Robust Parameter Estimation Research Articles

An improved parameter estimation of HFM signals based on IRLS linear fitting of extracted group delay

To address the issue of robust parameter estimation of hyperbolic frequency modulated (HFM) signals under low signal-to-noise ratios (SNRs), an improved algorithm based on iteratively reweighted least squares (IRLS) linear fitting of extracted group delay is proposed. The algorithm includes three main steps. First, a novel method for estimating the frequency distribution range (FDR) of an HFM signal is presented, which involves analyzing the transient features of the amplitude spectrum (AS). Second, the spectrum phase (SP) is unwrapped in the estimated FDR to extract the group delay (GD) of the HFM signal. Last, parameter estimation of the HFM signal is achieved by fitting the GD, which is a linear function of the reciprocal of the frequency, using the IRLS linear fitting method. The simulation results have shown that for SNR ≥ -14 dB, the normalized root mean square errors (NRMSEs) estimated by the proposed estimator are 1.5 dB lower than those estimated by the spectrum phase unwrapping (SPU) estimator, including the starting frequency and period slope. Furthermore, experimental results based on sea trial data have also verified the validity and feasibility of the proposed estimator.

On robust estimation of the Gauss–Markov model with a singular covariance matrix

Although the robust parameter estimation has been intensively investigated in statistics and measurement science, no one considers the robust estimation within the Gauss–Markov model (GMM) with a singular covariance matrix. In this contribution, a method of finding the robust solutions in the singular linear model has been suggested based on the generalization of the unified least-squares objective function. The equivalent cofactor matrix in the robust objective function is established by the bifactor strategy based on the IGG III function. The robustness of the proposed robust algorithms is demonstrated with the examples of geodetic coordinates transformation and the free network deformation analysis.

Performance Comparison of Meta-Heuristics Applied to Optimal Signal Design for Parameter Identification.

This paper presents a comparative study that explores the performance of various meta-heuristics employed for Optimal Signal Design, specifically focusing on estimating parameters in nonlinear systems. The study introduces the Robust Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (rSOESGOPE) methodology, which is originally derived from the well-known Particle Swarm Optimization (PSO) algorithm. Through a real-life case study involving an Autonomous Surface Vessel (ASV) equipped with three Degrees of Freedom (DoFs) and an aerial holonomic propulsion system, the effectiveness of different meta-heuristics is thoroughly evaluated. By conducting an in-depth analysis and comparison of the obtained results from the diverse meta-heuristics, this study offers valuable insights for selecting the most suitable optimization technique for parameter estimation in nonlinear systems. Researchers and experimental tests in the field can benefit from the comprehensive examination of these techniques, aiding them in making informed decisions about the optimal approach for optimizing parameter estimation in nonlinear systems.

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver. Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations and in vivo data of a patient suffering from hepatic tumor lesions. Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% for k trans, 22% ± 6% for v e and 89% ± 5% for v p than the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For the in vivo data, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p < 0.0001). Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

A demonstration of the value of recapture data for informing moult phenology models for avian species with imperfect moult data

The Underhill–Zucchini model has revolutionised the study of moult in the context of birds’ annual cycles, but, as for all statistical models, inferences are vulnerable to violations of model assumptions. In particular, the standard Underhill–Zucchini models for moult phenology are vulnerable to imperfect moult data arising, for example, from non-random sampling and/or the misclassification of non-moulting birds. Similarly, inference is challenging for species with dispersed moult periods (population-level moult extending beyond an annual cycle). Using ringing data from Cape Weavers Ploceus capensis and SAFRING data for Cape Sugarbirds Promerops cafer, we demonstrate how recent extensions to the Underhill–Zucchini framework can help the robust estimation of moult parameters in such situations, in particular when within-season recapture data is available.

Analysis of one-shot device testing data under logistic-exponential lifetime distribution with an application to SEER gallbladder cancer data

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER gallbladder cancer data. The two-parameter logistic-exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method genetic algorithm.

An EM algorithm for estimating the parameters of the skew generalized t-normal distribution with application to robust finite mixture modeling

The present article describes an EM-type algorithm for estimation of the skew generalized t-normal (SGTN) distribution. The family of SGTN distributions can provide certain types of flexibility such as heavy tails and high kurtosis. The complexity of the SGTN distribution is traced to the ratio of the t density and distribution function of a normal distribution in the likelihood equations. To cope with this problem, we develop a feasible ECME algorithm for computing maximum likelihood estimates of model parameters via a selection mechanism. The proposed approach provides a robust parameter estimation method for the finite mixture model. Standard errors for the parameter estimates can be obtained via a general information-based method. Experimental results on simulated data and one real data example demonstrate the efficacy and usefulness of the proposed methodology.

