Estimation Of Model Parameters Research Articles

Effect of vaccinations and school restrictions on the spread of COVID-19 in different age groups in Germany

With the emergence of SARS-CoV-2, various non-pharmaceutical interventions were adopted to control virus transmission, including school closures. Subsequently, the introduction of vaccines mitigated not only disease severity but also the spread of SARS-CoV-2. This study leveraged an adapted SIR model and non-linear mixed-effects modeling to quantify the impact of remote learning, school holidays, the emergence of Variants of Concern (VOCs), and the role of vaccinations in controlling SARS-CoV-2 spread across 16 German federal states with an age-stratified approach. Findings highlight a significant inverse correlation (Spearman's ρ = −0.92, p < 0.001) between vaccination rates and peak incidence rates across all age groups. Model-parameter estimation using the observed number of cases stratified by federal state and age allowed to assess the effects of school closure and holidays, considering adjustments for vaccinations and spread of VOCs over time. Here, modeling revealed significant (p < 0.001) differences in the virus's spread among pre-school children (0–4), children (5–11), adolescents (12–17), adults (18–59), and the elderly (60+). The transition to remote learning emerged as a critical measure in significantly reducing infection rates among children and adolescents (p < 0.001), whereas an increased infection risk was noted among the elderly during these periods, suggesting a shift in infection networks due to altered caregiving roles. Conversely, during school holiday periods, infection rates among adolescents mirrored those observed when schools were open. Simulation exercises based on the model provided evidence that COVID-19 vaccinations might serve a dual purpose: they protect the vaccinated individuals and contribute to the broader community's safety.

Irradiance separation model parameter estimation from historical cloud cover statistical properties

Irradiance separation models allow the decomposition of Global Horizontal Irradiance into Diffuse Horizontal and Direct Normal Irradiances. These models need fitting to the irradiance characteristics of the location of interest using locally measured ground data. For locations that only measure Global Horizontal Irradiance, current state of the art establishes the use of parameters obtained for another location that measures the three components, with similar climate characteristics. Nevertheless, this results in a lack of localized character for estimates and requires fitting model parameters for all possible climates, which can be infeasible given data availability. This work presents a novel approach based on the hypothesis that the separation model's parameters are a function of the statistical properties of satellite-derived cloud cover estimates. The proposed methodology was evaluated in 23 sites covering all main Köppen-Geiger climatic types and different cloud coverage properties using the Boland-Ridley-Lauret diffuse fraction model. The model performs similarly as locally adjusting the model, with Root Mean Square Errors of 0.087–0.15 diffuse fraction units versus 0.077–0.127 for locally optimized parameters, and offers adequate performance across climates and cloud characteristics. These results encourage future research by generalizing parameter estimation for other diffuse fraction models. The main applications for this research are the estimation of irradiance components where no local data is available for model fitting and the enhancement or complementarity of satellite estimates of surface irradiance. Furthermore, it allows the estimation of missing irradiance components due to equipment failure in locations with insufficient data for a representative, locally adapted model.

Bayesian parameter estimation using truncated normal distributions as priors for parameters in fundamental models of chemical processes

AbstractModellers of chemical processes with knowledge about plausible parameter values use Bayesian parameter estimation methods to account for their prior beliefs. Some modellers specify prior distributions with finite parameter ranges, such as uniform distributions and truncated normal distributions, because they better account for knowledge about realistic parameter ranges than normal prior distributions with parameter values ranging between and . We derive closed‐form objective functions for Bayesian parameter estimation with truncated normal priors and uniform priors, for the first time, so that parameter estimation can be performed by solving simple optimization problems rather than using complex sampling‐based techniques. A parametric bootstrapping method that considers truncated normal priors and model nonlinearity is proposed to determine 95% confidence intervals and joint confidence regions. A pharmaceutical case study is used to show the effectiveness of the proposed objective functions and bootstrapping methodology. Confidence regions from bootstrapping are similar to linearization‐based confidence regions that do not account for truncation when truncated areas in normal prior distributions are relatively small. More truncation, which corresponds to more‐precise prior knowledge about the parameters, results in smaller joint confidence regions. The proposed methods will be attractive for parameter estimation in complex process models because they can be less computationally intensive than Markov chain Monte Carlo methods that provide similar results.

