Parameter Estimation Performance Research Articles

Stability and optimal control of a cholera transmission model with waning vaccine-induced immunity and phage–vibrio interactions

Cholera is still a significant worldwide health concern that continues to affect many regions around the world, posing a persistent threat to human health with its severity unabated. In this paper, a cholera transmission model with waning vaccine-induced immunity and phage–vibrio interactions is investigated. The two important thresholds for distinguishing whether cholera is epidemic or not are obtained, and fundamental properties of the system are studied. The global asymptotic stability of the system is analyzed in detail by constructing suitable Lyapunov functions. To seek the suitable strategies for preventing and controlling cholera infection, we introduced four time-dependent controls into the model to assess the effectiveness of each strategy by applying Pontryagin’s maximum principle. In addition, using the reported cholera case numbers in Yemen, we perform parameter estimation and data fitting, further, a sensitivity analysis of thresholds is conducted.

Secrecy-Constrained UAV-Mounted RIS-Assisted ISAC Networks: Position Optimization and Power Beamforming

This paper investigates secrecy solutions for integrated sensing and communication (ISAC) systems, leveraging the combination of a reflecting intelligent surface (RIS) and an unmanned aerial vehicle (UAV) to introduce new degrees of freedom for enhanced system performance. Specifically, we propose a secure ISAC system supported by a UAV-mounted RIS, where an ISAC base station (BS) facilitates secure multi-user communication while simultaneously detecting potentially malicious radar targets. Our goal is to improve parameter estimation performance, measured by the Cramér–Rao bound (CRB), by jointly optimizing the UAV position, transmit beamforming, and RIS beamforming, subject to constraints including the UAV flight area, communication users’ quality of service (QoS) requirements, secure transmission demands, power budget, and RIS reflecting coefficient limits. To address this non-convex, multivariate, and coupled problem, we decompose it into three subproblems, which are solved iteratively using particle swarm optimization (PSO), semi-definite relaxation (SDR), majorization–minimization (MM), and alternating direction method of multipliers (ADMM) algorithms. Our numerical results validate the effectiveness of the proposed scheme and demonstrate the potential of employing UAV-mounted RIS in ISAC systems to enhance radar sensing capabilities.

Stellar-mass black-hole binaries in LISA: characteristics and complementarity with current-generation interferometers

Stellar-mass black-hole binaries are the most numerous gravitational-wave sources observed to date. Their properties make them suitable for observation both by ground- and space-based detectors. Starting from synthetic catalogues constructed based on observational constraints from ground-based detectors, we explore the detection rates and the characteristic parameters of the stellar-mass black-hole binaries observable by LISA during their inspiral, using signal-to-noise ratio thresholds as a detection criterion. We find that only a handful of these sources will be detectable with signal-to-noise ratio larger than 8: about 5 sources on average in 4 years of mission duration, among which only one or two are multiband ones (i.e. merging in less than 15 years). We find that detectable sources have chirp mass 10 M ⊙ ≲ ℳ c ≲ 100 M ⊙, residual time-to-coalescence 4 yr ≲ τc ≲ 100 yr, and redshift z ≲ 0.1, much closer than those observed up to now by ground-based detectors. We also explore correlations between the number of LISA detectable sources and the parameters of the population, suggesting that a joint measurement with the stochastic signal might be informative of the population characteristics. By performing parameter estimation on a subset of sources from the catalogues, we conclude that, even if LISA measurements will not be directly informative on the population due to the low number of resolvable sources, it will characterise a few, low-redshift candidates with great precision. Furthermore, we construct for the first time the LISA waterfall plot for low chirp-mass systems, as a function of their time to coalescence and inclination. We demonstrate that LISA will also be able to discriminate and characterize, through very precise parameter estimation, a population of binaries with higher masses, ℳ c ∼ 𝒪(103) M ⊙, at the boundary of ground-based detectors sensitivity.

A Novel Self-Supervised Learning-Based Method for Dynamic CT Brain Perfusion Imaging.

Dynamic computed tomography (CT)-based brain perfusion imaging is a non-invasive technique that can provide quantitative measurements of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT). However, due to high radiation dose, dynamic CT scan with a low tube voltage and current protocol is commonly used. Because of this reason, the increased noise degrades the quality and reliability of perfusion maps. In this study, we aim to propose and investigate the feasibility of utilizing a convolutional neural network and a bi-directional long short-term memory model with an attention mechanism to self-supervisedly yield the impulse residue function (IRF) from dynamic CT images. Then, the predicted IRF can be used to compute the perfusion parameters. We evaluated the performance of the proposed method using both simulated and real brain perfusion data and compared the results with those obtained from two existing methods: singular value decomposition and tensor total-variation. The simulation results showed that the overall performance of parameter estimation obtained from the proposed method was superior to that obtained from the other two methods. The experimental results showed that the perfusion maps calculated from the three studied methods were visually similar, but small and significant differences in perfusion parameters between the proposed method and the other two methods were found. We also observed that there were several low-CBF and low-CBV lesions (i.e., suspected infarct core) found by all comparing methods, but only the proposed method revealed longer MTT. The proposed method has the potential to self-supervisedly yield reliable perfusion maps from dynamic CT images.

