Stable Parameter Estimates Research Articles

Results from the further development of CGI inversion on simulation and field data systems

AbstractA new series expansion-based method, the Combined Geoelectric Weighted Inversion (CGWI) procedure is presented and tested by using synthetic and in-field measured datasets. The method is an improved version of the Combined Geoelectric Inversion (CGI) robustified by involving Cauchy-Steiner weights in an Iteratively Reweighted Least Squares technique. The new procedure is compared to the Fourier series expansion-based 1.5D and the CGI methods as well as to the broadly applied RES2DINV inversion procedure. The field measurements are performed during stone exploration in an active quarry on the south-western slopes of the Mátra mountains, in northern Hungary. It is shown that the CGWI method gives stable and robust parameter estimation with acceptable accuracy. The comparison with other inversion methods is based on data distances, estimation errors and correlation parameters calculated on the base of the parameter correlation matrix.

Estimating Missing values in Randomized Complete Block design using EM Algorithm

This research explores the application of the Expectation-Maximization (EM) algorithm to address missing data challenges in Randomized Complete Block Designs (RCBD). Traditional imputation methods often introduce biases, prompting the need for a robust solution. The EM algorithm, anchored in a mixed effects model, iteratively estimates missing values, demonstrating its efficacy in a practical RCBD scenario. Through 15 iterations, the algorithm converges to stable parameter estimates. Root Mean Square Error (RMSE) and bias calculations validate the accuracy of imputations. This study establishes the EM algorithm as a powerful tool for enhancing the integrity of analyses in RCBD experiments with missing data.. KEYWORDS :Expectation-Maximization Algorithm, Randomized complete block design (RCBD), Mixed effects model, Root mean square error (RMSE), Machine learning approaches.

Latent Variable Forests for Latent Variable Score Estimation.

We develop a latent variable forest (LV Forest) algorithm for the estimation of latent variable scores with one or more latent variables. LV Forest estimates unbiased latent variable scores based on confirmatory factor analysis (CFA) models with ordinal and/or numerical response variables. Through parametric model restrictions paired with a nonparametric tree-based machine learning approach, LV Forest estimates latent variable scores using models that are unbiased with respect to relevant subgroups in the population. This way, estimated latent variable scores are interpretable with respect to systematic influences of covariates without being biased by these variables. By building a tree ensemble, LV Forest takes parameter heterogeneity in latent variable modeling into account to capture subgroups with both good model fit and stable parameter estimates. We apply LV Forest to simulated data with heterogeneous model parameters as well as to real large-scale survey data. We show that LV Forest improves the accuracy of score estimation if parameter heterogeneity is present.

A 2PLM-RANK multidimensional forced-choice model and its fast estimation algorithm.

High-stakes non-cognitive tests frequently employ forced-choice (FC) scales to deter faking. To mitigate the issue of score ipsativity derived, many scoring models have been devised. Among them, the multi-unidimensional pairwise preference (MUPP) framework is a highly flexible and commonly used framework. However, the original MUPP model was developed for unfolding response process and can only handle paired comparisons. The present study proposes the 2PLM-RANK as a generalization of the MUPP model to accommodate dominance RANK format response. In addition, an improved stochastic EM (iStEM) algorithm is devised for more stable and efficient parameter estimation. Simulation results generally supported the efficiency and utility of the new algorithm in estimating the 2PLM-RANK when applied to both triplets and tetrads across various conditions. An empirical illustration with responses to a 24-dimensional personality test further supported the practicality of the proposed model. To further aid in the application of the new model, a user-friendly R package is also provided.

A compensation method of carrier magnetic interference under pathological conditions for geomagnetic navigation

Geomagnetic navigation has become a hot spot in current research because of its characteristics of passiveness and good concealment. However, the magnetic interference from various ferromagnetic substances, electronic equipment, etc., of the carrier will be superimposed on the geomagnetic field, causing magnetometer measurement errors, thus affecting navigation accuracy. In practice, due to the limited maneuverability of the carrier, sufficient geomagnetic observation data cannot be obtained, resulting in the observation equation used for carrier magnetic interference compensation to be seriously pathological. To achieve the compensation of carrier magnetic interference, this paper proposes the total least squares method based on the ridge regression using the L curve to solve ridge parameters. This method can effectively suppress the measurement noise that exists on both sides of the observation equation, and is suitable for alleviating the pathological effects of carrier magnetic interference compensation. Experimental results show that the compensated magnetometer measurement error is reduced to 3% of the carrier magnetic interference by using the method proposed in this paper, which obtains more stable and accurate parameter estimates.

