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Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data. [ABSTRACT FROM AUTHOR]

Real-time monitoring and quantitative measurement of molecular exchange between different microdomains are useful to characterize the local dynamics in porous media and biomedical applications of magnetic resonance. Diffusion exchange spectroscopy (DEXSY) is a noninvasive technique for such measurements. However, its application is largely limited by the involved long acquisition time and complex parameter estimation. In this study, we introduce a physics-guided deep neural network that accelerates DEXSY acquisition in a data-driven manner. The proposed method combines sampling pattern optimization and physical parameter estimation into a unified framework. Comprehensive simulations and experiments based on a two-site exchange system are conducted to demonstrate this new sampling optimization method in terms of accuracy, repeatability, and efficiency. This general framework can be adapted for other molecular exchange magnetic resonance measurements. [ABSTRACT FROM AUTHOR]

Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion‐based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand‐new Markov chain Monte Carlo algorithm coupled with an effective adjust‐bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion‐based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness. [ABSTRACT FROM AUTHOR]

Objective. Modern medical imaging plays a vital role in clinical practice, enabling non-invasive visualization of anatomical structures. Dynamic contrast enhancement (DCE) imaging is a technique that uses contrast agents to visualize blood flow dynamics in a time-resolved manner. It can be applied to different modalities, such as computed tomography (CT) and electrical impedance tomography (EIT). This study aims to develop a common theoretical and practical hemodynamic extraction basis for DCE modelling across modalities, based on the gamma-variate function. Approach. The study introduces a framework to generate time-intensity curves for multiple DCE imaging modalities from user-defined hemodynamic parameters. Thus, extensive datasets were simulated for both DCE-CT and EIT, representing different hemodynamic scenarios. Additionally, gamma-variate extensions to account for several physiological effects were detailed in a modality-agnostic manner, and three corresponding fitting strategies, namely nonlinear, linear, and a novel hybrid approach, were implemented and compared on the basis of accuracy of parameter estimation, first pass reconstruction, speed of computation, and failure rate. Main results. As a result, we found the linear method to be the most modality-dependent, exhibiting the greatest bias, variance and failure rates, although remaining the fastest alternative. The hybrid method at least matches the state-of-the-art nonlinear method's accuracy, while improving its robustness and speed by 10 times. Significance. Our research suggests that the hybrid method may bring noteworthy accuracy and efficiency improvements in handling the high-dimensionality of DCE imaging in general, being a step towards real-time processing. Moreover, our generative model presents a potential asset to produce benchmarking and data augmentation datasets across modalities. [ABSTRACT FROM AUTHOR]

The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Gas lift is one of the most common artificial lift methods used to enhance oil well production. Oscillations in production flow rate, known as casing heading instability, are a common issue in gas lift systems. Designing an automatic control system is a recommended solution to prevent casing heading and improve the performance of a gas lift system. One of the major challenges in designing such a control system is the uncertainty of the system parameters and state variables. In this paper, the analytical gas lift model presented in previous studies was modified to account for the real gas flow in the annulus. Then, a parameter estimator and a state observer were designed using a square root Kalman filter to estimate the uncertain parameter and state variables. The simulation results have shown that the improved model is more reliable. The designed Linear Quadratic Gaussian (LQG) control, along with the estimator and observer, can stabilize the gas lift system under uncertain conditions. The main contribution of this work is the development of an integrated system for controlling and estimating the gas lift system. This system ensures reliable performance even in the presence of changes in wellbore and reservoir conditions. [ABSTRACT FROM AUTHOR]

This paper presents a new method to estimate the parameters of multi-cage models of induction motors using only the information provided by manufacturers available in technical data sheets. The parameters are obtained through the solution of an optimization problem solved through the particle swarm optimization algorithm. We tested and validated the model using models with two, three, four, and five cages in the rotor. Besides, experimental results of 200 induction motors with power ranging from 22 to 90 kW proved that the method provides reliable estimates of the parameters that can correctly reproduce both the dynamic and steady-state behavior of induction motors. The accurate knowledge of the estimated parameters is essential to several control schemes, particularly those based on vector field orientation. [ABSTRACT FROM AUTHOR]

Geostatistical seismic inversion is an important method for establishing high‐resolution reservoir parameter models. There is no accurate representation method for reservoir structural features, and prior information about structural features cannot be incorporated into geostatistical inversion. Based on the assumption of the sparsity of stratigraphic sedimentary features, the same type of structural feature is used to represent the sedimentary pattern of reservoirs within the same facies. Different sparse representation patterns are used to represent the differences in sedimentary patterns between facies. Although changes in depositional environment might result in the multi‐scale characteristics of geological structures for varying sedimentary rhythms, this paper proposes a facies‐constrained geostatistical inversion method based on multi‐scale sparse representation to better accommodate such situation. Using the method of sparse representation combined with wavelet transform, the multi‐scale sedimentary structural features of reservoirs are learned from well‐logging data. Seismic facies and multi‐scale features are used as prior information for geostatistical inversion. Further, the likelihood function is constructed using seismic data to obtain the posterior probability distribution of reservoir parameters. Finally, the accurate inversion result is obtained by using multi‐scale sparse representation as a constraint in the posterior probability distribution of reservoir parameters. Compared with conventional geostatistical methods, this algorithm can better match the structural features of reservoir parameters with varying geological conditions. Field data tests have shown the effectiveness of this method in improving the accuracy and resolution of reservoir parameter structural features. [ABSTRACT FROM AUTHOR]