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Exponential stochastic volatility model with Laplace returns and its variants

This paper explores the exponential stochastic volatility model generated by first-order exponential Markov sequences to model financial time series. The stationary exponential Markov sequences used to generate the volatility model are the linear exponential autoregressive model, minification model, new exponential autoregressive time series model, and an exponential mixture of autoregressive and minification processes. The statistical properties of the models are studied and the estimation of model parameters is carried out using the generalized method of moments. An approximate Kalman filtering method and a non-linear filtering approach are employed to diagnose the models. To verify the correctness of the estimations, simulation studies are conducted, and two real datasets are used to demonstrate how the models are applied. Furthermore, a comparison of the suggested models is performed using the measures root mean square error, mean absolute error, and Value at Risk via a backtesting procedure.

Parameter estimation in a whole-brain network model of epilepsy: Comparison of parallel global optimization solvers.

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

Bayesian estimation of covariate assisted principal regression for brain functional connectivity.

This paper presents a Bayesian reformulation of covariate-assisted principal regression for covariance matrix outcomes to identify low-dimensional components in the covariance associated with covariates. By introducing a geometric approach to the covariance matrices and leveraging Euclidean geometry, we estimate dimension reduction parameters and model covariance heterogeneity based on covariates. This method enables joint estimation and uncertainty quantification of relevant model parameters associated with heteroscedasticity. We demonstrate our approach through simulation studies and apply it to analyze associations between covariates and brain functional connectivity using data from the Human Connectome Project.

Uncertain statistics models for characterizing annual total energy production

In the field of annual total energy production, it is hard to determine whether the experimental data is linear or nonlinear growth characteristics. Therefore, different regression models are used to test the properties of the observed data. This article uses actual data to perform parameter estimation and residual analysis of linear and nonlinear regression models. In addition, uncertain nonlinear time series model is used to fit the experimental data in order to find a more suitable statistics model after obtaining the growth properties of the observed data. A test is introduced to prove that the disturbance terms presented in the regression and time series models are actually uncertain variables, not random variables. Moreover, the uncertain hypothesis tests show that the uncertain time series model is in better agreement with the real data of the annual total energy production.

Locally sparse and robust partial least squares in scalar-on-function regression

We present a novel approach for estimating a scalar-on-function regression model, leveraging a functional partial least squares methodology. Our proposed method involves computing the functional partial least squares components through sparse partial robust M regression, facilitating robust and locally sparse estimations of the regression coefficient function. This strategy delivers a robust decomposition for the functional predictor and regression coefficient functions. After the decomposition, model parameters are estimated using a weighted loss function, incorporating robustness through iterative reweighting of the partial least squares components. The robust decomposition feature of our proposed method enables the robust estimation of model parameters in the scalar-on-function regression model, ensuring reliable predictions in the presence of outliers and leverage points. Moreover, it accurately identifies zero and nonzero sub-regions where the slope function is estimated, even in the presence of outliers and leverage points. We assess our proposed method’s estimation and predictive performance through a series of Monte Carlo experiments and an empirical dataset—that is, data collected in relation to oriented strand board. Compared to existing methods our proposed method performs favorably. Notably, our robust procedure exhibits superior performance in the presence of outliers while maintaining competitiveness in their absence. Our method has been implemented in the robsfplsr package in .

