Estimation Of Model Parameters Research Articles

CHANGEPOINTS DETECTION OF PANDEMIC WAVE IN REAL-TIME: APPLICATIONS TO THE TRANSMISSION OF COVID-19

The COVID-19 pandemic has spread throughout the world. Most countries experienced the pandemic in multiple waves. The Richards model predicts when a pandemic will peak and end in a particular area. However, this model can only be used in the single-wave case. The research aims to identify a changepoint detection method capable of delineating pandemic wave boundaries, thus enabling the resolution of multiple wave cases using the Richards model. This article uses two methods to detect changepoints: the Pruned Exact Linear Time (PELT) and the interpolation method. PELT method determines the changepoint based on changes in the statistical properties of the sequence of observations which can be in the form of differences in the mean or variance of each set of observations. In contrast, the linear interpolation method determines the changepoint based on the slope of a data pattern. The two methods complement each other, where the interpolation method is used to determine whether the pandemic is still in a single wave or has multiple waves, followed by determining wave boundaries using the PELT method. Richards model parameter estimation is carried out after the wave boundaries are obtained, and initial data is taken from the last wave using the PELT method. The prediction results show the peak of the pandemic in a particular region and when it will end, which can be used to inform medium-term strategies for the government to overcome the ongoing pandemic. This information helps prevent a resurgence of infections, which would negatively affect the COVID-19 mortality rate and the area's economic situation.

Cross-validatory Z-Residual for Diagnosing Shared Frailty Models

Accurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance residuals lack a well-characterized reference distribution for censored regression, making numerical statistical tests based on these residuals challenging. Recently, the introduction of Z-residuals for diagnosing survival models addresses this limitation. However, concerns arise from conventional methods that utilize the entire dataset for both model parameter estimation and residual assessment, which may cause optimistic biases. This paper introduces cross-validatory Z-residuals as an innovative approach to address these limitations. Employing a cross-validation (CV) framework, the method systematically partitions the dataset into training and testing sets to reduce the optimistic bias. Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful (e.g. power increased from 0.2 to 0.6). and more discriminative (e.g. AUC increased from 0.58 to 0.85) than Z-residuals without CV. We also compare the performance of Z-residuals with and without CV in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers, which Z-residuals without CV fail to identify. The CV Z-residual is a more powerful tool than the No-CV Z-residual for checking survival models, particularly in goodness-of-fit tests and outlier detection. We have published a generic function, which is collected in an R package called Zresidual, for computing CV Z-residual for the output of the widely used survival R package.

Estimation of Contagion: Bayesian Model Averaging on Tail Dependence of Mixture Copula

This study introduces a novel approach to estimate tail dependence in financial contagion using mixture copulas. Addressing the challenges of weight parameter estimation in conventional models, we propose a Bayesian model averaging method to determine optimal copula weights. Through both simulations and empirical studies, the proposed method demonstrates improved robustness and accuracy, particularly when handling extreme weight scenarios. These advancements offer more reliable measurements of financial contagion, contributing to enhanced risk management and policy-making in interconnected financial markets.

Bayesian finite element model inversion of offshore wind turbine structures for joint parameter-load estimation

Operating in harsh and unsteady marine environment, offshore wind turbine (OWT) structures are exposed to unpredictable wind and wave loads. Identifying the structural loads and their effects on the OWTs allow for predicting the remaining fatigue life of these structures and improving the structural design procedure. In this paper, a finite element (FE) model inversion method is presented to estimate the unknown loads and model parameters of OWTs using sparse measurement data. A realistic FE model of an OWT structure with jacket substructure is created in the open-source simulation platform, OpenSees. A Bayesian inference framework is presented to integrate the measured data with the FE model to estimate unknown wind loads and mass of rotor-nacelle assembly. To evaluate the performance of this data assimilation framework, the effect of sensor type, number of sensors, and modeling errors on the estimation accuracy of wind loads and model parameters are investigated through different case studies where synthetic data are used as measurements. The results of this study are important to guide instrumentation of new OWT structures, and to understand the potential limitations and sources of error in the real-world application of this data assimilation framework for joint model parameter and input load estimation.

Bayesian grouping-Gibbs sampling estimation of high-dimensional linear model with non-sparsity

In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients β∈Rp. However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions β into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (k) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.