A current challenge with adaptive controllers is to define efficient tuning methods of the controller parameters. Unlike linear systems, nonlinear systems may need parameters that are continuously tuned at different operating points to provide stability and desired behaviours. This study aims to develop a solution for tuning proportional–integral–derivative (PID) controller parameters as opposed to changing the operating points of a nonlinear system. Most tuning methods calculate parameters according to the system's step or frequency response. However, adaptive controllers have self-tuneable parameters or control rules. The proposed algorithm in this paper contains a controller, an estimator, and a reference model, and uses the system model. Unlike the model reference adaptive control method, the proposed controller has tuneable controller parameters estimated by the extended Kalman–Bucy filter. The filter estimates the controller parameters to make the system perform like the auxiliary ideal reference model to ensure minimum-time consumption. Hence, this study aims to develop an algorithm that will automatically calculate controller parameters for each operating point of the controlled chaotic or nonlinear system to minimize settling time at each operating point. The proposed algorithm is implemented in a unified chaotic system in which the estimator and controller of the system run together. Simulation results confirm the performance of the proposed algorithm. In addition, the simulation results provide strong evidence that the proposed algorithm can be an effective tool for controlling nonlinear or chaotic systems. [ABSTRACT FROM AUTHOR]

Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors of the estimated curve. Centring constraints are often applied by default because they are thought to yield lowest standard errors out of any constraint, but this claim has not been investigated. We show that whether centring constraints are optimal depends on the response distribution and parameterization, and that for natural exponential family responses under the canonical parametrization, centring constraints are optimal only for Gaussian response. [ABSTRACT FROM AUTHOR]

Modelling multivariate survival data is complicated by the complex association structure among the responses. To balance model flexibility and interpretability, we propose a semiparametric copula model to modulate multivariate survival data, with the marginal distributions of the response components described by semiparametric linear transformation models. To conduct inference about the model parameters, we develop a two‐stage maximum likelihood method and a three‐stage pseudo‐likelihood estimation procedure. We investigate the impact of model misspecification on the estimation of covariate effects and identify a scenario in which consistent estimation of the marginal parameters is retained even when the copula model is misspecified. The proposed methods are justified both theoretically and empirically. An application to a real dataset is provided to demonstrate the utility of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we study the problem of parameter estimation for measurement error models by combining the Bayes method with the instrumental variable approach, deriving the posterior distribution of parameters under different priors with known and unknown variance parameters, respectively, and calculating the Bayes estimator (BE) of the parameters under quadratic loss. However, it is difficult to obtain an explicit expression for BE because of the complex multiple integrals involved. Therefore, we adopt the linear Bayes method, which does not specify the form of the prior and avoids these complicated integral calculations, to obtain an expression for the linear Bayes estimator (LBE) for different priors. We prove that this LBE is superior to the two‐stage least squares estimator under the mean squared error matrix criterion. Numerical simulations show that our LBE is very close to the real parameter whether the variance parameters are known or unknown, and it gradually approaches BE as the sample size increases. Our results indicate that this instrumental variable approach is valid for measurement error models. [ABSTRACT FROM AUTHOR]

Zika virus outbreak is creating a global public health hazard due to its increasing prevalence rate and neurological complication in affected individuals. In this work we have developed and studied an ODE compartmental Zika model with non-linear saturated incidence function and three control measures including prevention control from vector bite, treatment control of infected host and vector killing control. Our theoretical analysis shows that the disease free equilibrium is locally as well as globally asymptotically stable when the basic reproduction number is less than unity. The virus is uniformly persistent when the basic reproduction number is greater than unity. An endemic equilibrium point exists and locally stable when the basic reproduction number is greater than unity. The model is validated by fitting the model to real reported data of 2016 Zika outbreak in Puerto Rico and estimated the model parameters. We also have studied the basic reproduction number and effective reproduction number of the outbreak. Sensitivity analysis has been carried out to find most sensitive parameters. The optimal control and efficiency analysis has been done to find the policy of control variables. Lastly, the manuscript is ended by some conclusions. [ABSTRACT FROM AUTHOR]

This article considers the parameter identification problems of stochastic systems which described by the finite impulse response moving average model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The data filtering technique is to use a filter to filter the input and output data of the system disturbed by colored noise so as to improve the identification accuracy. By using the data filtering technique, this article proposes a filtering‐based recursive extended least squares (F‐RELS) algorithm. The convergence analysis indicates that the parameter estimates can converge to their true values. Compared with the recursive extended least squares algorithm, the proposed F‐RELS algorithm can obtain more accurate parameter estimation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Outlier detection is an important aspect of statistical process monitoring (SPM) because outliers affect the performance of control charts. SPM researchers study the negative impact of outliers on control charts for monitoring location parameters. However, there is little research on outlier detection in multivariate charts for monitoring process dispersion. This study aims to investigate the impact of outliers in multivariate control charts for monitoring covariance matrix of a process, and then to recommend techniques for detecting potential outliers present from Phase I samples. We propose a new multivariate dispersion chart that employs the determinant of logarithm of estimated covariance matrix as the monitoring statistic. Through Monte Carlo simulations, the results show how outliers from the first phase affect the overall performance of multivariate charts. The results also demonstrate that the minimum volume ellipsoid (MVE) estimator is effective in reducing the effect of outliers on the proposed control scheme than the other compared estimators. [ABSTRACT FROM AUTHOR]

