Estimation Of Model Parameters Research Articles

Multi-node system modeling and monitoring with extended directed graphical models

Complex manufacturing systems usually contain a large number of variables. Dominated by certain engineering mechanisms, these variables show complicated relationships that cannot be effectively expressed by simple correlation matrices or functions, thus increasing the difficulty of modeling and monitoring these systems. The directed graphical model (DGM) has been used as a flexible tool for describing the relationship among variables in complex systems. However, the DGM treats all variables equally and fails to consider the structural information among them that usually exists. To address this problem, an extended directed graphical model (EDGM) and related parameter estimation, monitoring, and structure learning methods are proposed in this work. Taking prior engineering knowledge into consideration, the EDGM assigns variables into groups and uses groups of variables as nodes in the graph model. By adding hidden state variables to each node, the EDGM can effectively represent the relationship within and between nodes and provide promising monitoring performance. Numerical experiments and a real-world case study of the monocrystalline silicon growth process are performed to verify the effectiveness of the proposed methods.

The Estimation of Heavy Tails in Non-linear Models

A generalized student t distribution technique based on estimation of bilinear generalized autoregressive conditional heteroskedasticity (BL-GARCH) model is introduced. The paper investigates from empirical perspective, aspects of the model related to the economic and financial risk management and its impacts on volatility forecasting. The purposive sampling technique was applied to select four banks for the study, namely First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB). The four banks are selected, because their daily stock prices are considered to be more susceptible to volatility than those of other banks within the sampled period (January 2007–May 2022). The data collected were analyzed using MATLAB R2008b Software. The results show that the newly introduced generalized student t distribution is the most general of all the useful distributions applied in the BL-GARCH model parameter estimation. It serves as a general distribution for obtaining empirical characteristics such as volatility clustering, leptokurtosis and leverage effects between returns and conditional variances as well as capturing heavier and lighter tails in high frequency financial time series data.

Parameter estimation and estimability analysis in pharmaceutical models with uncertain inputs

AbstractA methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

Brain perfusion imaging by multi-delay arterial spin labeling: Impact of modeling dispersion and interaction with denoising strategies and pathology.

Arterial spin labeling (ASL) acquisitions at multiple post-labeling delays may provide more accurate quantification of cerebral blood flow (CBF), by fitting appropriate kinetic models and simultaneously estimating relevant parameters such as the arterial transit time (ATT) and arterial cerebral blood volume (aCBV). We evaluate the effects of denoising strategies on model fitting and parameter estimation when accounting for the dispersion of the label bolus through the vasculature in cerebrovascular disease. We analyzed multi-delay ASL data from 17 cerebral small vessel disease patients (50 ± 9 y) and 13 healthy controls (52 ± 8 y), by fitting an extended kinetic model with or without bolus dispersion. We considered two denoising strategies: removal of structured noise sources by independent component analysis (ICA) of the control-label image timeseries; and averaging the repetitions of the control-label images prior to model fitting. Modeling bolus dispersion improved estimation precision and impacted parameter values, but these effects strongly depended on whether repetitions were averaged before model fitting. In general, repetition averaging improved model fitting but adversely affected parameter values, particularly CBF and aCBV near arterial locations in patients. This suggests that using all repetitions allows better noise estimation at the earlier delays. In contrast, ICA denoising improved model fitting and estimation precision while leaving parameter values unaffected. Our results support the use of ICA denoising to improve model fitting to multi-delay ASL and suggest that using all control-label repetitions improves the estimation of macrovascular signal contributions and hence perfusion quantification near arterial locations. This is important when modeling flow dispersion in cerebrovascular pathology.

Inference of microbial covariation networks using copula models with mixture margins.

Quantification of microbial covariations from 16S rRNA and metagenomic sequencing data is difficult due to their sparse nature. In this article, we propose using copula models with mixed zero-beta margins for the estimation of taxon-taxon covariations using data of normalized microbial relative abundances. Copulas allow for separate modeling of the dependence structure from the margins, marginal covariate adjustment, and uncertainty measurement. Our method shows that a two-stage maximum-likelihood approach provides accurate estimation of model parameters. A corresponding two-stage likelihood ratio test for the dependence parameter is derived and is used for constructing covariation networks. Simulation studies show that the test is valid, robust, and more powerful than tests based upon Pearson's and rank correlations. Furthermore, we demonstrate that our method can be used to build biologically meaningful microbial networks based on a dataset from the American Gut Project. R package for implementation is available at https://github.com/rebeccadeek/CoMiCoN.

