Parameter Estimation Research Articles

Arterial input function estimation compensating for inflow and partial voluming in dynamic contrast-enhanced MRI.

Both inflow and the partial volume effect (PVE) are sources of error when measuring the arterial input function (AIF) in dynamic contrast-enhanced (DCE) MRI. This is relevant, as errors in the AIF can propagate into pharmacokinetic parameter estimations from the DCE data. A method was introduced for flow correction by estimating and compensating the number of the perceived pulse of spins during inflow. We hypothesized that the PVE has an impact on concentration-time curves similar to inflow. Therefore, we aimed to study the efficiency of this method to compensate for both effects simultaneously. We first simulated an AIF with different levels of inflow and PVE contamination. The peak, full width at half-maximum (FWHM), and area under curve (AUC) of the reconstructed AIFs were compared with the true (simulated) AIF. In clinical data, the PVE was included in AIFs artificially by averaging the signal in voxels surrounding a manually selected point in an artery. Subsequently, the artificial partial volume AIFs were corrected and compared with the AIF from the selected point. Additionally, corrected AIFs from the internal carotid artery (ICA), the middle cerebral artery (MCA), and the venous output function (VOF) estimated from the superior sagittal sinus (SSS) were compared. As such, we aimed to investigate the effectiveness of the correction method with different levels of inflow and PVE in clinical data. The simulation data demonstrated that the corrected AIFs had only marginal bias in peak value, FWHM, and AUC. Also, the algorithm yielded highly correlated reconstructed curves over increasingly larger neighbourhoods surrounding selected arterial points in clinical data. Furthermore, AIFs measured from the ICA and MCA produced similar peak height and FWHM, whereas a significantly larger peak and lower FWHM was found compared with the VOF. Our findings indicate that the proposed method has high potential to compensate for PVE and inflow simultaneously. The corrected AIFs could thereby provide a stable input source for DCE analysis.

Extended fiducial inference: toward an automated process of statistical inference

Abstract While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set—‘inferring the uncertainty of model parameters on the basis of observations’—has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. Extended Fiducial inference involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. Extended Fiducial inference also provides an innovative framework for semisupervised learning.

Interferometric image reconstruction using closure invariants and Machine Learning

Abstract Interferometric closure invariants encode calibration-independent details of an object’s morphology. Excepting simple cases, a direct backward transformation from closure invariants to morphologies is not well established. We demonstrate using simple Machine Learning models that closure invariants can aid in morphological classification and parameter estimation. We consider six phenomenologically parametrised morphologies: point-like, uniform circular disc, crescent, dual disc, crescent with elliptical accretion disc, and crescent with double jet lobes. Using logistic regression (LR), multi-layer perceptron (MLP), and random forest models on closure invariants obtained from a sparsely covered aperture, we find that all methods except LR can classify morphologies with ≳80 per cent accuracy, which improves with greater aperture coverage. Separately from the classification problem, given an independently confirmed class, we estimate parameters of uniform circular disc, crescent, and dual disc morphologies using simple MLP models, and parametrically reconstruct images. The estimated parameters and images correspond well with inputs, but the accuracy worsens when degeneracies between parameters are present. This independent approach to interferometric imaging under challenging observing conditions such as that faced by the Event Horizon Telescope and Very Long Baseline Interferometry in general can complement other methods in robustly constraining an object’s morphology.

Leveraging Item Parameter Drift to Assess Transfer Effects in Vocabulary Learning

ABSTRACT Longitudinal models typically emphasize between-person predictors of change but ignore how growth varies within persons because each person contributes only one data point at each time. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift over time. While traditionally viewed as a nuisance under the label of “item parameter drift” (IPD), IPD may be of substantive interest if it reflects how learning manifests on different items or subscales at different rates. In this study, we apply the Explanatory Item Response Model to assess IPD in a causal inference context. Simulation results show that when IPD is not accounted for, both parameter estimates and standard errors can be affected. We illustrate with an empirical application to the persistence of transfer effects from a content literacy intervention , revealing how researchers can leverage IPD to achieve a more fine-grained understanding of how vocabulary learning develops over time.