This paper presents an in‐depth analysis of the exponentiated half‐logistic Weibull (EHLW) distribution, investigating its fundamental statistical properties and exploring parameters estimation using both maximum likelihood and Bayesian approaches. Specifically, our focus centers on the analysis of stress–strength reliability, denoted as R=P(X>Y)$R=P(X>Y)$, where the strength variable X$X$ follows EHLW distribution, and the stress variable Y$Y$ follows either Weibull distribution or the EHLW distribution. The estimation of the parameter R$R$ is discussed in both scenarios, employing both Maximum Likelihood and Bayesian approaches. Furthermore, we calculate that the asymptotic confidence interval, percentile bootstrap interval, and the highest probability density credible interval are obtained for the stress–strength parameter R$R$. In order to assess the efficiency of these estimation techniques, simulation studies are conducted, providing valuable insights into the performance of each estimation approach. Finally, the proposed reliability model is applied to real datasets, highlighting its practical significance. [ABSTRACT FROM AUTHOR]

This study addresses the problem of performance reliability degradation and lifetime prediction in complex systems with high reliability but insufficient information. It comprehensively considers the effects of various uncertainties, such as measurement, cognitive, and stochastic uncertainties, and proposes a generalized normal grey cloud Bayesian Wiener process (GNGCBWP) stochastic degradation model. First, based on the historical degradation information of the system, the interval grey number sequence of the degradation increment is constructed, and the performance degradation path of the system is analyzed to determine the degradation model type. Then, combining the normal grey cloud and Bayesian estimation theory, the relevant definitions and theorems of generalized normal grey cloud Bayesian estimation (GNGCBE) are proposed. Finally, the parameter estimation results obtained using the GNGCBE method are substituted into the grey Wiener process degradation model to dynamically analyze performance reliability degradation and predict the remaining useful life (RUL) in real‐time. And the validity and scientificity of the proposed model is verified through a case study of laser equipment. Moreover, the comparison results of the models indicate that the proposed model has advantages in dynamic analysis of performance reliability degradation and real‐time RUL prediction for highly reliable complex systems with limited or poor degradation information. It can significantly reduce the impact of multiple uncertainties on the analysis results and improve the accuracy and reliability of the final prediction results. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and nonparametric inference. This paper explores inference for a maximum RSS procedure with unequal samples (MRSSU) with multiple dependent failure causes. When the lifetimes of units are characterized by a proposed complementary competing risks model, classical likelihood and Bayesian approaches are discussed for parameters and reliability estimation. Maximum likelihood estimators of model parameters and associated existence and uniqueness are established, and approximate confidence intervals are constructed using asymptotic theory and delta methods. With respect to general flexible priors, Bayesian estimates of interested quantities are also performed and a Monte Carlo sampling algorithm is proposed for complex posterior computation. Additionally, when extra historical information between the competing risks parameters is available, likelihood and Bayesian estimation are also studied under an order restriction case. Different methods are compared based on extensive simulation studies, and another real data example is demonstrated for application propose. [ABSTRACT FROM AUTHOR]

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penalized weighted least squares estimator. The proposed method can be also applied to a model with possible non-zero mean time-dependent additive errors. Asymptotic properties of the proposed estimator are investigated under mild conditions on a weight matrix and the error process. A simulation study demonstrates that the proposed estimation works well in both parameter estimation and selection with time-dependent error. The analysis and comparison with an existing method for head-neck position tracking data show better performance of the proposed method in terms of the variance accounted for. [ABSTRACT FROM AUTHOR]

Modal parameter estimation of a bridge with the vibration responses measured from an instrumented vehicle moving at a controlled speed is an active area of research. It is challenging to determine bridge natural frequencies and their associated mode shapes, as the measured output-only responses of an instrumented vehicle contain the desired dynamic responses of the bridge, along with the other confounding components related to vehicle dynamics, driving frequency component, and dynamics associated with the roughness profile of the road. These bridge responses are often masked by the dynamic responses associated with the vehicle, and road surface profile. Measurement noise components add to the existing problem of separating bridge frequency from various other said components. In this paper, an attempt has been made to extract bridge frequencies and mode shapes through the output-only responses collected from a traversing vehicle and using singular value decomposition (SVD) combined with the Teager-Kaiser energy operator (TKEO). Numerical investigations are made on the proposed SVD-TKEO-based modal identification technique in the presence of measurement noise. Parametric studies are conducted to investigate the influence of vehicle speed and road surface roughness on the quality of the identified bridge modal parameters using the proposed technique Numerical simulations carried out, show that the proposed SVD-TKEO-based algorithm performs well in identifying bridge mode shapes, even with relatively higher vehicle traveling speed, and handles even roughness of the road surface profile reasonably well. Lab-level experimental studies using vehicle bridge interaction setup, are also carried out using the SVD-based modal parameter estimation technique to explore its practical use. [ABSTRACT FROM AUTHOR]

This work provides a Bayesian reinterpretation of model falsification. We show that model falsification can be viewed as an approximate Bayesian computation (ABC) approach when hypotheses (models) are sampled from a prior. To achieve this, we recast model falsifiers as discrepancy metrics and density kernels such that they may be adopted within ABC and generalized ABC (GABC) methods. We call the resulting frameworks model-falsified ABC and model-falsified GABC, respectively. As a result of our reinterpretation, the set of unfalsified models can be shown to be realizations of an approximate posterior. We consider both error- and likelihood-domain model falsification. Model-falsified (G)ABC is used to address two practical types of inverse problems, although with synthetic measurements. The first two problems concern parameter estimation and include applications of ABC to the inference of a statistical model in which the likelihood can be difficult to compute, and the identification of a cubic-quintic dynamical system. The third example involves model selection for the base isolation system of a four-degree-of-freedom base-isolated structure. The performance of model-falsified ABC and GABC is compared with that of Bayesian inference. The results show that model-falsified (G)ABC can be used to solve inverse problems in a computationally efficient manner. The results are also used to compare the various falsifiers in terms of their capability to approximate the posterior and some of its important statistics. Furthermore, we show that model falsifier–based density kernels can be used in kernel regression to infer unknown model parameters and compute structural responses under epistemic uncertainty. [ABSTRACT FROM AUTHOR]