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

In recent years, advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections, prevention, and control. Unlike other system parameters, i.e., incubation and recovery rates, the case reporting rate, Ψ, and the time-dependent effective reproduction number, Re(t), are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way. In this study, we propose a novel iteratively-regularized trust-region optimization algorithm, combined with SuSvIuIvRD compartmental model, for stable reconstruction of Ψ and Re(t) from reported epidemic data on vaccination percentages, incidence cases, and daily deaths. The innovative regularization procedure exploits (and takes full advantage of) a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator. The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9, 2021, to November 25, 2021. Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12% and 37%, with most states being in the range from 15% to 25%. This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of ”silent spreaders” and the limitations of testing.

A nested semiparametric method for case‐control study with missingness

AbstractWe propose a nested semiparametric model to analyze a case‐control study where genuine case status is missing for some individuals. The concept of a noncase is introduced to allow for the imputation of the missing genuine cases. The odds ratio parameter of the genuine cases compared to controls is of interest. The imputation procedure predicts the probability of being a genuine case compared to a noncase semiparametrically in a dimension reduction fashion. This procedure is flexible, and vastly generalizes the existing methods. We establish the root‐ asymptotic normality of the odds ratio parameter estimator. Our method yields stable odds ratio parameter estimation owing to the application of an efficient semiparametric sufficient dimension reduction estimator. We conduct finite sample numerical simulations to illustrate the performance of our approach, and apply it to a dilated cardiomyopathy study.

Automatized localization of induced geothermal seismicity using robust time-domain array processing

The surveillance of geothermal seismicity is typically conducted using seismic networks, deployed around the power plants and subject to noise conditions in often highly urbanized areas. In contrast, seismic arrays can be situated at greater distances and allow monitoring of different power plants from one central location, less affected by noise interference. However, the effectiveness of arrays to monitor geothermal reservoirs is not well investigated and the increased distance to the source coincides with a decreased accuracy of the earthquake localizations. It is therefore essential to establish robust data processing and to obtain precise estimates of the location uncertainties. Here, we use time-domain array data processing and solve for the full 3-D slowness vector using robust linear regression. The approach implements a Biweight M-estimator, which yields stable parameter estimates and is well suited for real-time applications. We compare its performance to conventional least squares regression and frequency wavenumber analysis. Additionally, we implement a statistical approach based on changepoint analysis to automatically identify P- and S-wave arrivals within the recorded waveforms. The method can be seen as a simplification of autoregressive prediction. The estimated onsets facilitate reliable calculations of epicentral distances. We assess the performance of our methodology by comparison to network localizations for 77 induced earthquakes from the Landau and Insheim deep-geothermal reservoirs, situated in Rhineland-Palatinate, Germany. Our results demonstrate that we can differentiate earthquakes originating from both reservoirs and successfully localize the majority of events within the magnitude range of ML -0.2 to ML 1.3. The discrepancy between the two localization methods is mostly less than 1 km, which falls within the statistical errors. However, a few localizations deviate significantly, which can be attributed to poor observations during the winter of 2021/2022.

COMPARISON OF ROBUST ESTIMATION ON MULTIPLE REGRESSION MODEL

This study aimed to compare the robustness of the OLS method with a robust regression model on data that had outliers. The methods used on the robust regression model were M-estimation, MM-estimation, and S-estimation. The step taken was to check the characteristics of the data against outliers. Furthermore, the data were modeled with and without outliers using the OLS method and the M-, MM-, and S-estimations. The results were very different between the data with and without the outlier models in the OLS method. It was reflected in the intercept and standard error variables generated from the models. Meanwhile, the regression model with the M-, MM-, and S-estimations was quite stable and able to withstand the presence of outliers. Based on the three estimations that were robust against the outliers, the MM-estimation was the best candidate because, in addition to having a stable intercept parameter estimation, it also had the smallest standard error, which was 61.9 in the resulting model.