Oxygen, angiogenesis, cancer and immune interplay in breast tumour microenvironment: a computational investigation.

Breast cancer is a challenging global health problem among women. This study investigates the intricate breast tumour microenvironment (TME) dynamics utilizing data from mammary-specific polyomavirus middle T antigen overexpression mouse models (MMTV-PyMT). It incorporates endothelial cells (ECs), oxygen and vascular endothelial growth factors (VEGF) to examine the interplay of angiogenesis, hypoxia, VEGF and immune cells in cancer progression. We introduce an approach to impute immune cell fractions within the TME using single-cell RNA-sequencing (scRNA-seq) data from MMTV-PyMT mice. We quantify our analysis by estimating cell counts using cell size data and laboratory findings from existing literature. We perform parameter estimation via a Hybrid Genetic Algorithm (HGA). Our simulations reveal various TME behaviours, emphasizing the critical role of adipocytes, angiogenesis, hypoxia and oxygen transport in driving immune responses and cancer progression. Global sensitivity analyses highlight potential therapeutic intervention points, such as VEGFs' role in EC growth and oxygen transportation and severe hypoxia's effect on cancer and the total number of cells. The VEGF-mediated production rate of ECs shows an essential time-dependent impact, highlighting the importance of early intervention in slowing cancer progression. These findings align with clinical observations demonstrating the VEGF inhibitors' efficacy and suggest a timely intervention for better outcomes.

Functional Concurrent Regression Mixture Models Using Spiked Ewens-Pitman Attraction Priors.

Functional concurrent, or varying-coefficient, regression models are a form of functional data analysis methods in which functional covariates and outcomes are collected concurrently. Two active areas of research for this class of models are identifying influential functional covariates and clustering their relations across observations. In various applications, researchers have applied and developed methods to address these objectives separately. However, no approach currently performs both tasks simultaneously. In this paper, we propose a fully Bayesian functional concurrent regression mixture model that simultaneously performs functional variable selection and clustering for subject-specific trajectories. Our approach introduces a novel spiked Ewens-Pitman attraction prior that identifies and clusters subjects' trajectories marginally for each functional covariate while using similarities in subjects' auxiliary covariate patterns to inform clustering allocation. Using simulated data, we evaluate the clustering, variable selection, and parameter estimation performance of our approach and compare its performance with alternative spiked processes. We then apply our method to functional data collected in a novel, smartphone-based smoking cessation intervention study to investigate individual-level dynamic relations between smoking behaviors and potential risk factors.

Improved Particle Swarm Optimization Algorithm Based Robust Parameter Estimation of Photovoltaic Array Model under Partial Shading Conditions

Parameter estimation of the photovoltaic (PV) array model is able to improve the accuracy of model parameter setting, and also obtain a model consistent with actual situations. It plays a very important role in the maximum power point tracking of PV array and the improvement of micro‐grid and at the same time further affects the sustainable development of new energy sources. In order to reduce the impact of gross errors on the results of parameter estimation, Correntropy based parameter estimation for PV array model under partial shading conditions is structured for robust estimation. In view of the fact that traditional particle swarm optimization (PSO) algorithm tends to converge prematurely and has poor local optimization capabilities and it is hard to resolve nonlinear parameter estimation problems with many nonlinear constraints, an algorithm (IPSO_SQP) that combines the improved particle swarm optimization (IPSO) algorithm with sequential quadratic programming (SQP) is proposed to identify the parameters of photovoltaic (PV) arrays under partial shading conditions. to recognize the parameters of PV array under partial shading conditions. The algorithm optimizes the performance of conventional algorithms by introducing nonlinear dynamic updating of inertia weights and learning factors, as well as the Cauchy mutation operator. It is reflected in the use of improved nonlinear iterative formulations to balance the global and local search capabilities of the algorithm, followed by the introduction of the Cauchy mutation operator to avoid the algorithm from falling into local optima and satisfy the nonlinear constraints to obtain a better solution. After simulation and experimental tests, the results indicate that the IPSO_SQP algorithm has high performance and precision in the robust parameter estimation of PV array model under partial shading conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