With large volume of passengers boarding and alighting through subway platforms, the stations are getting crowded, resulting in drops in the level of service and safety concerns, especially for subway systems operating at capacity during peak hours. Thus, it is crucial for subway agencies to sense changes in travel demand and adjust their management schemes accordingly. In this paper we propose a statistical approach to estimate dynamic passenger flows with automated data. First, we develop a dynamic logistic model for calculating passenger tap-out times, which can be employed to infer passenger flow characteristics at the aggregate level. In addition, a new passenger-to-train assignment model for any subway route is derived based on the dynamic model. Subsequently, we apply an expectation-maximization algorithm to estimate the model parameters with automated fare collection and automated vehicle location data. Finally, a cross-validation method is employed to validate our approach with data obtained from several routes in Beijing subway system in China. Results of 95% prediction intervals indicate the effectiveness of the models and the proposed estimation methods. • Propose a dynamic logistic model for inferring and predicting subway passenger tap-out times. • Apply an expectation-maximization algorithm for model parameters estimation. • Develop a novel passenger-to-train assignment strategy. • No prior distributions of parameters or additional information required in the proposed methods. • Results show good effectiveness of the models and acceptable accuracy of the prediction methods. [ABSTRACT FROM AUTHOR]

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

Multielectrode electrochemical biosensors promise on-the-spot inspection of target compounds in biofluids, reducing costs in personalized healthcare. However, sensor sensitivity may decrease after each use due to biofouling, where chemical attachments on sensor electrodes curtail sensing signals. Current biofouling characterization techniques rely on time-consuming offline tests and analysis, making them impractical for on-the-spot signal correction. Alternatively, we propose to statistically model and correct the biofouling-induced signal changes. However, in addition to biofouling, the signals are influenced by multiple sources of variation, each with different levels of impact. To effectively characterize and separate biofouling effects from the major sources of variability, we establish a multiresolution functional mixed-effect model based on domain knowledge. A biosensing signal is first decomposed into a smooth trend and local peaks. The smooth trend models the effects of population-level biofluid composition, as well as patient and electrode effects to isolate variability sources. Changes in local peak location and amplitude indicate biofouling. These local peaks are modeled using a sparse subset of high-order functional terms. By modeling the changes of those high-order terms, we can characterize and predict the biofouling between consecutive measurements. We propose a sequential parameter estimation procedure that ensures model identifiability. A nonparametric regression model is developed for biofouling prediction. The proposed strategy is validated through simulation and real case studies, effectively correcting biofouling-affected signals from new patients. [ABSTRACT FROM AUTHOR]

We introduce an alternative closed-form objective function α-ELBO for improved parameter estimation in the Gaussian process ( G P ) based on the Rényi α-divergence. We use a decreasing temperature parameter α to iteratively deform the objective function during optimization. Ultimately, our objective function converges to the exact log-marginal likelihood function of G P. At early optimization stages, α-ELBO can be viewed as a regularizer that smoothes some unwanted critical points. At late stages, α-ELBO recovers the exact log-marginal likelihood function that guides the optimizer to solutions that best explain the observed data. Theoretically, we derive an upper bound of the Rényi divergence under the proposed objective and derive convergence rates for a class of smooth and non-smooth kernels. Case studies on a wide range of real-life engineering applications demonstrate that our proposed objective is a practical alternative that offers improved prediction performance over several state-of-the-art inference techniques. [ABSTRACT FROM AUTHOR]

The immersed tunnel is considered an effective solution for traffic problems across rivers and seas. The sand filling layer, as an important part of immersed tunnel foundation treatments, directly affects segment attitude stability. Due to difficulties in quality control of concealed construction and the complex hydrodynamic environment, the sand filling layer is prone to compaction defects, further leading to changes in segment attitude. However, limited by structural concealment and state complexity, most studies consider the sand filling layer part of the foundation to study its impact on settlement while neglecting its influence on segment attitude. This research proposes an evaluation method for the sand filling layer state based on elastic wave testing and the elastic wave characteristic parameters selected come from analysis of the time domain, frequency domain and time-frequency domain. By classifying the elastic wave characteristic parameters through the K-means clustering method, the relationship between the state of the sand filling layer and the elastic wave characteristic parameters is established. The state of the sand filling layer is divided into dense, incompact, and void. A numerical model is established based on the Guangzhou BI-UT immersed tunnel with incompact and void sand filling layer states to simulate deformation and torsion. The results indicate that the settlement of the tunnel segment is low in the eastern region and high in the western region due to the presence of a less dense sand filling layer, with a maximum differential settlement of 0.04 m. The evaluation method plays a crucial role in guiding the construction of immersed tube tunnels. [ABSTRACT FROM AUTHOR]

This paper conducts a theoretical analysis of ground settlements due to shield tunneling in multi-layered soils which are usually encountered in urban areas. The proposed theoretical solution which is based on the general form of the Mindlin's solution and Loganathan-Poulos formula can comprehensively consider the in-process tunneling parameters including: unbalanced face pressure, shield-soil friction, unbalanced tail grouting pressure, unbalanced secondary grouting pressure, overloading during tunneling and the ground volume loss. The method is verified by comparing with the field data from the Qinghuayuan Tunnel Project in terms of the ground surface settlements along the longitudinal and transverse direction. Due to the local settlement or heave caused by the certain tunneling parameters, the ground surface settlements calculated using current solution along the longitudinal direction presents an irregular S-shaped curve instead of the traditional S-shaped curve. Results also find that the effect of the unbalanced secondary grouting pressure and the overloading during tunneling cannot be ignored. [ABSTRACT FROM AUTHOR]