Developing Theoretical Models for Atherosclerotic Lesions: A Methodological Approach Using Interdisciplinary Insights

Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques.

Impact of waning immunity against SARS-CoV-2 severity exacerbated by vaccine hesitancy.

The SARS-CoV-2 pandemic has generated a considerable number of infections and associated morbidity and mortality across the world. Recovery from these infections, combined with the onset of large-scale vaccination, have led to rapidly-changing population-level immunological landscapes. In turn, these complexities have highlighted a number of important unknowns related to the breadth and strength of immunity following recovery or vaccination. Using simple mathematical models, we investigate the medium-term impacts of waning immunity against severe disease on immuno-epidemiological dynamics. We find that uncertainties in the duration of severity-blocking immunity (imparted by either infection or vaccination) can lead to a large range of medium-term population-level outcomes (i.e. infection characteristics and immune landscapes). Furthermore, we show that epidemiological dynamics are sensitive to the strength and duration of underlying host immune responses; this implies that determining infection levels from hospitalizations requires accurate estimates of these immune parameters. More durable vaccines both reduce these uncertainties and alleviate the burden of SARS-CoV-2 in pessimistic outcomes. However, heterogeneity in vaccine uptake drastically changes immune landscapes toward larger fractions of individuals with waned severity-blocking immunity. In particular, if hesitancy is substantial, more robust vaccines have almost no effects on population-level immuno-epidemiology, even if vaccination rates are compensatorily high among vaccine-adopters. This pessimistic scenario for vaccination heterogeneity arises because those few individuals that are vaccine-adopters are so readily re-vaccinated that the duration of vaccinal immunity has no appreciable consequences on their immune status. Furthermore, we find that this effect is heightened if vaccine-hesitants have increased transmissibility (e.g. due to riskier behavior). Overall, our results illustrate the necessity to characterize both transmission-blocking and severity-blocking immune time scales. Our findings also underline the importance of developing robust next-generation vaccines with equitable mass vaccine deployment.

A review of inverse problems for generalized elastic media: formulations, experiments, synthesis

AbstractStarting from the seminal works of Toupin, Mindlin and Germain, a wide class of generalized elastic models have been proposed via the principle of virtual work, by postulating expressions of the elastic energy enriched by additional kinematic descriptors or by higher gradients of the placement. More recently, such models have been adopted to describe phenomena which are not consistent with the Cauchy-Born continuum, namely the size dependence of apparent elastic moduli observed for micro and nano-objects, wave dispersion, optical modes and band gaps in the dynamics of heterogeneous media. For those structures the mechanical response is affected by surface effects which are predominant with respect to the bulk, and the scale of the external actions interferes with the characteristic size of the heterogeneities. Generalized continua are very often referred to as media with microstructure although a rigorous deduction is lacking between the specific microstructural features and the constitutive equations. While in the forward modelling predictions of the observations are provided, the actual observations at multiple scales can be used inversely to integrate some lack of information about the model. In this review paper, generalized continua are investigated from the standpoint of inverse problems, focusing onto three topics, tightly connected and located at the border between multiscale modelling and the experimental assessment, namely: (i) parameter identification of generalized elastic models, including asymptotic methods and homogenization strategies; (ii) design of non-conventional tests, possibly integrated with full field measurements and advanced modelling; (iii) the synthesis of meta-materials, namely the identification of the microstructures which fit a target behaviour at the macroscale. The scientific literature on generalized elastic media, with the focus on the higher gradient models, is fathomed in search of questions and methods which are typical of inverse problems theory and issues related to parameter estimation, providing hints and perspectives for future research.

Flexible Modeling of Nonstationary Extremal Dependence using Spatially-Fused LASSO and Ridge Penalties

Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Parametric max-stable processes (MSPs) are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make inference feasible. However, this assumption is unrealistic for data observed over a large or complex domain. We develop a computationally-efficient method for estimating extremal dependence using a globally nonstationary but locally-stationary MSP construction, with the spatial domain divided into a fine grid of subregions, each with its own dependence parameters. We use LASSO (L 1) or ridge (L 2) penalties to obtain spatially-smooth parameter estimates. We then develop a novel data-driven algorithm to merge homogeneous neighboring subregions. The algorithm facilitates model parsimony and interpretability. To make our model suitable for high-dimensional data, we exploit a pairwise likelihood to perform inference and discuss its computational and statistical efficiency. We apply our proposed method to model monthly maximum temperature data at over 1400 sites in Nepal and the surrounding Himalayan and sub-Himalayan regions; we show significant improvements in model fit compared to a stationary model. Furthermore, we demonstrate that the estimated merged partition is interpretable from a geographic perspective and leads to better model diagnostics by adequately reducing the number of parameters.