Computational issues in parameter estimation for hidden Markov models with template model builder

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach.

Pseudo-Bayesian Small-Area Estimation

Abstract In sample surveys, a subpopulation is referred to as a “small area” or “small domain” if it does not have a large enough sample that alone will yield an adequately accurate estimate of a characteristic. In small-area estimation, the sample size from various subpopulations is often too small to accurately estimate its mean, and so one borrows strength from similar subpopulations through an appropriate model based on relevant covariates. The empirical best linear unbiased prediction (EBLUP) method has been the dominant frequentist model-based approach in small-area estimation. This method relies on estimation of model parameters based on the marginal distribution of the data. As an alternative to this method, the observed best prediction (OBP) method estimates the parameters by minimizing an objective function that is implied by the total mean squared prediction error. We use this objective function in the Fay–Herriot model to construct a pseudo-posterior distribution for the model parameters under nearly noninformative priors for them. Data analysis and simulation show that the pseudo-Bayesian estimators (PBEs) compete favorably with the OBPs and EBLUPs. The PBE estimates are robust to mean misspecification and have good frequentist properties. Being Bayesian by construction, they automatically avoid negative estimates of standard errors, enjoy a dual justification, and provide an attractive alternative to practitioners.

A practical guide for the generation of model-based virtual clinical trials

Mathematical modeling has made significant contributions to drug design, development, and optimization. Virtual clinical trials that integrate mathematical models to explore patient heterogeneity and its impact on a variety of therapeutic questions have recently risen in popularity. Here, we outline best practices for creating virtual patients from mathematical models to ultimately implement and execute a virtual clinical trial. In this practical guide, we discuss and provide examples of model design, parameter estimation, parameter sensitivity, model identifiability, and virtual patient cohort creation. Our goal is to help researchers adopt these approaches to further the use of virtual population-based analysis and virtual clinical trials.

Parameter estimation of solar PV models with artificial humming bird optimization algorithm using various objective functions

Parameter estimation of solar PV models with artificial humming bird optimization algorithm using various objective functions

Approximate Bayesian computation for the natural history of breast cancer, with application to data from a Milan cohort study.

We explore models for the natural history of breast cancer, where the main events of interest are the start of asymptomatic detectability of the disease (through screening) and the time of symptomatic detection (through symptoms). We develop several parametric specifications based on a cure rate structure, and present the results of the analysis of data collected as part of a motivating study from Milan. Participants in the study were part of a regional breast cancer screening program, and their ten-year trajectories were obtained from administrative data available from the Italian national health care system. We first present a tractable model for which we develop the likelihood contributions of the observed trajectories and perform maximum likelihood inference on the latent process. Likelihood based inference is not feasible for more flexible models, and we implement approximate Bayesian computation (ABC) for inference. Issues that arise from the use of ABC for model choice and parameter estimation are discussed, including the problem of choosing appropriate summary statistics. The estimated parameters of the underlying disease process allow for the study of the effect of different examination schedules (age range and frequency of screening examinations) on a population of asymptomatic subjects.

Genetic least square estimation approach to wind power curve modelling and wind power prediction

Wind power curve (WPC) is an important index of wind turbines, and it plays an important role in wind power prediction and condition monitoring of wind turbines. Motivated by model parameter estimation of logistic function in WPC modelling, aimed at the problem of selecting initial value of model parameter estimation and local optimum result, based on the combination of genetic algorithm and least square estimation method, a genetic least square estimation (GLSE) method of parameter estimation is proposed, and the global optimum estimation result can be obtained. Six evaluation indices including the root mean square error, the coefficient of determination R2, the mean absolute error, the mean absolute percentage error, the improved Akaike information criterion and the Bayesian information criterion are used to select the optimal power curve model in the different candidate models, and avoid the model’s over-fitting. Finally, to predict the annual energy production and output power of wind turbines, a two-component Weibull mixture distribution wind speed model and five-parameter logistic function power curve model are applied in a wind farm of Jiangsu Province, China. The results show that the GLSE approach proposed in this paper is feasible and effective in WPC modelling and wind power prediction, which can improve the accuracy of model parameter estimation, and five-parameter logistic function can be preferred compared with high-order polynomial and four-parameter logistic function when the fitting accuracy is close.

