Parameter Estimation Research Articles

A Hard Re-descending Hybrid Robust Regression Estimation Technique Using Direct Weights

A hybrid approach of M and R estimators using an iterative procedure is proposed to detect outliers and estimation of regression parameters for linear models. We consider the deviation of each residual from its median to measure the likelihood of the corresponding data point to be an outlier. Also, the proposed work develops a reliable algorithm to estimate parameters of regression model that is unaffected by outliers. The significance of the proposed work is a novel hybrid approach of weighing the observations based on the order of residuals. Our proposal is illustrated using Monte Carlo simulation and analysed for few benchmark data sets.

Statistical analysis of multivariate binary time series based on a neural network model

This article is devoted to the statistical analysis of multivariate binary time series. For solving this problem a parsimonious neural network model of Markov’s ergodic chain of order s was determined. Consistent statistical estimators for model parameters and estimation algorithms of parameters and forecasting algorithms of future states of time series were developed. The results of computer experiments on simulated and real data are presented.

Pediatric cirrhotic cardiomyopathy: literature review and effect size estimations of selected parameters.

This review provides estimates of the standardized mean difference among selected cardiac parameters in children with and without cirrhosis. Tailored diagnostic criteria and comprehensive assessment methods will be essential for accurate diagnosis and effective management of pediatric CCM. • CCM adds to the burden of care of patients with cirrhosis. • Diagnostic criteria for adults are evolving, but there are no specific criteria for pediatric CCM. • Cardiac function in children with cirrhosis indicates some parameters not considered in adults are altered. • Effect size estimations for certain parameters provide a guideline for future research into pediatric CCM.

Estimation of shifted weibull distribution parameters using optimization algorithms for optimal investment decisions making

This study examines the estimation of parameters for the Shifted Weibull Distribution (SWD) using several robust metaheuristic algorithms, with a focus on enhancing precision and reliability in investment data analysis. Utilizing investment return data from the Malaysian property sector, we evaluate the performance of five metaheuristic models: Election Algorithm (EA), Artificial Dragonfly Algorithm (ADA), Genetic Algorithm (GA), Differential Evolution (DE), and Ant Colony Optimization (ACO). The evaluation criteria include Bayesian Information Criterion (BIC), Root Mean Squared Error (RMSE), and accuracy. Results reveal that EA consistently outperforms other models, achieving the lowest BIC value of 147.2 and an impressive accuracy rate of 94.90% at a sample size of 1,000. The Genetic Algorithm (GA) shows the lowest RMSE of 0.99, indicating strong predictive performance. Tukey's HSD test highlights significant accuracy variations among the models, with EA and GA notably outperforming ACO and DE. However, RMSE and BIC metrics do not demonstrate clear variations among the models. These findings underscore the superior performance of the EA model in the context of SWD parameter estimation, making it the preferred choice for modeling investment return data. Future research should explore additional factors influencing model performance and validate these models with diverse real-world datasets to further enhance their applicability in financial decision-making.

Quantum metrology of Schwinger effect

We propose a scheme for the quantum metrology of the Schwinger effect and the dynamics of Gaussian interference power (GIP). The ongoing reliability of the estimation strategy for the probe state prepared in particle–particle modes is demonstrated. Although the GIP sensitively depends on the strength of the external electric field and the transverse momentum, the advantage of quantum parameter estimation is still maintained even in the limit of an infinite electric field and zero transverse momentum. It is shown that the entanglement between the particle–particle modes provides a guarantee for obtaining higher precision for the black-box estimation. In contrast, for the probe state prepared in particle–antiparticle modes, the advantage of quantum parameter estimation can also be ensured even though there is no entanglement in the probe state. Put differently, some non-entanglement quantum correlations play the role of quantum resources in the estimation for particle–antiparticle modes.

Target Fitting Method for Spherical Point Clouds Based on Projection Filtering and K-Means Clustered Voxelization.

Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 μm, which is significantly better than RANSAC's value of 25.41 μm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters.