Simultaneous whole-liver water and mapping with isotropic resolution during free-breathing.

To develop and validate a data acquisition scheme combined with a motion-resolved reconstruction and dictionary-matching-based parameter estimation to enable free-breathing isotropic resolution self-navigated whole-liver simultaneous water-specific ( ) and ( ) mapping for the characterization of diffuse and oncological liver diseases. The proposed data acquisition consists of a magnetization preparation pulse and a two-echo gradient echo readout with a radial stack-of-stars trajectory, repeated with different preparations to achieve different and contrasts in a fixed acquisition time of 6 min. Regularized reconstruction was performed using self-navigation to account for motion during the free-breathing acquisition, followed by water-fat separation. Bloch simulations of the sequence were applied to optimize the sequence timing for insensitivity at 3 T, to correct for relaxation-induced blurring, and to map and using a dictionary. The proposed method was validated on a water-fat phantom with varying relaxation properties and in 10 volunteers against imaging and spectroscopy reference values. The performance and robustness of the proposed method were evaluated in five patients with abdominal pathologies. Simulations demonstrate good insensitivity of the proposed method in measuring and values. The proposed method produces co-registered and maps with a good agreement with reference methods (phantom: ; ). The proposed and mapping exhibits good repeatability and can be robustly performed in patients with pathologies. The proposed method allows whole-liver and quantification with high accuracy at isotropic resolution in a fixed acquisition time during free-breathing.

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

ROBUST GEOGRAPHICALLY WEIGHTED REGRESSION WITH LEAST ABSOLUTE DEVIATION (LAD) ESTIMATION AND M-ESTIMATION ON GRDP OF WEST JAVA PROVINCE

Geographically Weighted Regression (GWR) is an analytical method for data that contains spatial heterogeneity effects. However, parameter estimation in the GWR model has a weakness, namely it is prone to outliers and can cause the parameter estimation to be biased. This can be overcome by the Robust Geographically Weighted Regression (RGWR) method which is more robust against the presence of outliers. This method is suitable for Gross Regional Domestic Product (GRDP) data in West Java Province, which contains outliers and also has spatial effects. The data used in this study are secondary data obtained from the Central Statistics Agency (BPS) of West Java Province. The purpose of this study is to compare the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation (LAD) Estimation and M-estimation and also to find out the factors that affect the Gross Regional Domestic Product (GRDP) in West Java Province in 2021 based on the model resulting from. Selection of the best model is seen based on the value of the coefficient of determination (R2) and Mean Squared of Error (MSE). The research results show that the Robust Geographically Weighted Regression (RGWR) method with M-estimation is much more effective in estimating the distribution of GRDP in West Java Province in 2021, seen from the larger coefficient of determination and the smaller Mean Square Error (MSE). The variables that have a significant influence on GRDP in West Java Province in 2021 are the variables of foreign investment and local income.

Improving monitoring network design to detect leaks at hazardous facilities: Lessons from a CO2 storage site

Exploring the challenges posed by uncertainties in numerical modeling for hazardous material storage, this study introduces methodologies to improve monitoring networks for detecting subsurface leakages. The proposed approaches were applied to the Korea CO2 Storage Environmental Management (K-COSEM) test site, undergoing calibration, validation and uncertainty analysis through hydraulic and controlled-CO2 release tests. The calibration phase involved inter-well tracer and multi-well pumping tests, leveraging the Parameter ESTimation (PEST) model to determine the aquifer flow and solute transport properties of the K-COSEM site. To tackle uncertainties with limited observation data, we adopted Latin Hypercube simulation. Our uncertainty analysis confirmed model accuracy in simulating observed CO2 breakthrough curves. We also explored a probabilistic method to identify the environmental change point (EnCP) through correlation analysis with the distance from the CO2 injection well, revealing a linear trend and pinpointed potential preferential flow pathways by assessing detection probabilities. Evaluating CO2 detection capabilities was crucial for optimizing monitoring well placement, highlighting strategic well selection based on detection probabilities. This study advances managing uncertainties in hydrogeological modeling, underscoring the importance of sophisticated models in designing monitoring networks for hazardous leak detection in complex subsurface conditions.