Online estimation of lithium-ion battery equivalent circuit model parameters and state of charge using time-domain assisted decoupled recursive least squares technique

Online estimation of lithium-ion battery equivalent circuit model parameters and state of charge using time-domain assisted decoupled recursive least squares technique

In Situ Estimation of Erosion Model Parameters Using an Advection‐Diffusion Model and Bayesian Inversion

AbstractWe describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Markov Chain Monte Carlo sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters.

Bayesian optimal sensor placement for parameter estimation under modeling and input uncertainties

A Bayesian optimal sensor placement (OSP) framework for parameter estimation in nonlinear structural dynamics models is proposed, based on maximizing a utility function built from appropriate measures of information contained in the input–output response time history data. The information gain is quantified using Kullback–Leibler divergence (KL-div) between the prior and posterior distribution of the model parameters. The design variables may include the type and location of sensors. Asymptotic approximations, valid for large number of data, provide valuable insight into the measure of information. Robustness to uncertainties in nuisance (non-updatable) parameters associated with modeling and excitation uncertainties is considered by maximizing the expected information gain over all possible values of the nuisance parameters. In particular, the framework handles the case where the excitation time history is measured by installed sensors but remains unknown at the experimental design phase. Introducing stochastic excitation models, the expected information gain is taken over the large number of uncertain parameters used to model the random variability in the input time histories. Monte Carlo or sparse grid methods estimate the multidimensional probability integrals arising in the formulation. Heuristic algorithms are used to solve the optimization problem. The effectiveness of the method is demonstrated for a multi-degree of freedom (DOF) spring–mass chain system with restoring elements that exhibit hysteretic nonlinearities.

Analysis of Factors Influencing the Population Growth Rate in West Sumatra Using Geographically Weighted Logistic Regression

The model of Geographically Weighted Logistic Regression (GWLR) was the development of a model of logistic regression that was implemented to data in spatial. GWLR model parameter estimation was carried out at each location for observation using spatial weighting. The research purposes was to reveal the GWLR model on the dichotomous data of the Population Growth Rate (PGR) indicator in each Districts/Cities in West Sumatra in 2020 and learn more factors that influence the probability that the population growth rate will increase in 19 Districts/Cities in West Sumatra in 2020. The parameters estimation of the GWLR model uses the Maximum Likelihood Estimation (MLE) method. Spatial weighting for parameter estimation is determined using the Fixed Gaussian Kernel weighting function and determining the optimal bandwidth using Akaike's Information Citerion (AIC) criteria. The variable of response that is categorical in this study is the rate of population growth in each districts/cities in West Sumatra in 2020 and the predictor variables are the couples number of childbearing age, the live births number, the in-migration number, and the out-migration number. The reseacrh result obtained from research were that the GWLR model is better than the logistic regression model and 4 groups of Districts/Cities are formed based on factors that affect the increase in population growth rate.

SPECIFICATION ANALYSIS OF STRUCTURAL CREDIT RISK MODEL WITH STOCHASTIC VOLATILITY

In this research, we conduct specification analysis of structural credit risk models with stochastic volatility using term structure of Credit Default Swap (CDS) spreads and equity volatility form high-frequency return data. We also test five representatives of structural credit risk models using samples of 93 single name CDS contracts from January 2010 -2022. The model we consider are; the standard Merton(1974) model, the Black & Cox (1976) model with flat barrier, the Longstaff and Schwartz(1995)model with stochastic interest rates, the Collin- Dufresne and Goldstein (2001) model with stationary leverage, and the double exponential jump diffusion model used in Huang & Huang(2003). Our study provides consistent econometric estimation of the pricing model parameters and specification tests based on the joint behavior of time-series asset dynamics and cross-sectional pricing errors. Our empirical tests reject strongly the standard Merton (1974) model, the Black and Cox (1976) with flat barrier model, the Longstaff, Schwartz (1995) model with stochastic interest rates. The double exponential jump-diffusion barrier model used in (Huang and Huang, 2003) improves significantly over the five models. The best model is the stationary leverage model of Collin-Dufresne and Goldstein (2001), which we cannot reject at 0.5 level of significance in our sample firm. However, our empirical results document the inability of the existing structural models to capture the dynamic behavior of CDS spreads and equity volatility, especially for high investment grade names derivatives. These points to a potential role of time-varying asset volatility, a feature that is missing in the standard structural models.