Event-triggered lifted robust MPC stabilization control for space telescope on dual-rate actuated rigid spacecraft systems

This study addresses the pose stabilization control problem for enhancing a space telescope mounted on a spacecraft system under a dual-rate actuated setup. An input-lifting approach is utilized to manage the dual rates in the control components, specifically the orbital space telescope and its loading platform. To counteract external spatial perturbations and spacecraft system uncertainties, an integrated control scheme is proposed, combining real-time model parameter estimation, active compensation control, and event-triggered lifted robust model predictive control (ET-LRMPC). The event-triggered mechanism in the proposed algorithm minimizes computational resource consumption while maintaining effective spacecraft control. Numerical simulations demonstrate that the proposed control scheme achieves favorable results under persistent external perturbations and model uncertainties. In terms of the overshoot, the algorithm proposed reduces the control effect by up to 87.1% in the spatial displacement of the payload and 98.6% in the Euler attitude angle compared to the conventional control algorithm. For the control of the base, the amount of overshoots with respect to the conventional control in spatial displacement and Euler attitude angle is reduced by 49% and 97.1%.

Variable selection and estimation for recurrent event model with covariates subject to measurement error

This article focuses on variable selection in the Andersen–Gill model for recurrent event analysis, particularly when covariates are subject to measurement errors. We propose a comprehensive three-stage procedure that incorporates simulation–extrapolation with various penalty functions. This approach allows for the simultaneous selection of significant covariates, estimation of regression parameters, and adjustment for measurement errors. Through extensive simulation studies, we demonstrate that our method outperforms approaches that fail to account for measurement errors or the need for variable selection. Specifically, our procedure excels in removing unimportant error-prone covariates and accurately estimating the coefficients of important variables. The results also reveal that the magnitude of measurement error has a substantial negative impact on variable selection outcomes. Additionally, we apply our method to a real-world dataset, further illustrating its practical effectiveness and robustness.

Results and Discussion of Dengue Model with Temperature Effects in Interval Environment

We have investigated a dengue model with temperature effects under interval uncertainty in this work. This study observed the Aedes aegypti temperature-dependent entomological parameters that affect dengue illness transmission dynamics in Taiwan's subtropical zone. A vector-host transmission model was used to examine how temperature fluctuations influence the development of pre-adult mosquitoes, their egg-laying rates, adult mortality, and the incubation rate of viruses within them. This study showed that although estimations of entomological parameters were positively correlated with slow temperature rises, no such correlation was detected with mosquito mortality or maturation rates, underscoring the slow rate of maturation of pre-adult mosquitoes. The findings suggest that the dynamic modeling of vector-host interactions is significantly influenced by temperature. Additionally, our modeling indicates that a temperature range of about 32°C is ideal for dengue transmission. In the future, control measure modeling and cost-effectiveness assessments may benefit from these insights.

Bayesian modeling and optimization for split-plot experiments with multiple responses

In many industrial processes, cost or time constraints make some input variables harder to change or control than others. An appropriate experimental design method is restricted randomization, which results in split-plot experiments. Empirical models that connect multiple quality characteristics with input variables play a crucial role in robust parameter design for split-plot experiments. At present, many modeling methods typically adopt the single response model for analyzing industrial processes in the split-plot experiments without considering correlation among multiple responses, correlation among whole plots, and uncertainty of model parameters. However, ignoring these issues can lead to poor product or process design. To solve these issues, this paper suggests a novel Bayesian modeling and optimization approach. We first construct a Bayesian multi-response linear mixed-effects model and obtain the posterior distribution for model parameters by employing Bayesian theorem. Then, the Gibbs sampling procedure is employed for the estimation of model parameters. Finally, the overall weighted desirability optimization function meeting the specification is developed to avoid acquiring ideal input settings with outliers. A simulation and an engineering case study demonstrate the validity of the proposed method. In comparison to existing methods, the optimization results given the proposed method are more robust and reliable.

Simulating Bacterial Membrane Models at the Atomistic Level: A Force Field Comparison.