Analysis of Xgamma distribution using adaptive Type-I progressively censored competing risks data with applications

This paper considers the competing risks model with two causes of death to analyze time-to-event data for a group of male mice exposed to three hundred roentgen radiation for 5–6 weeks. The analysis is based on the assumption that the parent distribution is the Xgamma distribution and the data are gathered using an adaptive Type-I progressively censored sample. Two estimation approaches are considered to complete the analysis: maximum likelihood and Bayesian methods. Besides acquiring the estimations of the model parameters, the estimations of the reliability and failure rate are also discussed. Both point and interval estimates using both estimation approaches are studied. In Bayesian estimations, the squared error loss function is used and the Markov Chain Monte Carlo technique is proposed to get samples from the joint posterior distribution. The various methods are compared using simulation studies to compare their performance. The mentioned radiation data set is investigated and the analysis showed the suitability of the competing risks model with Xgamma distribution to analyze the data and to estimate the reliability metrics.

An inverse identification method for automatic estimation of heat source model parameters for laser directed energy deposition

An inverse identification method for automatic estimation of heat source model parameters for laser directed energy deposition

Asymptotic normality of local linear functional regression estimator based upon censored data

This article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0 < α < 1 . To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided.

ScaDA: A novel statistical method for differential analysis of single-cell chromatin accessibility sequencing data.

Single-cell ATAC-seq sequencing data (scATAC-seq) has been widely used to investigate chromatin accessibility on the single-cell level. One important application of scATAC-seq data analysis is differential chromatin accessibility (DA) analysis. However, the data characteristics of scATAC-seq such as excessive zeros and large variability of chromatin accessibility across cells impose a unique challenge for DA analysis. Existing statistical methods focus on detecting the mean difference of the chromatin accessible regions while overlooking the distribution difference. Motivated by real data exploration that distribution difference exists among cell types, we introduce a novel composite statistical test named "scaDA", which is based on zero-inflated negative binomial model (ZINB), for performing differential distribution analysis of chromatin accessibility by jointly testing the abundance, prevalence and dispersion simultaneously. Benefiting from both dispersion shrinkage and iterative refinement of mean and prevalence parameter estimates, scaDA demonstrates its superiority to both ZINB-based likelihood ratio tests and published methods by achieving the highest power and best FDR control in a comprehensive simulation study. In addition to demonstrating the highest power in three real sc-multiome data analyses, scaDA successfully identifies differentially accessible regions in microglia from sc-multiome data for an Alzheimer's disease (AD) study that are most enriched in GO terms related to neurogenesis and the clinical phenotype of AD, and AD-associated GWAS SNPs.

Agreement and Consistency of Absolute and Relative Corticospinal Stimulus-Response Curves for Upper, Lower, and Axial Musculature in Healthy Adults.

To assess the agreement and consistency of absolute and relative stimulus-response curve (SRC) parameter estimates for upper extremity, lower extremity, and axial muscles. Thirty (15 W, age: 27.0 ± 6.3 y, height: 171.9 ± 8.9 cm, weight: 80.2 ± 19.3 kg) healthy adults completed absolute (5% to 100% stimulator output) and relative (65% to 160% motor threshold) SRCs of the first dorsal interosseous, vastus lateralis, and rectus abdominis during submaximal isometric contractions. Mean motor-evoked potential amplitudes were fit with nonlinear regression to derive MEPmax, V50, and slope. Absolute agreement and consistency were assessed with ICCs, Cronbachs alphas, and Bland-Altman plots. Independent t-tests were used to examine differences in motor threshold, physical activity, strength, and muscle activity among participants with valid and invalid SRC parameters. Absolute and relative SRCs displayed good agreement and consistency for MEPmax and V50 but not slope. Motor thresholds were lower among participants with valid absolute SRCs for the rectus abdominis and vastus lateralis. Motor threshold, physical activity, strength, and muscle activity did not differ among those with valid and invalid parameters for all relative SRCs and absolute SRCs for the first dorsal interosseous. Absolute and relative SRCs produce similar MEPmax and V50 estimates in the first dorsal interosseous, vastus lateralis, and rectus abdominis. The validity of absolute and relative SRC results may differ depending on individual characteristics and tested muscles.