A fast dynamic causal modeling regression method for fMRI

Dynamic Causal Modeling (DCM) is a crucial tool for studying brain effective connectivity, offering valuable insights into brain network dynamics through functional magnetic resonance imaging (fMRI) and electrophysiology (EEG and MEG). However, its high computational complexity limits its applicability in large-scale network analysis. To address this issue, we propose a regression algorithm that integrates the Generalized Linear Model (GLM) with Sparse DCM, termed GSD. This algorithm enhances computational performance through three key optimizations: (1) utilizing the symmetry of the Fourier transform to convert complex frequency domain calculations into real number operations, thereby reducing computational complexity; (2) applying GLM and filtering techniques to minimize the effects of noise and confounds, enhancing parameter estimation accuracy; and (3) defining a new cost function to optimize variational inference and filter parameters, further improving parameter estimation accuracy. We validated the GSD algorithm using three public fMRI datasets: simulated Smith small-world network data, attention and motion measured data, and face recognition repetition effect measured data. The experimental results demonstrate that the GSD algorithm reduces computation time by over 50 % while maintaining parameter estimation performance comparable to traditional methods. These findings offer a new perspective on balancing model interpretability and computational efficiency, potentially broadening the application of DCM across various fields.

Fast distance and velocity estimation in parameter agility radar using CM-CS-OMP and CM-MUSIC methods

Radar applications face the challenges of interference and signal processing demands. Existing parameter-agility anti-jamming methods grapple with high computational complexity. To address this challenge, our paper proposes two methods: Conjugate Mixing Compressed Sensing Orthogonal Matching Pursuit (CM-CS-OMP) and Conjugate Mixing Multiple Signal Classification (CM-MUSIC). These methods significantly reduce signal processing complexity by constructing parameter agility signal pairs for conjugate mixing to eliminate the distance phase term in the post-matched filtering signal. Subsequently, we estimate velocity within the CS and MUSIC frameworks. While CM-CS-OMP excels in scenarios with a small number of targets and performs better at low signal-to-noise ratios, CM-MUSIC is more efficient in multi-target environments due to its lower sensitivity to the number of targets, offering complementary advantages depending on the application context. Through theoretical analysis and simulation experiments, we demonstrate that the CM-CS-OMP and CM-MUSIC methods significantly reduce processing complexity, achieving a time cost reduction of approximately 90% compared to existing CS-OMP techniques, with only a negligible decrease in parameter estimation performance. This trade-off between complexity and performance opens new avenues in radar signal processing for autonomous driving and Internet of Things applications, offering a balance crucial for these technologies’ practical deployment.

Rapid parameter estimation for merging massive black hole binaries using continuous normalizing flows

Abstract Detecting the coalescences of massive black hole binaries (MBHBs) is one of the primary targets for space-based gravitational wave observatories such as laser interferometer space antenna, Taiji, and Tianqin. The fast and accurate parameter estimation of merging MBHBs is of great significance for the global fitting of all resolvable sources, as well as the astrophysical interpretation of gravitational wave signals. However, such analyses usually entail significant computational costs. To address these challenges, inspired by the latest progress in generative models, we explore the application of continuous normalizing flows (CNFs) on the parameter estimation of MBHBs. Specifically, we employ linear interpolation and trig interpolation methods to construct transport paths for training CNFs. Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector’s response function. This transformation is integrated within CNFs, allowing us to train the model using a simplified dataset, and then perform parameter estimation on more general data, hence also acting as a crucial factor in improving the training speed. In conclusion, for the first time, within a comprehensive and reasonable parameter range, we have achieved a complete and unbiased 11-dimensional rapid inference for MBHBs in the presence of astrophysical confusion noise using CNFs. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling.

Recursive-RARE-based three-dimensional parameter estimation of near-field source considering amplitude attenuation

This paper addresses the issue for near-field (NF) localization considering amplitude attenuation, proposing a recursive rank-reduction (RARE) method for three-dimensional (3-D) parameter estimation of NF sources incident on a symmetrical cross array. The proposed method constructs several one-dimensional (1-D) spectral peak search estimators to obtain two-dimensional angle and range parameters. Initially, using the received data from symmetrical array elements in one axis, a 1-D spectral peak search estimator is constructed. The origins of two types of pseudo peaks within this estimator are analyzed, and then, corresponding pseudo peaks removal methods, namely the initial screening method and the recursive RARE method, are presented to obtain the estimate of the first angle parameter. Subsequently, the estimated results are fed into another 1-D spectral peak search estimator constructed from the original received data to obtain the range parameter. Finally, the same process is applied to the other axis to obtain the second angle and range parameters, followed by a parameter matching operation for 3-D parameters. Compared to existing NF source localization methods, the proposed method more effectively eliminates pseudo peaks, and demonstrates superior parameter estimation performance under conditions of small number of snapshots and low signal-to-noise ratio, as validated by several simulation results.