On the use of tsunami-source data for high-resolution fault imaging of offshore earthquakes

The source imaging for offshore earthquakes using terrestrial geodetic data has a limited estimation performance due to the low data resolution. One approach to overcome this limitation is the use of seafloor geodetic data. In this study, we focus on tsunami-source data, which is the spatial distribution of vertical crustal displacements above the source area and can be derived from tsunami waveform records. We evaluate how the use of this spatial seafloor geodetic data improves the estimation of a rectangular fault model. Here, the fault model of the 2016 off-Fukushima earthquake in Japan, which was a shallow intraplate earthquake (Mw 7.0), was estimated by three inversions: terrestrial Global Navigation Satellite System (GNSS) data only, tsunami-source data only, and a combination of the GNSS data and tsunami-source data. A Bayesian inversion approach was used to understand the distribution of the estimated fault parameters and their relationship. The results indicated that the terrestrial GNSS data have a low resolution for the analysis of the offshore earthquake, which resulted in a biased solution with large uncertainty. Conversely, the use of tsunami-source data significantly improved the resolution and reliability of source imaging and reduced the dependency among fault parameters. These results suggested that the high-spatial-resolution information of tsunami source is a powerful tool in source imaging of offshore shallow earthquakes. Moreover, the combined use of the two different geodetic data leads to a more robust estimation of fault parameters. We believe that the use of tsunami-source data is useful, not only for the post hoc source analysis, but also for estimating an earthquake rupture area just after a large earthquake, where GNSS data are currently used.Graphical

Considerations on effort, precision and accuracy for long-term monitoring of African lions (Panthera leo), when using Bayesian spatial explicit capture-recapture models, in fenced protected areas.

Intensive management is frequently required in fenced wildlife areas to reduce deleterious effects of isolation. Decisions on how best to manage such wildlife are ideally informed by regular and reliable estimates of spatiotemporal fluctuations in population size and structure. However, even in small, fenced areas, it is difficult and costly to regularly monitor key species using advanced methods. This is particularly the case for large carnivores, which typically occur at low density and are elusive yet are central to management decision-making due to their top-down effects in ecosystems and attracting tourism. In this study, we aimed to provide robust estimates of population parameters for African lions (Panthera leo) and use the data to inform a resource-efficient long-term monitoring programme. To achieve this, we used unstructured spatial sampling to collect data on lions in Pilanesberg National Park, a small (~550 km2) fenced protected area in South Africa. We used Bayesian spatial capture-recapture models to estimate density, abundance, sex ratio and home range size of lions over the age of 1 year. Finally, to provide guidance on resource requirements for regular monitoring, we rarefied our empirical data set incrementally and analysed the subsets. Lion density was estimated to be 8.8 per 100 km2 (posterior SD = 0.6), which was lower than anticipated by park management. Sex ratio was estimated close to parity (0.9♀:1♂), consistent with emerging evidence in fenced lion populations, yet discordant with unfenced populations, which are usually ~2♀:1♂ in healthy, source populations. Our rarefied data suggest that a minimum of 4000 km search effort needs to be invested in future monitoring to obtain accurate and precise estimates, while assuming similar detection rates. This study demonstrates an important utility of Bayesian spatial explicit capture-recapture methods for obtaining robust estimates of lion densities and other important parameters in fence-protected areas to inform decision-making.

Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems.

We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system's global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth's climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.

A simple modeling framework for prediction in the human glucose-insulin system.

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

A Bayesian Framework for Estimating Weibull Distribution Parameters: Applications in Finance, Insurance, and Natural Disaster Analysis

This research presents a Bayesian framework for parameter estimation in the two-parameter Weibull distribution, with applications in finance and investment data analysis. The Weibull distribution is widely used for modeling stock pricing movements and making uncertain predictions in financial datasets. The proposed Bayesian approach assumes a gamma prior distribution for the scale parameter, with a known shape parameter. A simulation study using simulated financial data compares the Bayesian method with maximum likelihood estimators in terms of accuracy, error accumulation, and computational time across various sample sizes and parameter values. Results indicate the Bayesian approach performs similarly to maximum likelihood for small samples, while demonstrating computational efficiency for larger financial datasets. The proposed Bayesian model's application to simulated financial data showcases its practical relevance in real-world scenarios. This Bayesian framework offers a valuable tool for handling uncertainty and making informed decisions in financial data analysis, providing robust parameter estimation and uncertainty quantification in finance and investment domains.