Revisiting the Briggs Ancient DNA Damage Model: A Fast Maximum Likelihood Method to Estimate Post-Mortem Damage.

One essential initial step in the analysis of ancient DNA is to authenticate that the DNA sequencing reads are actually from ancient DNA. This is done by assessing if the reads exhibit typical characteristics of post-mortem damage (PMD), including cytosine deamination and nicks. We present a novel statistical method implemented in a fast multithreaded programme, ngsBriggs that enables rapid quantification of PMD by estimation of the Briggs ancient damage model parameters (Briggs parameters). Using a multinomial model with maximum likelihood fit, ngsBriggs accurately estimates the parameters of the Briggs model, quantifying the PMD signal from single and double-stranded DNA regions. We extend the original Briggs model to capture PMD signals for contemporary sequencing platforms and show that ngsBriggs accurately estimates the Briggs parameters across a variety of contamination levels. Classification of reads into ancient or modern reads, for the purpose of decontamination, is significantly more accurate using ngsBriggs than using other methods available. Furthermore, ngsBriggs is substantially faster than other state-of-the-art methods. ngsBriggs offers a practical and accurate method for researchers seeking to authenticate ancient DNA and improve the quality of their data.

State of Charge Estimation for Lithium-Ion Battery Based on Fractional-Order Kreisselmeier-Type Adaptive Observer

For the safe and efficient use of lithium-ion batteries, the state of charge (SOC) is a particularly important state variable. In this paper, we propose a method for the online estimation of SOC and model parameters based on a fractional-order equivalent circuit model. Firstly, we constructed a fractional-order battery model that includes pseudo-capacitance and determined the values of the circuit elements offline using the least squares method from actual input–output data based on the driving profile of an automobile. Compared to the integer-order battery model, we confirmed that the proposed fractional-order battery model has higher accuracy. Secondly, we constructed a fractional-order Kreisselmeier-type adaptive observer as an observer that performs state estimation and parameter adjustment simultaneously. Applying the general adaptive law to the battery model results in a redundant design with many adjustable parameters, so we proposed an adaptive law that reduces the number of adjustable parameters without compromising the stability of the observer. The effectiveness of the proposed method was verified through numerical simulations. As a result, the high estimation accuracy and convergence of the proposed adaptive law were confirmed.

Development of a high-fidelity digital twin using the discrete element method for a continuous direct compression process. Part 1. Calibration workflow

In this work, a high-fidelity digital twin was developed to support the design and testing of control strategies for drug product manufacturing via direct compression. The high-fidelity digital twin platform was based on typical pharmaceutical equipment, materials, and direct compression continuous processes. The paper describes in detail the material characterization, the Discrete Element Method (DEM) model and the DEM model parameter calibration approach and provides a comparison of the system’s response to the experimental results for stepwise changes in the API concentration at the mixer inlet. A calibration method for a cohesive DEM contact model parameter estimation was introduced. To assure a correct prediction for a wide range of processes, the calibration approach contained four characterization experiments using different stress states and different measurement principles, namely the bulk density test, compression with elastic recovery, the shear cell, and the rotating drum. To demonstrate the sensitivity of the DEM contact parameters to the process response, two powder characterization data sets with different powder flowability were applied. The results showed that the calibration method could differentiate between the different material batches of the same blend and that small-scale material characterization tests could be used to predict the residence time distribution in a continuous manufacturing process.

Fitness-guided particle swarm optimization with adaptive Newton-Raphson for photovoltaic model parameter estimation

This study introduces a new approach for parameter optimization in the four-diode photovoltaic (PV) model, employing a Dynamic Fitness-Guided Particle Swarm Optimization (DFGPSO) algorithm and Enhanced Newton-Raphson (ENR) method. The new DFGPSO algorithm is specifically designed to address the intrinsic challenges in PV modelling, such as local optima entrapment and slow convergence rates that typically hinder traditional optimization methods. By integrating a dynamically evolving fitness function derived from advanced swarm intelligence, the proposed approach significantly enhances global search capabilities. This new fitness function adapts continuously to the search landscape, facilitating rapid convergence towards optimal solutions and effectively navigating the complex, non-linear, and multi-modal parameter space of the PV model. Moreover, the robustness of the DFGPSO algorithm is substantially improved through the strategic incorporation of the ENR method. This integration not only provides accurate initial guesses for the particle positions, thus expediting the convergence process, but also minimizes computational burden, making the method more efficient. Comprehensive simulation studies across various case scenarios demonstrate that the proposed method markedly outperforms existing state-of-the-art optimization algorithms. It delivers faster convergence, enhanced accuracy, and robust performance under diverse environmental conditions, establishing a reliable and precise tool for optimizing PV system performance. This advancement promises significant improvements in energy yield and system reliability for the PV industry.