A method for LFM signal parameter estimation based on MWC system and STFT-DPT

A method of estimating linear frequency modulation (LFM) signal parameters using compressed sampling (CS) data of a Modulated Wideband Converter (MWC) system is proposed. The short-time Fourier transform algorithm is used to analyze the CS signal of the MWC system, and the obtained CS signal frequency will present a form of multi-segment distribution. By intercepting the CS signal corresponding to the first segment frequency and analyzing the intercepted segment signal with discrete polynomial transform and Rife algorithm, the chirp rate and initial frequency estimation of the segment CS signal can be preliminarily estimated. According to the random sequence with cyclic displacement, the spectrum shift relationship between the input signal and the output signal can be calculated. Therefore, the parameter of the original signal can be estimated by using single channel CS data. Then, all channels are analyzed with the same method, and a more stable parameter estimation result can be obtained than the single channel output. Finally, combined with the simulation experiment, the proposed method can be used to estimate the initial frequency and chirp rate of the LFM signal using CS data effectively.

On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation

We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn–Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the identifiability of single and multiple parameters up to certain scaling invariances is established. A regularized equation error approach is proposed for the stable numerical solution of the parameter identification problems, and convergence of the regularized approximations is proven under reasonable assumptions on the data noise. The viability of the theoretical results and the proposed methods is demonstrated in numerical tests.

Spatial modelling of agro-ecologically significant grassland species using the INLA-SPDE approach

The use of spatially referenced data in agricultural systems modelling has grown in recent decades, however, the use of spatial modelling techniques in agricultural science is limited. In this paper, we test an effective and efficient technique for spatially modelling and analysing agricultural data using Bayesian hierarchical spatial models (BHSM). These models utilise analytical approximations and numerical integration called Integrated Nested Laplace Approximations (INLA). We critically analyse and compare the performance of the INLA and INLA-SPDE (Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation) approaches against the more commonly used generalised linear model (glm), by modelling binary geostatistical species presence/absence data for several agro-ecologically significant Australian grassland species. The INLA-SPDE approach showed excellent predictive performance (ROCAUC 0.9271–0.9623) for all species. Further, the glm approach not accounting for spatial autocorrelation had inconsistent parameter estimates (switching between significantly positive and negative) when the dataset was subsetted and modelled at different scales. In contrast, the INLA-SPDE approach which accounted for spatial autocorrelation had stable parameter estimates. Using approaches which explicitly account for spatial autocorrelation, such as INLA-SPDE, improves model predictive performance and may provide a significant advantage for researchers by reducing the potential for Type I or false-positive errors in inferences about the significance of predictors.

Synthetic-to-real domain adaptation with deep learning for fitting the intravoxel incoherent motion model of diffusion-weighted imaging.

Intravoxel incoherent motion (IVIM) is a type of diffusion-weighted imaging (DWI), and IVIM model parameters (water molecule diffusion rate Dt , pseudo-diffusion coefficient Dp , and tissue perfusion fraction Fp ) have been widely used in the diagnosis and characterization of malignant lesions. This study proposes a deep-learning model with synthetic-to-real domain adaptation to fit the IVIM model parameters of DWI. Ninety-eight consecutive patients diagnosed with hepatocellular carcinoma between January 2017 and September 2020 were included in the study, and routine IVIM-DWI serial examinations were performed using a 3.0T magnetic resonance imaging system in preoperative MR imaging. The proposed method is mainly composed of two modules: a convolutional neural network-based IVIM model fitting network to map b-value images to the IVIM parameter maps and a domain discriminator to improve the accuracy of the IVIM parameter maps in the real data. The proposed method was compared with previously reported fitting methods, including the nonlinear least squares (NLSs), IVIM-NEToptim , and self-supervised U-network methods. The IVIM parameter-fitting performance was assessed by measuring the DWI reconstruction performance and testing the robustness of each method against noise using noise-corrupted data. The DWI reconstruction performance demonstrates that the proposed method has better reconstruction accuracy for DWI with a low signal-to-noise ratio, which implies that the proposed method improves the fitting accuracy of the IVIM parameters. Noise-corrupt experiments show that the proposed method is more robust against noise-corrupted signals. With the proposed method, no outliers were found in Dt , and outliers were reduced for Fp in the abnormal regions (proposed method: 1.85%; NLS: 5.90%; IVIM-NEToptim : 6.61%; and self-U-net: 25.36%). Moreover, experiments show that the proposed method has a more stable parameter estimation performance than the existing methods in the absence of real data. IVIM parameters can be estimated using a synthetic-to-real domain-adaptation framework with deep learning, and the proposed method outperforms previously reported methods.