Robust explicit estimators using the power-weighted repeated medians

This paper consists of two parts. The first part of the paper is to propose an explicit robust estimation method for the regression coefficients in simple linear regression based on the power-weighted repeated medians technique that has a tuning constant for dealing with the trade-offs between efficiency and robustness. We then investigate the lower and upper bounds of the finite-sample breakdown point of the proposed method. The second part of the paper is to show that based on the linearization of the cumulative distribution function, the proposed method can be applied to obtain robust parameter estimators for the Weibull and Birnbaum-Saunders distributions that are commonly used in both reliability and survival analysis. Numerical studies demonstrate that the proposed method performs well in a manner that is approximately comparable with the ordinary least squares method, whereas it is far superior in the presence of data contamination that occurs frequently in practice.

AdpPL: An adaptive phase linking-based distributed scatterer interferometry with emphasis on interferometric pair selection optimization and adaptive regularization

The distributed scatterer (DS) interferometry (DSI) technology is a powerful geodetic tool for measuring the deformation over abundant land covers. As a state-of-the-art DSI technology, the SqueeSAR approach considered the statistical behavior of the decorrelated DS and proposed the phase triangulation algorithm (PTA) as the pioneering implementation of the phase linking (PL) theory to estimate the equivalent single-reference (ESR) phases from all interferometric combinations. Subsequently, many advanced estimators of the systematic phase series have been introduced. Interestingly, this paper has demonstrated that the utilization of weakly coherent interferometric pairs is not conducive to the theoretical accuracy improvement of the PL theory in case of the fast decorrelation scenario. Moreover, the reduction of the small baseline scales will worsen the positive definite degree of the time series coherence matrix, which makes the ill-posed solution problem more serious. Therefore, this paper proposes a novel adaptive PL (AdpPL) method integrating the following two innovations for mapping surface deformation: 1) in terms of the interferometric pair selection optimization (IPSO), this paper performs the homogeneity measure-based IPSO (HoMeIPSO) method to remove the lowly coherent candidate subset progressively and select the moderate interferometric pairs adaptively; 2) in terms of the robust parameter estimation, an adaptive regularization (AdpReg) approach suggests selecting an optimal damping factor according to the minimum fitting error of all interferogram observables. Experimental results demonstrate that the proposed method can restore the systematic phase series more clearly and detect the deformation area with spatially highly dynamic characteristics successfully.

RegCloser: a robust regression approach to closing genome gaps

BackgroundClosing gaps in draft genomes leads to more complete and continuous genome assemblies. The ubiquitous genomic repeats are challenges to the existing gap-closing methods, based on either the k-mer representation by the de Bruijn graph or the overlap-layout-consensus paradigm. Besides, chimeric reads will cause erroneous k-mers in the former and false overlaps of reads in the latter.ResultsWe propose a novel local assembly approach to gap closing, called RegCloser. It represents read coordinates and their overlaps respectively by parameters and observations in a linear regression model. The optimal overlap is searched only in the restricted range consistent with insert sizes. Under this linear regression framework, the local DNA assembly becomes a robust parameter estimation problem. We solved the problem by a customized robust regression procedure that resists the influence of false overlaps by optimizing a convex global Huber loss function. The global optimum is obtained by iteratively solving the sparse system of linear equations. On both simulated and real datasets, RegCloser outperformed other popular methods in accurately resolving the copy number of tandem repeats, and achieved superior completeness and contiguity. Applying RegCloser to a plateau zokor draft genome that had been improved by long reads further increased contig N50 to 3-fold long. We also tested the robust regression approach on layout generation of long reads.ConclusionsRegCloser is a competitive gap-closing tool. The software is available at https://github.com/csh3/RegCloser. The robust regression approach has a prospect to be incorporated into the layout module of long read assemblers.

Robust Bayesian Estimation of EEG-Based Brain Causality Networks.

The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows. We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters. The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy. Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.