Bridging Hydrological Ensemble Simulation and Learning Using Deep Neural Operators

AbstractEnsemble‐based simulation and learning (ESnL) has long been used in hydrology for parameter inference, but computational demands of process‐based ESnL can be quite high. To address this issue, we propose a deep neural operator learning approach. Neural operators are generic machine learning algorithms that can learn functional mappings between infinite‐dimensional spaces, providing a highly flexible tool for scientific machine learning. Our approach is built upon DeepONet, a specific deep neural operator, and is designed to address several common problems in hydrology, namely, model parameter estimation, prediction at ungaged locations, and uncertainty quantification. Here we demonstrate the effectiveness of our DeepONet‐based workflow using an existing large model ensemble created for an eastern U.S. watershed that is instrumented with 10 streamflow gages. Results suggest DeepONet achieves high efficiency in learning an ML surrogate model from the model ensemble, with the modified Kling‐Gupta Efficiency exceeding 0.9 on holdout test sets. Parameter inference, carried out using the trained DeepONet surrogate model and genetic algorithm, also yields robust results. Additionally, we formulate and train a separate DeepONet model for physics‐informed, seq‐to‐seq streamflow forecasting, which further reduces biases in the pre‐trained DeepONet surrogate model. While this study focuses primarily on a single watershed, our approach is general and may be extended to enable learning from model ensembles across multiple basins or models. Thus, this research represents a significant contribution to the application of hybrid machine learning in hydrology.

Power modeling of degraded PV systems: Case studies using a dynamically updated physical model (PV-Pro)

Power modeling, widely applied for health monitoring and power prediction, is crucial for the efficiency and reliability of Photovoltaic (PV) systems. The most common approach for power modeling uses a physical equivalent circuit model, with the core challenge being the estimation of model parameters. Traditional parameter estimation either relies on datasheet information, which does not reflect the system's current health status, especially for degraded PV systems, or requires additional I-V characterization, which is generally unavailable for large-scale PV systems. Thus, we build upon our previously developed tool, PV-Pro (originally proposed for degradation analysis), to enhance its application for power modeling of degraded PV systems. PV-Pro extracts model parameters from production data without requiring I-V characterization. This dynamic model, periodically updated, can closely capture the actual degradation status, enabling precise power modeling. PV-Pro is compared with popular power modeling techniques, including persistence, nominal physical, and various machine learning models. The results indicate that PV-Pro achieves outstanding power modeling performance, with an average nMAE of 1.4 % across four field-degraded PV systems, reducing error by 17.6 % compared to the best alternative technique. Furthermore, PV-Pro demonstrates robustness across different seasons and severities of degradation. The tool is available as a Python package at https://github.com/DuraMAT/pvpro.

Integrating dynamic models and neural networks to discover the mechanism of meteorological factors on Aedes population.

Aedes mosquitoes, known as vectors of mosquito-borne diseases, pose significant risks to public health and safety. Modeling the population dynamics of Aedes mosquitoes requires comprehensive approaches due to the complex interplay between biological mechanisms and environmental factors. This study developed a model that couples differential equations with a neural network to simulate the dynamics of mosquito population, and explore the relationships between oviposition rate, temperature, and precipitation. Data from nine cities in Guangdong Province spanning four years were used for model training and parameter estimation, while data from the remaining three cities were reserved for model validation. The trained model successfully simulated the mosquito population dynamics across all twelve cities using the same set of parameters. Correlation coefficients between simulated results and observed data exceeded 0.7 across all cities, with some cities surpassing 0.85, demonstrating high model performance. The coupled neural network in the model effectively revealed the relationships among oviposition rate, temperature, and precipitation, aligning with biological patterns. Furthermore, symbolic regression was used to identify the optimal functional expression for these relationships. By integrating the traditional dynamic model with machine learning, our model can adhere to specific biological mechanisms while extracting patterns from data, thus enhancing its interpretability in biology. Our approach provides both accurate modeling and an avenue for uncovering potential unknown biological mechanisms. Our conclusions can provide valuable insights into designing strategies for controlling mosquito-borne diseases and developing related prediction and early warning systems.