Due to the growing demand for clean and sustainable energy sources, there has been an increasing interest in solar cells and photovoltaic panels. Nevertheless, determining the right design parameters to achieve the most efficient energy output that aligns with the energy system's needs can be quite challenging. This complexity arises from the intricate models and the inherent inaccuracies in the available information. To tackle this challenge, this paper introduces the adaptive sine–cosine particle swarm optimization algorithm (ASCA-PSO) as a method for estimating the parameters of solar cells and photovoltaic modules. The ASCA-PSO approach combines the strengths of the SCA and PSO algorithms in a two-tier process. In this process, SCA search agents explore the search space, while the PSO search agents leverage the outcomes derived from SCA exploration. This study evaluates the effectiveness of ASCA-PSO in accurately estimating the parameters of single- and double-diode models using data from two commercial solar cells. The findings are compared with those of cutting-edge methods. It is demonstrated that ASCA-PSO can identify global solutions for multifaceted and intricate objective functions. Furthermore, it proves to be a viable option for designing solar cells even in the presence of noise. [ABSTRACT FROM AUTHOR]

Market impact is an important problem faced by large institutional investors and active market participants. In this paper, we rigorously investigate whether price trajectory data from the metaorder increases the efficiency of estimation, from the view of the Fisher information, which is directly related to the asymptotic efficiency of statistical estimation. We show that, for popular market impact models, estimation methods based on partial price trajectory data, especially those containing early trade prices, can outperform established estimation methods (e.g. VWAP-based) asymptotically. We discuss theoretical and empirical implications of such phenomenon, and how they could be readily incorporated into practice. [ABSTRACT FROM AUTHOR]

Electrical tomography sensors have been widely used for pipeline parameter detection and estimation. Before they can be used in formal applications, the sensors must be calibrated using enough labeled data. However, due to the high complexity of actual measuring environments, the calibrated sensors are inaccurate since the labeling data may be uncertain, inconsistent, incomplete, or even invalid. Alternatively, it is always possible to obtain partial data with accurate labels, which can form mandatory constraints to correct errors in other labeling data. In this paper, a semi-supervised fuzzy clustering algorithm is proposed, and the fuzzy membership degree in the algorithm leads to a set of mandatory constraints to correct these inaccurate labels. Experiments in a dredger validate the proposed algorithm in terms of its accuracy and stability. This new fuzzy clustering algorithm can generally decrease the error of labeling data in any sensor calibration process. [ABSTRACT FROM AUTHOR]

The type parameter helps in scattering mechanism analysis and scattering centre identification. However, current approximate solution methods based on spectral estimation are noise‐sensitive and exhibit low accuracy. In this letter, a high‐precision approach for the type parameter based on the alternating direction method of multipliers (ADMM) is proposed. Logarithmic transformation is used to separate the type parameter and the amplitude from the coupling term, and initially obtain the closed‐form solution of the type parameter. Then, the regularization term of l2‐norm is used for denoising. Finally, a joint optimization model based on ADMM is constructed to effectively estimate the type parameter. Simulation results confirm the high accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

Currently, the urgent needs of sustainable mobility and green energy generation are driving governments and researchers to explore innovative energy storage systems. Concurrently, lithium-ion batteries are one of the most extensively employed technologies. The challenges of battery modeling and parameter estimation are crucial for building reliable battery management systems that ensure optimal battery performance. State of charge (SOC) estimation is particularly critical for predicting the available capacity in the battery. Many methods for SOC estimation rely on the knowledge of the open-circuit voltage (OCV) curve. Another significant consideration is understanding how these curves evolve with battery degradation. In the literature, the effect of cycle aging on the OCV is primarily addressed through the look-up tables and correction factors applied to the OCV curve for fresh cells. However, the variation law of the OCV curve as a function of the battery cycling is not well-characterized. Building upon a simple analytical function with five parameters proposed in the prior research to model the OCV as a function of the absolute state of discharge, this study investigates the dependency of these parameters on the moved charge, serving as an indicator of the cycling level. Specifically, the analysis focuses on the impact of cycle aging in the low-, medium-, and high-SOC regions. Three different cycle aging tests were conducted in these SOC intervals, followed by the extensive experimental verification of the proposed model. The results were promising, with mean relative errors lower than 0.2% for the low- and high-SOC cycling regions and 0.34% for the medium-SOC cycling region. Finally, capacity estimation was enabled by the model, achieving relative error values lower than 1% for all the tests. [ABSTRACT FROM AUTHOR]

