PV) plants. This study focuses on enhancing accuracy in PV system parameter extraction, essential for optimizing PV models under diverse environmental conditions. Utilizing primary PV models (single diode, double diode, and three diode) and PV module models, the research emphasizes the importance of accurate parameter identification. In response to the limitations of existing metaheuristic algorithms, the study introduces the enhanced prairie dog optimizer (En-PDO). This novel algorithm integrates the strengths of the prairie dog optimizer (PDO) with random learning and logarithmic spiral search mechanisms. Evaluation against the PDO, and a comprehensive comparison with eighteen recent algorithms, spanning diverse optimization techniques, highlight En-PDO’s exceptional performance across different solar cell models and CEC2020 functions. Application of En-PDO to single diode, double diode, three diode, and PV module models, using experimental datasets (R.T.C. France silicon and Photowatt-PWP201 solar cells) and CEC2020 test functions, demonstrates its consistent superiority. En-PDO achieves competitive or superior root mean square error values, showcasing its efficacy in accurately modeling the behavior of diverse solar cells and performing optimally on CEC2020 test functions. These findings position En-PDO as a robust and reliable approach for precise parameter estimation in solar cell models, emphasizing its potential and advancements compared to existing algorithms.