Adaptive elevator kinematics optimization based dual response algorithm for determining proper levels in plaster milling process parameters

This study proposes a novel hybrid approach, called Adaptive/Elevator Kinematics Optimization algorithm based on dual response algorithm (A/EKO-DRA), to enhance the robust parameters estimation and design of the plaster milling process. The A/EKO-DRA method reduces variability while maintaining the desired output target, thereby minimizing the impact of variance on the expected stucco combined water. The performance of the A/EKO-DRA is compared with conventional processes through numerical examples and simulations. The results show that the A/EKO-DRA method has the lowest mean absolute errors among other methods in terms of parameter estimation, and it achieves the response mean of 5.927 percent, which meets the target value of 5.9 percent for industrial enclosures, with much reduction in the response variance. Overall, the A/EKO-DRA method is a promising approach for optimizing the plaster milling process parameters.

Joint estimation of survival and dispersal effectively corrects the permanent emigration bias in mark-recapture analyses

Robust and reliable estimates of demographic parameters are essential to understand population dynamics. Natal dispersal is a common process in monitored populations and can cause underestimations of survival and dispersal due to permanent emigration. Here, we present a multistate Bayesian capture-mark-recapture approach based on a joint estimation of natal dispersal kernel and detection probabilities to address biases in survival, dispersal, and related demographic parameters when dispersal information is limited. We implement this approach to long-term data of a threatened population: the Bonelli’s eagle in Catalonia (SW Europe). To assess the method’s performance, we compare demographic estimates structured by sex, age, and breeding status in cases of limited versus large data scales, with those of classical models where dispersal and detection probabilities are estimated separately. Results show substantial corrections of demographic estimates. Natal dispersal and permanent emigration probabilities were larger in females, and consequently, female non-breeder survival showed larger differences between separate and joint estimation models. Moreover, our results suggest that estimates are sensitive to the choice of the dispersal kernel, fat-tailed kernels providing larger values in cases of data limitation. This study provides a general multistate framework to model demographic parameters while correcting permanent emigration biases caused by natal dispersal.

A federated learning differential privacy algorithm for non-Gaussian heterogeneous data

Multi-center heterogeneous data are a hot topic in federated learning. The data of clients and centers do not follow a normal distribution, posing significant challenges to learning. Based on the assumption that the client data have a multivariate skewed normal distribution, we improve the DP-Fed-mv-PPCA model. We use a Bayesian framework to construct prior distributions of local parameters and use expectation maximization and pseudo-Newton algorithms to obtain robust parameter estimates. Then, the clipping algorithm and differential privacy algorithm are used to solve the problem in which the model parameters do not have a display solution and achieve privacy guarantee. Furthermore, we verified the effectiveness of our model using synthetic and actual data from the Internet of vehicles.

Population dynamics and harvest management of eastern mallards

AbstractManaging sustainable harvest of wildlife populations requires regular collection of demographic data and robust estimates of demographic parameters. Estimates can then be used to develop a harvest strategy to guide decision‐making. Mallards (Anas platyrhynchos) are an important species in the Atlantic Flyway for many users and they exhibited exponential growth in the eastern United States between the 1970s and 1990s. Since then, estimates of mallard abundance have declined 16%, prompting the Atlantic Flyway Council and United States Fish and Wildlife Service to implement more restrictive hunting regulations and develop a new harvest strategy predicated on an updated population model. Our primary objective was to develop an integrated population model (IPM) for use in an eastern mallard harvest management strategy. We developed an IPM using annual estimates of breeding abundance, 2‐season banding and recovery data, and hunter‐harvest data from 1998 to 2018. When developing the model, we used novel model selection methods to test various forms of a sub‐model for survival including estimating the degree of harvest additivity and any age‐specific trends. The top survival sub‐model included a negative annual trend on juvenile survival. The IPM posterior estimates for population abundance tracked closely with the observed estimates and estimates of mean annual population growth rate ranged from 0.88 to 1.08. Our population model provided increased precision in abundance estimates compared to survey methods for use in an updated harvest strategy. The IPM posterior estimates of survival rates were relatively stable for adult cohorts, and annual growth rate was positively correlated with the female age ratio, a measure of reproduction. Either or both of those demographic parameters, juvenile survival or reproduction, could be a target for management efforts to address the population decline. The resulting demographic parameters provided information on the equilibrium population size and can be used in an adaptive harvest strategy for mallards in eastern North America.