Two New Families of Local Asymptotically Minimax Lower Bounds in Parameter Estimation.

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate and the true underlying parameter value (i.e., the estimation error), whereas the second is more specifically oriented to the moments of the estimation error. The proposed bounds are relatively easy to calculate numerically (in the sense that their optimization is over relatively few auxiliary parameters), yet they turn out to be tighter (sometimes significantly so) than previously reported bounds that are associated with similar calculation efforts, across many application examples. In addition to their relative simplicity, they also have the following advantages: (i) Essentially no regularity conditions are required regarding the parametric family of distributions. (ii) The bounds are local (in a sense to be specified). (iii) The bounds provide the correct order of decay as functions of the number of observations, at least in all the examples examined. (iv) At least the first family of bounds extends straightforwardly to vector parameters.

Hot spots around Sagittarius A*

Context. Observations of Sagittarius A* (Sgr A*) in the near-infrared (NIR) show irregular flaring activity. Flares coincide with the astrometric rotation of the brightness centroid and with looping patterns in fractional linear polarization. These signatures can be explained with a model of a bright hot spot, transiently orbiting the black hole. Aims. We extend the capabilities of the existing algorithms to perform parameter estimation and model comparison in the Bayesian framework using NIR observations from the GRAVITY instrument, and simultaneously fitting the astrometric and polarimetric data. Methods. Using the numerical radiative transfer code ipole, we defined several geometric models describing a hot spot orbiting Sgr A*, threaded with a magnetic field, and emitting synchrotron radiation. We then explored the posterior space of our models with a nested sampling code dynesty. We used Bayesian evidence to make comparisons between the models. Results. We have used 11 models to sharpen our understanding of the importance of various aspects of the orbital model, such as non-Keplerian motion, hot-spot size, and off-equatorial orbit. All considered models converge to realizations that fit the data well, but the equatorial super-Keplerian model is favoured by the currently available NIR dataset. Conclusions. We have inferred an inclination of ∼155 deg, which corroborates previous estimates, a preferred period of ∼70 minutes, and an orbital radius of ∼12 gravitational radii with the orbital velocity of ∼1.3 times the Keplerian value. A hot spot with a diameter smaller than 5 gravitational radii is favoured. Black hole spin is not constrained well.

Fixing imbalanced binary classification: An asymmetric Bayesian learning approach.

Most statistical and machine learning models used for binary data modeling and classification assume that the data are balanced. However, this assumption can lead to poor predictive performance and bias in parameter estimation when there is an imbalance in the data due to the threshold election for the binary classification. To address this challenge, several authors suggest using asymmetric link functions in binary regression, instead of the traditional symmetric functions such as logit or probit, aiming to highlight characteristics that would help the classification task. Therefore, this study aims to introduce new classification functions based on the Lomax distribution (and its variations; including power and reverse versions). The proposed Bayesian functions have proven asymmetry and were implemented in a Stan program into the R workflow. Additionally, these functions showed promising results in real-world data applications, outperforming classical link functions in terms of metrics. For instance, in the first example, comparing the reverse power double Lomax (RPDLomax) with the logit link showed that, regardless of the data imbalance, the RPDLomax model assigns effectively lower mean posterior predictive probabilities to failure and higher probabilities to success (21.4% and 63.7%, respectively), unlike Logistic regression, which does not clearly distinguish between the mean posterior predictive probabilities for these two classes (36.0% and 39.5% for failure and success, respectively). That is, the proposed asymmetric Lomax approach is a competitive model for differentiating binary data classification in imbalanced tasks against the Logistic approach.

Stochastic Model for Novel Mixture Distribution with Properties and Its Application

Medical research is the one of the most important applications of statistical analysis. A great deal of occasions, specific statistical considerations are needed for cancer research in order to determine the model that best fits the survival data. In this paper, the proposed a new two parameter continuous distribution. It is called a new mixture distribution (NMD). Some statistical properties of the distribution are derived such as, the moments, moments generating function, reliability analysis. Also, the distribution of order statistics is presented and entropies are derived. The application of the maximum likelihood estimate technique to the performance of traditional parameter estimation. Two authentic data sets describing cancer patients' survival are used to empirically demonstrate the potential importance and usability of the proposed distribution. Comparing the new mixture distribution to some other competing distribution, the analysis's results demonstrated that it performed quite well.