Improved Quality Parameter Estimation of Photovoltaic System Models based on SAO Algorithm

Improved Quality Parameter Estimation of Photovoltaic System Models based on SAO Algorithm

A multi-tier methodology for the estimation of individual-specific parameters of DEB models

Intraspecific variability plays a key role in modeling population dynamics and ecological interactions. It is also a fundamental issue for agriculture, livestock production, and aquaculture. Dynamic Energy Budget (DEB) theory is a metabolic theory that can provide insights for these applications, as it can accurately predict the response of an organism to changes in environmental conditions. However, DEB model parameters are typically estimated for the species using mean trait values, neglecting individual differences. With advancing data collection technologies, there is a growing need to leverage individual data to calibrate DEB models. In this paper, we propose a multi-tier methodology for estimating individual-specific DEB parameters based on techniques and principles of the standard DEB estimation procedure. Individual data is often not sufficiently complete, therefore we compliment it available data on organisms of the same species. To avoid estimation bias, we employ a hierarchical tier structure. Data is categorized into tiers, depending on how general it is. In each tier, only a subset of the parameters is estimated depending on available data. The estimation proceeds in a top-down approach, starting with the most general tier and culminating in the individual tier. Values obtained in previously estimated tiers are used as pseudo-data to anchor the parameter estimation. In this way, we obtain biologically sensible individual parameter estimates in an efficient manner. As a case study, we apply our methodology to a dataset that contains weight and feed intake measurements for 52 individuals of the Mertolenga cattle breed from two performance trials. We conclude that variability in the surface-specific maximum assimilation rate and the digestion efficiency is needed to accurately model the individual data. Furthermore, the analysis of tier parameters and individual parameter distributions uncovers differences in the diets fed to the animals.

Genetic divergence and truncation and simultaneous selection in inbred families (S1) of elephant grass for bioenergetic purposes via mixed models

The State University of North Fluminense Darcy Ribeiro (UENF) has been developing for fifteen years a breeding program that aims at the development of new cultivars of elephant grass due to its high potential and the low availability of cultivars developed by genetic breeding programs that meet the needs of producers in the State of Rio de Janeiro. In this sense, inbred families were also obtained as a way of fixing potential alleles for traits related to production, as the inbreeding process apparently does not strongly affect elephant grass in aspects related to inbreeding depression. This study aimed to estimate genetic diversity, variance components and prediction of genotypic values in 11 (S1) elephant grass families, and perform the truncation and simultaneous selection of traits using the selection index, by mixed models. The experimental design consisted of randomized blocks with 11 (S1) families, three replications, and six plants per plot. For variables dry matter production, percentage of dry matter, plant height, stem diameter, number of tillers and leaf blade width, was performed the estimation of genetic parameters and selection of the best genotypes based selection index using mixed model. The descriptors were subjected to correlation analysis, distance matrices were generated by the Mahalanobis method, and individuals were grouped by the UPGMA method. In the selection via mixed models (REML/BLUP), families 6, 11, 8, 1, 3, 7, and 9 contributed most of the genotypes selected for the evaluated traits, indicating their high potential to generate superior genotype. The selection indices via mixed models indicated that the multiplicative index presented a greater selection gain.The phenotypic correlations showed the possibility of performing an indirect selection from six evaluated traits.The genotypes were separated into 18 groups by the Mahalanobis distance, allowing the observation of a wide genetic diversity. The most divergent and productive genotypes were self-fertilized to obtain the second generation (S2), continuing the development program.