Parameter estimation of uncertain stock model using residual method optimized by genetic algorithm: valuation of vulnerable European and barrier options

Parameter estimation of uncertain stock model using residual method optimized by genetic algorithm: valuation of vulnerable European and barrier options

A new competing risks model with applications to blood cancer data

Competing risks models are invaluable probabilistic models in survival analysis, a particular part of medical research. Such models deal with research problems that involve multiple potential risk factors that compete with each other to cause death (i.e., failure from a statistical perspective). Competing risks models' flexibility must be thoroughly explored to guarantee suitability for multifaceted risk scenarios (e.g., modeling data of malicious diseases where factors such as treatment response and progression are intertwined). This article considers a new competing risks model called the additive generalized linear-exponential (AGLE) competing risks model. The proposed model is expected to be more robust and superior to other well-known models when modeling real-life data. A mathematical treatment for the properties of the new model is first considered. Afterward, model parameters estimation via various estimation methods is discussed. The critical role of estimating shape parameters in understanding blood cancer's survival and failure mechanisms is highlighted. Furthermore, the bias and root mean square error of different estimation methods are examined numerically through Monte Carlo simulations. The simulation study indicated that the maximum product of spacings estimation method for the model parameters has the optimal balance of bias and variance as the sample sizes increase. Two real-life blood cancer data sets are analyzed to illustrate the application of the proposed model. The analysis outcomes support the AGLE model's robustness, with low Kolmogorov-Smirnov statistics and high p-value, affirming its superior fit for blood cancer data compared to other well-known models.

Estimation of some AM2 model parameters from a derived empirical logistic function of methane production

Because of its capability to convert organic wastes into renewable energy and into some components useful for agriculture, the anaerobic digestion technology can reduce greenhouse gas emissions in the atmosphere and the pollution. Thus, anaerobic digestion can contribute to achieving some of sustainable development goals. Consequently, many theoretical and empirical approaches are proposed for estimating, predicting and optimizing the methane produced by anaerobic digestion. In this context, the logistic function is a mathematical model that can be used to approximate empirical data of the temporal methane production in anaerobic digestion. In a previous paper, under some appropriate approximations, we have derived from AM2 model a single analytical expression in a form of a logistic function for describing the evolution of methane production in batch bioreactors. In the present paper, by comparing the three standard parameters associated with the classical empirical logistic function with that of the derived one from AM2 model; some relationships between them have been established. These relations are exploited for estimating some coefficients and parameters of AM2 model with respect to empiric logistic function parameters and vice-versa. Moreover, this possibility enables more qualitative insight about the evolution of the methane production and the influence of AM2 parameters and coefficients as well as their interaction over its processes.

Relevance of Classical Test Theory in the Assessment of Learning in Tertiary Institutions in Nigeria

Over the years, measurement experts have been captivated by the description of students, which has resulted in the development of test theories such as Item Response Theory and Classical Test Theory. The traditional method of item analysis, known as "Classical Test Theory," asserts that an individual's observed score on an exam is equal to their true score and an error score, with all items in the test contributing equally to student performance. Assessment, in this context, refers to any method used to gauge a learner's current knowledge. The significance of Classical Test Theory in teaching, learning, and evaluating learning outcomes has spurred academic inquiry. This paper explored the application of Classical Test Theory in tertiary institution assessment, emphasizing its relevance in evaluating learning outcomes. Some notable points included the simplicity of mathematical procedures in classical test analysis and the straightforwardness of model parameter estimation. Additionally, this paper advocated for the utilization of statistical sophistication inherent in Classical Test Theory to interpret undergraduates' performance effectively. Lecturers were encouraged to familiarize themselves with its application to provide meaningful insights into students' performance.