Symbolic-numeric algorithm for parameter estimation in discrete-time models with exp

Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. In this paper, we propose a symbolic-numeric approach for parameter estimation in discrete-time models that involve univariate non-algebraic (locally) analytic functions such as exp. We illustrate the performance (precision) of our approach by applying our approach to two archetypal discrete-time models in biology (the flour beetle ‘LPA’ model and discrete Lotka-Volterra competition model). Unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values up to a specified precision given time-series data for the measured variables provided that there are finitely many parameter values that fit the data and that the used polynomial system solver can find all roots of the associated polynomial system with interval coefficients.

Detecting rough volatility: a filtering approach

In this paper, we focus on filtering and parameter estimation in stochastic volatility models when observations arise from high-frequency data. We are particularly interested in rough volatility models where spot volatility is driven by fractional Brownian motion with Hurst index H < 1 2 . Since volatility is not directly observable, we rely on particle filtering techniques for statistical inference regarding the current level of volatility and the parameters governing its dynamics. In order to obtain numerically efficient and recursive algorithms, we use the fact that a fractional Brownian motion can be represented through a superposition of Markovian semimartingales (Ornstein-Uhlenbeck processes). We analyze the performance of our approach on simulated data and we compare it to similar studies in the literature. The paper concludes with an empirical case study, where we apply our methodology to high-frequency data of a liquid stock.

Coagulo-Net: Enhancing the mathematical modeling of blood coagulation using physics-informed neural networks

Blood coagulation, which involves a group of complex biochemical reactions, is a crucial step in hemostasis to stop bleeding at the injury site of a blood vessel. Coagulation abnormalities, such as hypercoagulation and hypocoagulation, could either cause thrombosis or hemorrhage, resulting in severe clinical consequences. Mathematical models of blood coagulation have been widely used to improve the understanding of the pathophysiology of coagulation disorders, guide the design and testing of new anticoagulants or other therapeutic agents, and promote precision medicine. However, estimating the parameters in these coagulation models has been challenging as not all reaction rate constants and new parameters derived from model assumptions are measurable. Although various conventional methods have been employed for parameter estimation for coagulation models, the existing approaches have several shortcomings. Inspired by the physics-informed neural networks, we propose Coagulo-Net, which synergizes the strengths of deep neural networks with the mechanistic understanding of the blood coagulation processes to enhance the mathematical models of the blood coagulation cascade. We assess the performance of the Coagulo-Net using two existing coagulation models with different extents of complexity. Our simulation results illustrate that Coagulo-Net can efficiently infer the unknown model parameters and dynamics of species based on sparse measurement data and data contaminated with noise. In addition, we show that Coagulo-Net can process a mixture of synthetic and experimental data and refine the predictions of existing mathematical models of coagulation. These results demonstrate the promise of Coagulo-Net in enhancing current coagulation models and aiding the creation of novel models for physiological and pathological research. These results showcase the potential of Coagulo-Net to advance computational modeling in the study of blood coagulation, improving both research methodologies and the development of new therapies for treating patients with coagulation disorders.

A novel statistical approach to COVID-19 variability using the Weibull-Inverse Nadarajah Haghighi distribution

Researchers have devoted decades to striving to create a plethora of distinctive distributions in order to meet specific objectives. The argument is that traditional distributions have typically been found to lack fit in real-world situations, which include pharmaceutical studies, the field of engineering, hydrology, environmental science, and a number of others. The Weibull-inverse Nadarajah Haghighi (WINH) distribution is developed by combining the Weibull and inverse Nadarajah Haghighi distributions. The proposed distribution's fundamental characteristics have been established and analyzed. Several plots of the distributional properties, notably probability density function (PDF) with corresponding cumulative distribution function (CDF) are displayed. The estimation of model parameter is performed via the MLE procedure. Simulation-based research is conducted to demonstrate the performance of proposed estimator’s using some measure, like the average bias, variance, and associated mean square error (MSE). Two real datasets represent the morality due to COVID 19 in France and Canada are illustrated to see the practicality of the recommended model.