Data-driven solutions and parameter estimations of a family of higher-order KdV equations based on physics informed neural networks

Physics informed neural network (PINN) demonstrates powerful capabilities in solving forward and inverse problems of nonlinear partial differential equations (NLPDEs) through combining data-driven and physical constraints. In this paper, two PINN methods that adopt tanh and sine as activation functions, respectively, are used to study data-driven solutions and parameter estimations of a family of high order KdV equations. Compared to the standard PINN with the tanh activation function, the PINN framework using the sine activation function can effectively learn the single soliton solution, double soliton solution, periodic traveling wave solution, and kink solution of the proposed equations with higher precision. The PINN framework using the sine activation function shows better performance in parameter estimation. In addition, the experiments show that the complexity of the equation influences the accuracy and efficiency of the PINN method. The outcomes of this study are poised to enhance the application of deep learning techniques in solving solutions and modeling of higher-order NLPDEs.

A Highly Efficient Compressive Sensing Algorithm Based on Root-Sparse Bayesian Learning for RFPA Radar

Off-grid issues and high computational complexity are two major challenges faced by sparse Bayesian learning (SBL)-based compressive sensing (CS) algorithms used for random frequency pulse interval agile (RFPA) radar. Therefore, this paper proposes an off-grid CS algorithm for RFPA radar based on Root-SBL to address these issues. To effectively cope with off-grid issues, this paper derives a root-solving formula inspired by the Root-SBL algorithm for velocity parameters applicable to RFPA radar, thus enabling the proposed algorithm to directly solve the velocity parameters of targets during the fine search stage. Meanwhile, to ensure computational feasibility, the proposed algorithm utilizes a simple single-level hierarchical prior distribution model and employs the derived root-solving formula to avoid the refinement of velocity grids. Moreover, during the fine search stage, the proposed algorithm combines the fixed-point strategy with the Expectation-Maximization algorithm to update the hyperparameters, further reducing computational complexity. In terms of implementation, the proposed algorithm updates hyperparameters based on the single-level prior distribution to approximate values for the range and velocity parameters during the coarse search stage. Subsequently, in the fine search stage, the proposed algorithm performs a grid search only in the range dimension and uses the derived root-solving formula to directly solve for the target velocity parameters. Simulation results demonstrate that the proposed algorithm maintains low computational complexity while exhibiting stable performance for parameter estimation in various multi-target off-grid scenarios.

Notes on the Practical Application of Nested Sampling: MultiNest, (Non)convergence, and Rectification

Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has been applied to a wide variety of problems in the physical sciences. However, MultiNest results, like those of any sampling tool, can be unreliable, and accompanying convergence tests are a component of any analysis. Using analytically tractable test problems, I illustrate how MultiNest, when applied without rigorously chosen hyperparameters, (1) can produce systematically erroneous estimates of the Bayesian evidence, which are more significantly biased for problems of higher dimensionality; (2) can derive posterior estimates with errors on the order of ~100%; (3) can, particularly when sampling noisy likelihood functions, systematically underestimate posterior widths. Furthermore, I show how MultiNest, thanks to the advantageous speed at which it explores parameter space, can also be used to jump-start Markov chain Monte Carlo sampling or more rigorous nested sampling techniques, potentially accelerating more robust measurements of posterior distributions and Bayesian evidences, and overcoming the challenge of Markov chain Monte Carlo initialization.

Separable Synchronous Gradient‐Based Iterative Algorithms for the Nonlinear ExpARX System

ABSTRACTThis article is aimed to study the parameter identification of the ExpARX system. To overcome the computational complexity associated with a large number of feature parameters, a parameter separation scheme based on the different features of the identification model is introduced. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous interactive estimation method is introduced to eliminate the coupling parameters and perform parameter estimation in accordance with the hierarchical principle. For the purpose of achieving high‐accuracy performance and reducing complexity, a separable synchronous gradient iterative algorithm is derived by means of gradient search. In order to improve the identification accuracy, a separable synchronous multi‐innovation gradient iterative algorithm is proposed by introducing the multi‐innovation identification theory. In order to improve the convergence speed, a separable synchronous multi‐innovation conjugate gradient iterative algorithm is proposed by introducing the conjugate gradient theory. Finally, a simulation example and a real‐life example of piezoelectric ceramics are used to verify the effectiveness of the proposed algorithm.

A Novel Methodology for GB-SAR Estimating Parameters of the Atmospheric Phase Correction Model Based on Maximum Likelihood Estimation and the Gauss-Newton Algorithm.

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.