Investigating the Model Hypothesis Space: Benchmarking Automatic Model Structure Identification With a Large Model Ensemble

AbstractSelecting an appropriate model for a catchment is challenging, and choosing an inappropriate model can yield unreliable results. The Automatic Model Structure Identification (AMSI) method simultaneously calibrates model structural choices and model parameters, which reduces the workload of comparing different models. In this study we benchmark AMSI's capabilities in two ways, using 12 hydro‐climatically diverse Model Parameter Estimation Experiment catchments. First, we calibrate parameter values for 7,488 different model structures and test AMSI's ability to find the best‐performing models in this set. Second, we compare the performance of these 7,488 models and AMSI's selection to the performance of 45 commonly used, structurally more diverse, conceptual models. In both cases, we quantify model accuracy (through the Kling‐Gupta Efficiency) and model adequacy (through various hydrologic signatures). AMSI effectively identifies high‐accuracy models among the 7,488 options, with Kling‐Gupta‐Efficiency scores comparable to the best among the 45 models. However, model adequacy remains poor for the accurate models, regardless of the selection method. In nine of the tested catchments, none of the most accurate models replicate observed signatures with less than 50% errors; in the remaining three catchments, only a handful of models do so. This paper thus provides strong empirical evidence that relying on aggregated efficiency metrics is unlikely to result in hydrologically adequate models, no matter how the models themselves are selected. Nevertheless, AMSI has been shown to effectively search the model hypothesis space it was given. Combined with an improved calibration approach it can therefore offer new ways to address the challenges of model structure selection.

Conway-Maxwell-Poisson profile monitoring with rk-Shewhart control chart: a comparative study

A control chart is an essential tool in Statistical Quality Control for monitoring the production process. It provides a visual means of identifying process irregularities. In this study, we focus on the Shewhart control chart based on the rk-deviance residuals, namely rk-Shewhart control charts to examine the Conway–Maxwell–Poisson (COM-Poisson) profile, which is used to model the count data with varying degrees of dispersion. The primary goal of this study is to identify the biasing parameter that produces the best result among newly presented biasing parameters developed based on existing ones. It provides a short overview of the COM-Poisson distribution, its modeling, and rk parameter estimation in the case of multicollinearity, as well as the construction of the deviance-residual-based Shewhart chart. To evaluate the performance of the rk-Shewhart, we conduct an analysis using a real-life data set, considering various shift sizes. By employing different biasing parameters, we examine the effectiveness of the rk-Shewhart control chart. The performance evaluation outcomes of the rk-Shewhart charts are compared to the ML-deviance-based Shewhart chart and within themselves based on the biasing parameters. The results demonstrate the advantage of the rk-Shewhart charts over the ML-deviance-based control chart in detecting out-of-control signals. Among the considered biasing parameters, the rk-Shewhart chart utilizing the adjusted biasing parameter k_4 shows the best performance based on the ARL metric.

Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

Activity-based and agent-based transport model of Melbourne: an open multi-modal transport simulation model for Greater Melbourne

Activity- and agent-based models for simulating transport systems have attracted significant attention in recent years. However, building these types of models at a city-wide level and including motorized (i.e. cars and public transport) and non-motorized (i.e. walk and bicycle) modes of transport is a complicated and involved task. This paper presents an open workflow for creating large-scale multi-modal agent-based transport simulation models. The workflow brings together a number of external tools, for example, an activity-based demand generation tool and a road network generation tool, and a set of tools developed for the agent-based model parameter estimation, calibration, and simulation post-processing. We used this workflow to create an activity- and agent-based model for Melbourne and compared the output of the simulation model with observations from the real world in terms of mode share, road volume, travel time, and travel distance. Through these comparisons, we showed that our model is suitable for studying mode choice and road usage behavior of travelers. The calibrated model could be used to test road network change interventions. In addition, a similar workflow can be applied for building simulation models for other cities or could be expanded to include more complicated travel behaviors.