The electrochemical proton exchange membrane fuel cell (PEMFC) is an electrical generator that utilizes a chemical reaction mechanism to produce electricity, serving as a sustainable and environmentally friendly energy source. To thoroughly analyze and develop the features and performance of a PEMFC, it is essential to use a precise model that incorporates exact parameters to effectively suit the polarization curve. In addition, parameter extraction plays a crucial role in the simulation analysis, evaluation, optimum control, and fault detection of the proton exchange membrane fuel cell (PEMFC) system. Despite the development of many algorithms for parameter extraction in PEMFC, obtaining accurate and trustworthy results rapidly remains a challenge. This study presents a hybridized algorithm, namely differential evolution ameliorated (DEA) for reliably estimating PEMFC model parameters. To evaluate the proposed DEA-based parameter identification, a comparison analysis with previously published methods is conducted using MATLAB/SimulinkTM (R2016b, MathWorks, Natick, MA, USA) in terms of system correctness and convergence process. The proposed DEA algorithm is tested to extract the parameters of two PEMFC models: SR-12 500 W and 250 W. The sum of the squared errors (SSE) between the experimental and the obtained voltage data is defined as an objective function. The simulation results prove that the suggested DEA algorithm is capable of identifying the optimal PEMFC parameters rapidly and accurately in comparison with other optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, single-diode model (SDM) and double-diode model (DDM) parameters of the French RTC solar cell and the Photowatt PWP 201 photovoltaic (PV) module were extracted by combining five metaheuristic algorithms with three simulation current calculation methods (i.e., approximation method, Lambert W method and Newton–Raphson method), respectively. It was found that the parameter-extraction accuracies of the Lambert W (LW) method and the Newton–Raphson (NR) method are always approximately equal and higher than that of the approximation method. The best RMSEs (root mean square error) obtained by using the LW or the NR method on the solar cell and the PV module are 7.72986 × 10−4 and 2.05296 × 10−3 for SDM parameter extraction and 6.93709 × 10−4 and 1.99051 × 10−3 for DDM parameter extraction, respectively. The latter may be the highest parameter-extraction accuracy reported on the solar cell and the PV module so far, which is due to the adoption of more reasonable DDM parameter boundaries. Furthermore, the convergence curves of the LW and the NR method basically coincide, with a convergence speed faster than that of the approximation method. The robustness of a parameter-extraction method is mainly determined by the metaheuristic algorithm, but it is also affected by the simulation current calculation method and the parameter-extraction object. In a word, the approximation method is not suitable for application in PV-model parameter extraction because of incorrect estimation of the simulation current and the RMSE, while the LW and NR methods are suitable for the application for accurately calculating the simulation current and RMSE. In terms of saving computation resources and time, the NR method is superior to the LW method. [ABSTRACT FROM AUTHOR]

Forest structural parameters are crucial for assessing ecological functions and forest quality. To improve the accuracy of estimating these parameters, various approaches based on remote sensing platforms have been employed. Although remote sensing yields high prediction accuracy in uniform, even-aged, simply structured forests, it struggles in complex structures, where accurately predicting forest structural parameters remains a significant challenge. Recent advancements in unmanned aerial vehicle (UAV) photogrammetry have opened new avenues for the accurate estimation of forest structural parameters. However, many studies have relied on a limited set of remote sensing metrics, despite the fact that selecting appropriate metrics as powerful explanatory variables and applying diverse models are essential for achieving high estimation accuracy. In this study, high-resolution RGB imagery from DJI Matrice 300 real-time kinematics was utilized to estimate forest structural parameters in a mixed conifer–broadleaf forest at the University of Tokyo Hokkaido Forest (Hokkaido, Japan). Structural and textual metrics were extracted from canopy height models, and spectral metrics were extracted from orthomosaics. Using random forest and multiple linear regression models, we achieved relatively high estimation accuracy for dominant tree height, mean tree diameter at breast height, basal area, mean stand volume, stem density, and broadleaf ratio. Including a large number of explanatory variables proved advantageous in this complex forest, as its structure is influenced by numerous factors. Our results will aid foresters in predicting forest structural parameters using UAV photogrammetry, thereby contributing to sustainable forest management. [ABSTRACT FROM AUTHOR]

Computational cognitive models have been used extensively to formalize cognitive processes. Model parameters offer a simple way to quantify individual differences in how humans process information. Similarly, model comparison allows researchers to identify which theories, embedded in different models, provide the best accounts of the data. Cognitive modeling uses statistical tools to quantitatively relate models to data that often rely on computing/estimating the likelihood of the data under the model. However, this likelihood is computationally intractable for a substantial number of models. These relevant models may embody reasonable theories of cognition, but are often under-explored due to the limited range of tools available to relate them to data. We contribute to filling this gap in a simple way using artificial neural networks (ANNs) to map data directly onto model identity and parameters, bypassing the likelihood estimation. We test our instantiation of an ANN as a cognitive model fitting tool on classes of cognitive models with strong inter-trial dependencies (such as reinforcement learning models), which offer unique challenges to most methods. We show that we can adequately perform both parameter estimation and model identification using our ANN approach, including for models that cannot be fit using traditional likelihood-based methods. We further discuss our work in the context of the ongoing research leveraging simulation-based approaches to parameter estimation and model identification, and how these approaches broaden the class of cognitive models researchers can quantitatively investigate. Author summary: Computational cognitive models occupy an important position in cognitive science research, as they offer a simple way of quantifying cognitive processes (such as how fast someone learns, or how noisy they are in choice selection), and testing which cognitive theories offer a better explanation of the behavior. To relate cognitive models to the behavioral data, researchers rely on statistical tools that require estimating the likelihood of observed data under the assumptions of the cognitive model. This is, however, not possible to do for all models as some models present significant challenges to likelihood computation. In this work, we use artificial neural networks (ANNs) to bypass likelihood computation and approximation altogether, and demonstrate the success of this approach applied to model parameter estimation and model comparison. The proposed method is a contribution to ongoing development of modeling tools which will enable cognitive researchers to test a broader range of theories of cognition. [ABSTRACT FROM AUTHOR]