Recent Applications of System Identification Techniques at IPEV

This paper presents an overview of the system identification techniques developed and applied at the Flight Test and Research Institute during the last decade. System identification techniques have been used extensively to obtain aerodynamic models for a flight-test simulator, which was developed in house and specifically tailored for flight-test instruction and preparation for actual test flights. The methods applied were mostly the output error for data compatibility check and equation error in the time domain for model structure selection and parameter estimation. The most relevant applications are summarized in this paper, including identification of a high angle of attack model with compressibility effects for a jet trainer; estimation of drag polars at high subsonic regime for a jet fighter; identification of aerodynamic model in real-time for a propeller-driven fighter; application of flight-path reconstruction techniques to spin tests, in order to correct errors in the air data sensors; and identification of power effects on the longitudinal stability of a propeller-driven trainer. The examples show that system identification has become crucial to 1) obtain accurate aerodynamic models for training in the flight-test simulator and 2) develop more efficient flight-test techniques.

Filter inference: A scalable nonlinear mixed effects inference approach for snapshot time series data.

Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.

Joint assimilation of satellite soil moisture and streamflow data for the hydrological application of a two-dimensional shallow water model

Data assimilation (DA) in physically-based hydrodynamic models is conditioned by the difference in temporal and spatial scales of the observed data and the resolution of the model itself. In order to use remote sensing data in small-scale hydrodynamic modelling, it is necessary to explore innovative DA methods that can lead to a more plausible representation of the spatial variability of the parameters and processes involved. In the present study, satellite-derived soil moisture and in situ-observed streamflow data were jointly assimilated into a high-resolution hydrological-hydrodynamic model based on the Iber software, using the Tempered Particle Filter (TPF) for the dual estimation of model state variables and parameters. Twelve storm events occurring in a 199 km2 catchment located in NW Spain were used for testing the proposed approach. A 3-step procedure was followed: (1) sensitivity analysis of the model parameters; (2) joint assimilation of soil moisture and discharge data to estimate correlations between observations and model parameters; (3) joint assimilation of soil moisture and discharge data using an initial set of particles and parameter standard deviations derived from prior information. The numerical model correctly reproduces the observed data, with an average Nash-Sutcliffe efficiency (NSE) value of 0.74 over the 12 events when the prior information is used. The approach described is shown to be most efficient with storm events that produce isolated peak discharges.

Efficient estimation of groundwater contaminant source and hydraulic conductivity by an ILUES framework combining GAN and CNN

In the inverse estimation of groundwater model parameters (e.g., contaminant source parameters and hydraulic conductivity fields), data assimilation is the most commonly used method for solving the inverse problem. However, data assimilation requires iterative calculation, which tends to increase the computational costs. This is particularly problematic when dealing with high-dimensional problems. In this study, we propose a hybrid inversion framework, which combines a generative adversarial network (GAN) and a convolutional neural network (CNN) for groundwater model parameter estimation. The GAN is equipped with gradient penalties (WGAN-GP) to achieve fast characterization of high-dimensional aquifer structures with low-dimensional vectors (200 dimensions). Meanwhile, this study proposes an enhanced convolutional neural network (OANW), which introduces two-layer weights near the contamination source to achieve an effective surrogate of the process-based groundwater model. Moreover, an iterative local update ensemble smoother (ILUES) is applied for simultaneous identification of the contaminant source parameters and hydraulic conductivity fields in the inversion stage. The results demonstrate that by integrating WGAN-GP and OANW, the ILUES framework accurately characterizes the aquifer parameters and significantly improves the efficiency of the computational process.