Characterisation of human penile tissue properties using experimental testing combined with multi-target inverse finite element modelling

This paper presents an inverse finite element (FE) approach aimed at estimating multi-layered human penile tissues. The inverse FE approach integrates experimental force–displacement and boundary deformation data of penile tissues with a developed FE model and uses new experimental data on human penile tissue. The experimental study encompasses whole organ plate-compression tests and individual layer tensile and compression tests, providing comprehensive insights into the tissue's mechanical behaviour. The biomechanical characterisation of penile tissue is of crucial significance for understanding its mechanical behaviour under various physiological and pathological conditions. The FE model is constructed using the realistic geometry of the penile segment and appropriate constitutive models for each tissue layer to leverage the accuracy and consistency of the model. Through systematic variation of tissue parameters in the inverse FE algorithm, simulations achieve the best match with both force–displacement and deformed boundary results obtained from the whole organ plate-compression tests. Test results from individual tissue layers are also utilised to assess the estimated parameters. The proposed inverse FE approach allows for the estimation of penile tissue parameters with high precision and reliability, shedding light on the mechanical properties of this complex biological organ. This work has applications not only in urology but also for researchers in various disciplines of biomechanics. As a result, our study contributes to advancing the understanding of human penile tissue mechanics whilst the methodology could also be applied to a range of other soft biological tissues. Statement of significanceThis research uses a multi-target inverse finite element (FE) approach for estimating the material parameters of human penile tissues. By integrating experimental data and a realistic FE model, this study achieves high-precision constitutive model parameter estimation, offering key insights into penile tissue mechanics under various loading conditions. The significance of this work lies in the use of this inverse FE approach for fresh-frozen human penile tissues, to identify the mechanical properties and constitutive models for both segregated tunica albuginea and corpus cavernosum as well as intact penile tissue segments. The study's scientific impact lies in its advancement of the understanding of human urological tissue mechanics, impacting researchers and clinicians alike.

Toward a Semi-Supervised Learning Approach to Phylogenetic Estimation.

Models have always been central to inferring molecular evolution and to reconstructing phylogenetic trees. Their use typically involves the development of a mechanistic framework reflecting our understanding of the underlying biological processes, such as nucleotide substitutions, and the estimation of model parameters by maximum likelihood or Bayesian inference. However, deriving and optimizing the likelihood of the data is not always possible under complex evolutionary scenarios or even tractable for large datasets, often leading to unrealistic simplifying assumptions in the fitted models. To overcome this issue, we coupled stochastic simulations of genome evolution with a new supervised deep-learning model to infer key parameters of molecular evolution. Our model is designed to directly analyze multiple sequence alignments and estimate per-site evolutionary rates and divergence without requiring a known phylogenetic tree. The accuracy of our predictions matched that of likelihood-based phylogenetic inference when rate heterogeneity followed a simple gamma distribution, but it strongly exceeded it under more complex patterns of rate variation, such as codon models. Our approach is highly scalable and can be efficiently applied to genomic data, as we showed on a dataset of 26 million nucleotides from the clownfish clade. Our simulations also showed that the integration of per-site rates obtained by deep learning within a Bayesian framework led to significantly more accurate phylogenetic inference, particularly with respect to the estimated branch lengths. We thus propose that future advancements in phylogenetic analysis will benefit from a semi-supervised learning approach that combines deep-learning estimation of substitution rates, which allows for more flexible models of rate variation, and probabilistic inference of the phylogenetic tree, which guarantees interpretability and a rigorous assessment of statistical support.

Parameter Estimation Method for Virtual Power Plant Frequency Response Model Based on SLP

In adapting to the double-high development trend of high-voltage direct current (HVDC) receiving-end power systems and solving optimization problems in emergency frequency control (EFC) supporting virtual power plants (VPPs) in large-scale power systems, a parameter estimation method for a VPP frequency response model based on a successive linear programming (SLP) method is proposed. First, a “centralized/decentralized” hierarchical control architecture for VPP participation in EFC is designed. Second, the frequency response characteristics of multiple flexible resources are scientifically analyzed, and the system frequency response (SFR) model and equivalent model of VPP are constructed. Subsequently, parameter estimation of the VPP frequency response model is carried out based on the SLP method, aiming to balance the accuracy and computational efficiency of the model. Finally, the effectiveness of the proposed methodology is verified by using PSD-BPA to simulate and test the three-zone HVDC recipient area grid.