The prediction of the evolution of epidemics plays an important role in limiting the transmissibility and the burdensome consequences of infectious diseases, which leads to the employment of mathematical modeling. In this paper, we propose a stochastic particle filtering extended SEIRS model with repeated vaccination and time-dependent parameters, aiming to efficiently describe the demanding dynamics of time-varying epidemics. The validity of our model is examined using daily records of COVID-19 in Italy for a period of 525 days, revealing a notable capacity to uncover the hidden dynamics of the pandemic. The main findings include the estimation of asymptomatic cases, which is a well-known feature of the current pandemic. Unlike other proposed models that employ extra compartments for asymptomatic cases, which force the estimation of this proportion and significantly increase the model's complexity, our approach leads to the evaluation of the hidden dynamics of COVID-19 without additional computational burden. Other findings that confirm the model's appropriateness and robustness are its parameter evolution and the estimation of more ICU-admitted cases compared to the official records during the most prevalent infection wave of January 2022, attributed to the intensified increase in admissions that may have led to full occupancy in ICUs. As the vast majority of datasets contain time series of total recovered and vaccinated cases, we propose a statistical algorithm to estimate the currently recovered and protected through vaccination cases. This necessity arises from the attenuation of antibodies after vaccination/infection and is necessary for long-time interval predictions. Finally, we not only present a novel stochastic epidemiological model and test its efficiency but also investigate its mathematical properties, such as the existence and stability of epidemic equilibria, giving new insights to the literature. The latter provides additional details concerning the system's long-term behavior, while the conclusions drawn from the R0 index provide perspectives on the severity and future of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Adaptation can occur at remarkably short timescales in natural populations, leading to drastic changes in phenotypes and genotype frequencies over a few generations only. The inference of demographic parameters can allow understanding how evolutionary forces interact and shape the genetic trajectories of populations during rapid adaptation. Here we propose a new Approximate Bayesian Computation (ABC) framework that couples a forward and individual‐based model with temporal genetic data to disentangle genetic changes and demographic variations in a case of rapid adaptation. We test the accuracy of our inferential framework and evaluate the benefit of considering a dense versus sparse sampling. Theoretical investigations demonstrate high accuracy in both model and parameter estimations, even if a strong thinning is applied to time series data. Then, we apply our ABC inferential framework to empirical data describing the population genetic changes of the poplar rust pathogen following a major event of resistance overcoming. We successfully estimate key demographic and genetic parameters, including the proportion of resistant hosts deployed in the landscape and the level of standing genetic variation from which selection occurred. Inferred values are in accordance with our empirical knowledge of this biological system. This new inferential framework, which contrasts with coalescent‐based ABC analyses, is promising for a better understanding of evolutionary trajectories of populations subjected to rapid adaptation. [ABSTRACT FROM AUTHOR]

Suspended dust plays a critical role in regulating the Martian climate by influencing the atmospheric thermal gradient, altering the amount of infrared and visible energy absorbed and scattered by the atmosphere, and acting as condensation nuclei for CO 2 ice-clouds particles. There are many well demonstrated, dust-related effects on martian climate which depend on dustsize, concentration, chemical and bulk composition. Currently, an accurate estimation of these parameters is lacking as they are derived from indirect measurement of the optical depth acquired from the surface and orbital data. These indirect measurements require a priori assumptions on the grain distribution curve and are hence subject to possible biases. To overcome these limitations, an optical particles counter called MicroMED has been developed under the National Institute of Astrophysics (INAF) leadership. MicroMED can measure the sizes of individual dust grains in a specific volume of air thus providing the grain size distribution and concentration. MicroMED has been selected to join the Dust Complex payload on board the ExoMars 2022. The Flight Model of the instrument has been developed and optimized starting from two prototype BreadBoard versions. Here we present the sub-systems that constitute MicroMED and their testing and characterization process, performed using the Breadboard models. We discuss the optimizations and improvements introduced on the basis of the prototype results and the overall performances of the final design. [ABSTRACT FROM AUTHOR]

Background: Integration of a patient's non-invasive imaging data in a digital twin (DT) of the heart can provide valuable insight into the myocardial disease substrates underlying left ventricular (LV) mechanical discoordination. However, when generating a DT, model parameters should be identifiable to obtain robust parameter estimations. In this study, we used the CircAdapt model of the human heart and circulation to find a subset of parameters which were identifiable from LV cavity volume and regional strain measurements of patients with different substrates of left bundle branch block (LBBB) and myocardial infarction (MI). To this end, we included seven patients with heart failure with reduced ejection fraction (HFrEF) and LBBB (study ID: 2018-0863, registration date: 2019–10–07), of which four were non-ischemic (LBBB-only) and three had previous MI (LBBB-MI), and six narrow QRS patients with MI (MI-only) (study ID: NL45241.041.13, registration date: 2013–11–12). Morris screening method (MSM) was applied first to find parameters which were important for LV volume, regional strain, and strain rate indices. Second, this parameter subset was iteratively reduced based on parameter identifiability and reproducibility. Parameter identifiability was based on the diaphony calculated from quasi-Monte Carlo simulations and reproducibility was based on the intraclass correlation coefficient ( ICC ) obtained from repeated parameter estimation using dynamic multi-swarm particle swarm optimization. Goodness-of-fit was defined as the mean squared error ( χ 2 ) of LV myocardial strain, strain rate, and cavity volume. Results: A subset of 270 parameters remained after MSM which produced high-quality DTs of all patients ( χ 2 < 1.6), but minimum parameter reproducibility was poor ( ICC min = 0.01). Iterative reduction yielded a reproducible ( ICC min = 0.83) subset of 75 parameters, including cardiac output, global LV activation duration, regional mechanical activation delay, and regional LV myocardial constitutive properties. This reduced subset produced patient-resembling DTs ( χ 2 < 2.2), while septal-to-lateral wall workload imbalance was higher for the LBBB-only DTs than for the MI-only DTs (p < 0.05). Conclusions: By applying sensitivity and identifiability analysis, we successfully determined a parameter subset of the CircAdapt model which can be used to generate imaging-based DTs of patients with LV mechanical discoordination. Parameters were reproducibly estimated using particle swarm optimization, and derived LV myocardial work distribution was representative for the patient's underlying disease substrate. This DT technology enables patient-specific substrate characterization and can potentially be used to support clinical decision making. [ABSTRACT FROM AUTHOR]