Quantitatively characterizing reflexive responses to pitch perturbations.

Reflexive pitch perturbation experiments are commonly used to investigate the neural mechanisms underlying vocal motor control. In these experiments, the fundamental frequency-the acoustic correlate of pitch-of a speech signal is shifted unexpectedly and played back to the speaker via headphones in near real-time. In response to the shift, speakers increase or decrease their fundamental frequency in the direction opposing the shift so that their perceived pitch is closer to what they intended. The goal of the current work is to develop a quantitative model of responses to reflexive perturbations that can be interpreted in terms of the physiological mechanisms underlying the response and that captures both group-mean data and individual subject responses. A model framework was established that allowed the specification of several models based on Proportional-Integral-Derivative and State-Space/Directions Into Velocities of Articulators (DIVA) model classes. The performance of 19 models was compared in fitting experimental data from two published studies. The models were evaluated in terms of their ability to capture both population-level responses and individual differences in sensorimotor control processes. A three-parameter DIVA model performed best when fitting group-mean data from both studies; this model is equivalent to a single-rate state-space model and a first-order low pass filter model. The same model also provided stable estimates of parameters across samples from individual subject data and performed among the best models to differentiate between subjects. The three parameters correspond to gains in the auditory feedback controller's response to a perceived error, the delay of this response, and the gain of the somatosensory feedback controller's "resistance" to this correction. Excellent fits were also obtained from a four-parameter model with an additional auditory velocity error term; this model was better able to capture multi-component reflexive responses seen in some individual subjects. Our results demonstrate the stereotyped nature of an individual's responses to pitch perturbations. Further, we identified a model that captures population responses to pitch perturbations and characterizes individual differences in a stable manner with parameters that relate to underlying motor control capabilities. Future work will evaluate the model in characterizing responses from individuals with communication disorders.

Hybrid Method for Fitting Nonlinear Height–Diameter Functions

Regression analysis is widely applied in many fields of science to estimate important variables. In general, nonlinear regression is a complex optimization problem and presents intrinsic difficulties in estimating reliable parameters. Nonlinear optimization algorithms commonly require a precise initial estimate to return reasonable estimates. In this work, we introduce a new hybrid algorithm based on the association of a genetic algorithm with the Levenberg–Marquardt method (GALM) to adjust biological nonlinear models without knowledge of initial parameter estimates. The proposed hybrid algorithm was applied to 12 nonlinear models widely used in forest sciences and 12 databases under varying conditions considering classic hypsometric relationships to evaluate the robustness of this new approach. The hybrid method involves two stages; the curve approximation process begins with a genetic algorithm with a modified local search approach. The second stage involves the application of the Levenberg–Marquardt algorithm. The final performance of the hybrid method was evaluated using total fitting for all tested models and databases, confirming the reliability of the proposed algorithm in providing stable parameter estimates. The GA was able to predict the initial parameters, which assisted the LM in converging efficiently. The developed GALM method is effective, and its application is recommended for biological nonlinear analyses.

Learning-Based Distortion Correction and Feature Detection for High Precision and Robust Camera Calibration

Camera calibration is a crucial technique which significantly influences the performance of many robotic systems. Robustness and high precision have always been the pursuit of diverse calibration methods. State-of-the-art calibration techniques, however, still suffer from inexact corner detection, radial lens distortion and unstable parameter estimation. Therefore, in this paper, we improve the precision and robustness of calibration by widening these bottlenecks. In particular, effective distortion correction is performed by a learning-based method. Then, accurate sub-pixel feature location is achieved by the combination of robust learning detection, exact refinement and complete post-processing. To obtain stable parameter estimation, an image-level RANSAC-based calibration procedure is proposed. Ultimately, we assemble these methods into a novel and practical calibration framework. Compared with state-of-art methods, experiment results on both real and synthetic datasets under noise, bad lighting and distortion manifest the better robustness and higher precision of the proposed framework.