The potential of mixing model of wind speed distribution in Algerian High Plateaus

The evaluation of wind energy relies primarily on the probability density function PDF, which corresponds well with the wind speed data. Single PDFs are widely used in the assessment of wind. In contrast, homogeneous or heterogeneous mixed models are rarely used, especially in Algeria, where the bimodal wind speed distribution is expected. This research aims to investigate the potential of heterogeneous PDFs Generalized Extreme Value-Weibul and Normal-Extreme Value PDFs in assessing wind energy at three meteorological stations in the high plateau against the single widespread PDFs Weibull and GEV by analyzing five years of archived wind speed data. The estimation of mixed model parameters is obtained by applying the Expectation-Maximization algorithm, and the identification of the appropriate PDF is obtained by four goodness-of-fit (GOF) criteria and compared with the widespread single distributions. The results show that the mixed model surpasses widely the single model for all the GOF criteria used at the three selected sites. The proposed mixed model fits all the wind speed distributions related to unimodal and bimodal regimes.

Escalation of Human Resource Quality in National Health Resilience Through Estimating Multilevel Model Parameters with the Restricted Maximum Likelihood Approach to The 2019 UTBK Average

Multilevel modeling or Hierarchical Linear Modeling (HLM) is a statistical approach specifically used to analyze data with a two-level structure. This approach allows an understanding of the contribution of factors at both the individual and group levels to the response variable. One method commonly used in HLM is Restricted Maximum Likelihood (REML). REML is a parameter estimation method that is often applied in statistical models, especially linear models that incorporate random components. This allows more efficient parameter assessment compared to conventional estimation methods. In this research, multilevel model parameter estimation analysis was carried out using the limited maximum likelihood approach. The aim is to determine the multilevel linear regression model on the average UTBK score for health cluster study programs in 2019. This involves selecting the optimal node point based on the minimum Generalized Cross Validation (GCV) and identifying the factors that influence it. Predictor variables considered include interest and capacity of study programs at university level (Level-1), as well as the average UNBK and HDI scores at provincial level (Level-2). The findings of this research indicate that the most appropriate multilevel regression model is formed with three nodes with a minimum GCV value at Level-1 of 864.6593 and at Level-2 of 3.1816. At Level-1, the influencing factor is the interest variable and at Level-2 is the average provincial UNBK score in 2019 and the Human Development Index (HDI).

Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.

Snow depth retrieval method for PolSAR data using multi-parameters snow backscattering model

Snow depth (SD) is a crucial property of snow, its spatial and temporal variation is important for global change, snowmelt runoff simulation, disaster prediction, and freshwater storage estimation. Polarimetric Synthetic Aperture Radar (PolSAR) can precisely describe the backscattering of the target and emerge as an effective tool for SD retrieval. The backscattering component of dry snow is mainly composed of volume scattering from the snowpack and surface scattering from the snow-ground interface. However, the existing method for retrieving SD using PolSAR data has the problems of over-reliance on in-situ data and ignoring surface scattering from the snow-ground interface. We proposed a novel SD retrieval method for PolSAR data by fully considering the primary backscattering components of snow and through multi-parameter estimation to solve the snow backscattering model. Firstly, a snow backscattering model was formed by combining the small permittivity volume scattering model and the Michigan semi-empirical surface scattering model to simulate the different scattering components of snow, and the corresponding backscattering coefficients were extracted using the Yamaguchi decomposition. Then, the snow permittivity was calculated through generalized volume parameters and the extinction coefficient was further estimated through modeling. Finally, the snow backscattering model was solved by these parameters to retrieve SD. The proposed method was validated by Ku-band UAV SAR data acquired in Altay, Xinjiang, and the accuracy was evaluated by in-situ data. The correlation coefficient, root mean square error, and mean absolute error are 0.80, 4.49 cm, and 3.95 cm, respectively. Meanwhile, the uncertainties generated by different SD, model parameters estimation, solution method, and underlying surface are analyzed to enhance the generality of the proposed method.