In this paper, we use a previously developed measles model to forecast measles in Turkey for the period 1970–2021. We study the structural identifiability of the model both by hand and using software. By hand, we assume the prevalence and the total population size are given. Using software, we assume the incidence and the total population size are given. The model is structurally identifiable if one of the three parameters is fixed. We notice that Turkey has a significant change in time of the immigration rate and vaccination proportions, so we assume these two quantities are time-dependent. We fit the nonautonomous model to the measles incidences in Turkey for 1970–2021. We perform practical identifiability of the fitted model, and find that all parameters but one are practically identifiable. When fixing the unidentifiable parameter to a value derived from additional data, we obtain that all parameters are practically identifiable. [ABSTRACT FROM AUTHOR]

Quantile regression, known as a robust alternative to linear regression, has been widely used in statistical modeling and inference. In this paper, we propose a penalized weighted convolution‐type smoothed method for variable selection and robust parameter estimation of the quantile regression with high dimensional longitudinal data. The proposed method utilizes a twice‐differentiable and smoothed loss function instead of the check function in quantile regression without penalty, and can select the important covariates consistently using the efficient gradient‐based iterative algorithms when the dimension of covariates is larger than the sample size. Moreover, the proposed method can circumvent the influence of outliers in the response variable and/or the covariates. To incorporate the correlation within each subject and enhance the accuracy of the parameter estimation, a two‐step weighted estimation method is also established. Furthermore, we prove the oracle properties of the proposed method under some regularity conditions. Finally, the performance of the proposed method is demonstrated by simulation studies and two real examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with parameter estimation of Wiener systems with measurement noises employing correlation analysis method and adaptive Kalman filter. The presented Wiener system consists of two series blocks, that is, a dynamic block represented by auto‐regressive moving average (ARMA) model, and static nonlinear block established by neural fuzzy model. Aim at estimating separately the two blocks, the separable signals are introduced. First, applying the separable signals to decouple the identification of linear dynamic block from that of static nonlinear block, then ARMA model parameters are estimated employing correlation function‐based least squares principle. Moreover, aiming at handle with error caused by colored measurement noise, adaptive Kalman filter technique and cluster method are introduced to estimate parameter of the nonlinear block and noises model, enhancing parameter estimation precision. The accuracy and applicability of estimated scheme presented are verified through numerical simulation and nonlinear process, the results demonstrate that it is feasible for estimating the Wiener systems in the presence of colored measurement noises. [ABSTRACT FROM AUTHOR]

The lifetime data collected from the field are usually heavily censored, in which case, getting an accurate reliability evaluation based on heavily censored data is challenging. For heavily Type‐II censored data, the parameters estimation bias of traditional methods (i.e., maximum likelihood estimation (MLE) and least squares estimation (LSE)) are still large, and Bayesian methods are hard to specify the priors in practice. Therefore, considering the existing range of shape parameter for Weibull distribution, this study proposes two novel parameter estimation methods, the three‐step MLE method and the hybrid estimation method. For the three‐step MLE method, the initial estimates of shape and scale parameters are first respectively derived using MLE, then are updated by the single parameter MLE method with the range constraint of shape parameter. For the hybrid estimation method, the shape parameter is estimated by the LSE method with the existing range constraint of shape parameter, then the scale parameter estimate can be obtained by MLE. On this basis, two numerical examples are performed to demonstrate the consistency and effectiveness of the proposed methods. Finally, a case study on turbine engines is given to verify the effectiveness and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new three-parameter inverse Rayleigh distribution that extends the inverse Rayleigh distribution, constructed based on the generalized transmuted family of distributions proposed by Alizadeh, Merovci, and Hamedani. We explore statistical properties such as the quantile function, moments, harmonic mean, mean deviation, stress–strength reliability, and entropy. Parameter estimation is performed using various methods, including maximum likelihood, least squares, the method of the maximum product of spacings, and the method of Cramér–von Mises. The usefulness of the new three-parameter inverse Rayleigh distribution is illustrated by modeling a real dataset, demonstrating its superior fit compared to several other distributions. [ABSTRACT FROM AUTHOR]

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2 , a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well. [ABSTRACT FROM AUTHOR]

A novel two‐stage profile maximum likelihood estimator is proposed to estimate the source location and the systematic errors jointly, with the aim of addressing the problem of source localisation using angle‐only measurements from a single sensor with unknown sensor altitude and systematic measurement errors. The proposed two‐stage profile maximum likelihood estimator algorithm is capable of decoupling the azimuth and elevation angle measurements while transforming the original maximum likelihood optimisation problem into two sub‐problems, that is, two‐dimensional‐projected maximum likelihood estimator and relative altitude maximum likelihood estimator. In terms of the two‐dimensional‐projected maximum likelihood estimator, an algorithm combining pseudo‐linear estimating and Kalman filtering is proposed to generate an initial estimate. Subsequently, a Gauss–Newton iterative method is developed to estimate the two‐dimensional‐projected target location and the azimuth systematic error jointly. The relative height maximum likelihood estimator is initialised using a pseudo‐linear estimator. Next, a Gauss–Newton iterative algorithm is adopted to estimate the elevation systematic error and the relative height. As indicated by the result of the simulation studies, the proposed algorithm exhibits an estimation performance close to the Cramér–Rao lower bound with unknown sensor altitude and systematic measurement errors. [ABSTRACT FROM AUTHOR]