Elastic impedance inversion for stress indicator in weakly orthorhombic media

Hydraulic fracturing is a crucial technology for improving permeability and production of shale reservoirs. The precise estimation of the stress distribution has a significant guidance for optimizing the placement of hydraulic fracturing. Assuming that the shale gas reservoir is a weakly anisotropic medium with orthorhombic symmetry, a new stress indicator parameterized by rock mechanical parameters and fracture parameters is firstly presented to predict the differential horizontal stress ratio in shale gas reservoirs. Then, we derive a novel simplified P-to-P reflection coefficient and a logarithmic normalized elastic impedance (EI) as a function of Young's modulus, Poisson's ratio, Thomsen's WA parameter δb and normal excess compliance ZN. Next, we adopt azimuthal EI inversion in a Bayesian framework to estimate rock mechanics parameters and fracture parameters directly on a fractured shale gas field seismic data. Finally, the stress indicator is determined by utilizing four inverted parameters. Synthetic examples demonstrate that the proposed approach produces stable parameter estimates even with moderate noise, verifying the feasibility and effectiveness of the method. Test on a field data set illustrates that the inversion results can be reasonably estimated, and the stress indicator derived by the inversion accords with the geomechanics result. Compared with the previous method, the new stress indicator has a higher capability to describe stress characteristics in the shale reservoir. We conclude that this stress evaluation procedure can provide reliable guidance for well location deployment and hydraulic fracturing reformation.

Multi-Platform LiDAR for Non-Destructive Individual Aboveground Biomass Estimation for Changbai Larch (Larix olgensis Henry) Using a Hierarchical Bayesian Approach

Individual-tree aboveground biomass (AGB) estimation is vital for precision forestry and still worth exploring using multi-platform LiDAR data for high accuracy and efficiency. Based on the unmanned aerial vehicle and terrestrial LiDAR data, this study explores the feasibility of the individual tree AGB estimation of Changbai larch (Larix olgensis Henry) of eight plots from three different regions in Maoershan Forest Farm of Heilongjiang, China, using nonlinear mixed effect model with hierarchical Bayesian approach. Results showed that the fused LiDAR data estimated the individual tree parameters (i.e., diameter at breast height (DBH), tree height (TH), and crown projection area (CPA)) with high accuracies (all R2 > 0.9 and relatively low RMSE and rRMSE) using region-based hierarchical cross-section analysis (RHCSA) algorithm. Considering regions as random variables, the nonlinear mixed-effects AGB model with three predictor variables (i.e., DBH, TH, and CPA) performed better than its corresponding nonlinear model. In addition, the hierarchical Bayesian method provided better model-fitting performances and more stable parameter estimates than the classical method (i.e., nonlinear mixed-effect model), especially for small sample sizes (e.g., <50). This methodology (i.e., multi-platform LiDAR data and the hierarchical Bayesian method) provides a potential solution for non-destructive individual-tree AGB modeling with small sample size and high accuracy in both forestry and remote sensing communities.

On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission

Abstract A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed. The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number. The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA. The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases.

Locally active globally stable dynamical systems: Theory, learning, and experiments

State-dependent dynamical systems (DSs) offer adaptivity, reactivity, and robustness to perturbations in motion planning and physical human–robot interaction tasks. Learning DS-based motion plans from non-linear reference trajectories is an active research area in robotics. Most approaches focus on learning DSs that can (i) accurately mimic the demonstrated motion, while (ii) ensuring convergence to the target, i.e., they are globally asymptotically (or exponentially) stable. When subject to perturbations, a compliant robot guided with a DS will continue following the next integral curves of the DS towards the target. If the task requires the robot to track a specific reference trajectory, this approach will fail. To alleviate this shortcoming, we propose the locally active globally stable DS (LAGS-DS), a novel DS formulation that provides both global convergence and stiffness-like symmetric attraction behaviors around a reference trajectory in regions of the state space where trajectory tracking is important. This allows for a unified approach towards motion and impedance encoding in a single DS-based motion model, i.e., stiffness is embedded in the DS. To learn LAGS-DS from demonstrations we propose a learning strategy based on Bayesian non-parametric Gaussian mixture models, Gaussian processes, and a sequence of constrained optimization problems that ensure estimation of stable DS parameters via Lyapunov theory. We experimentally validated LAGS-DS on writing tasks with a KUKA LWR 4+ arm and on navigation and co-manipulation tasks with iCub humanoid robots.