Molecular dynamics (MD) simulations are currently an indispensable tool to understand both the dynamic and nanoscale organization of cell membrane models. A large number of quantitative parameters can be extracted from these simulations, but their reliability is determined by the quality of the employed force field and the simulation parameters. Much of the work on parametrizing and optimizing force fields for biomembrane modeling has been focused on homogeneous bilayers with a single phospholipid type. However, these may not perform effectively or could even be unsuitable for lipid mixtures commonly employed in membrane models. This work aims to fill this gap by comparing MD simulation results of several bacterial membrane models using different force fields and simulation parameters, namely, CHARMM36, Slipids, and GROMOS-CKP. Furthermore, the hydrogen isotope exchange (HIE) method, combined with GROMOS-CKP (GROMOS-H2Q), was also tested to check for the impact of this acceleration strategy on the performance of the force field. A common set of simulation parameters was employed for all of the force fields in addition to those corresponding to the original parametrization of each of them. Furthermore, new experimental order parameter values determined from NMR of several lipid mixtures are also reported to compare them with those determined from MD simulations. Our results reveal that most of the calculated physical properties of bacterial membrane models from MD simulations are substantially force field and lipid composition dependent. Some lipid mixtures exhibit nearly ideal behaviors, while the interaction of different lipid types in other mixtures is highly synergistic. None of the employed force fields seem to be clearly superior to the other three, each having its own strengths and weaknesses. Slipids are notably effective at replicating the order parameters for all acyl chains, including those in lipid mixtures, but they offer the least accurate results for headgroup parameters. Conversely, CHARMM provides almost perfect estimates for the order parameters of the headgroups but tends to overestimate those of the lipid tails. The GROMOS parametrizations deliver reasonable order parameters for entire lipid molecules, including multicomponent bilayers, although they do not reach the accuracy of Slipids for tails or CHARMM for headgroups. Importantly, GROMOS-H2Q stands out for its computational efficiency, being at least 3 times faster than GROMOS, which is already faster than both CHARMM and Slipids. In turn, GROMOS-H2Q yields much higher compressibilities compared to all other parametrizations.

A general framework for generative self-supervised learning in non-invasive estimation of physiological parameters using photoplethysmography

Aligning physiological parameter labels with large-scale photoplethysmographic (PPG) data for deep learning is challenging and resource-intensive. While self-supervised representation learning (SSRL) can handle limited annotated data, the challenge lies in learning robust shared representations from vast unlabeled data and integrating various contextual cues to learn distinctive representations. To alleviate these challenges, a generative SSRL framework TS2TC is proposed to collaboratively utilize the temporal, spectrogram, and temporal-spectrogram mixed domains to explore and incorporate the unique features of PPG for universal and non-invasive physiological parameter estimation. Initially, a pretext task named Cross-Temporal Fusion Generative Anchor (CTFGA) is designed, modeling temporal dependencies and reconstructing independent segments at a coarse level to provide robust global feature extraction and local semantic contextual representation. The framework also includes sub-signals from PPG with diverse frequency scales and order derivatives reflecting hemodynamics to facilitate learning shared representations at varying semantic levels. Secondly, an advanced cognitive-inspired dual-process transfer (DPT) strategy is formulated, consisting of prior-dependent autonomous processes and posterior observation reasoning processes, to leverage the independent and integrated advantages of shared and specific representations. Furthermore, TS2TC introduces a novel bilinear temporal-spectrogram fusion method in the mixed domain, aligning latent representations from different domains, and establishing fine-grained contextual interactions at the feature level across multiple sources of information. Extensive experiments on physiological parameter estimation tasks showed that the joint performance of CTFGA and DPT outperforms standard generative learning significantly. TS2TC achieved an average 2.49% improvement in RMSE over the current state-of-the-art estimation methods with only 10% training data.

Light-injection attack against practical continuous-variable measurement-device-independent quantum key distribution systems

Continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) can defend all detection-side attacks effectively. Therefore, the source side is the final battlefield for performing quantum hacking attacks. This paper investigates the practical security of a CV-MDI QKD system under a light-injection attack. Here, we first describe two different light-injection attacks, i.e., the induced-photorefractive attack and the strong-power injection attack. Then, we consider three attack cases where Eve only attacks one of the parties or both parties of the CV-MDI QKD system. Based on the analysis of the parameter estimation, we find that the legitimate communication parties will overestimate the secret key rate of the system under the effect of a light-injection attack. This opens a security loophole for Eve to successfully obtain secret key information in a practical CV-MDI QKD system. In particular, compared to the laser-damage attack, the above attacks use a lower power of injected light and have a more serious effect on the security of the system. To eliminate the above effects, we can enhance the practical security of the system by doping the lithium niobate material with various impurities or by using protective devices, such as optical isolators, circulators, optical power limiters, and narrow-band filters. Apart from these, we can also use an intensity monitor or a photodetector to detect the light-injection attack.

Multivariate time between events control charts for Gumbel's bivariate exponential distribution with estimated parameters

The traditional approach of statistical process control is to estimate the in-control parameters from reference samples obtained in Phase I and then apply them to Phase II monitoring, which affects the performance of the monitoring scheme. We analyzed the effect of parameter estimation on three multivariate time between events control charts for monitoring the Gumbel's bivariate exponential distribution, namely the joint multivariate exponentially weighted moving average and multivariate rate, the joint multivariate cumulative sum and multivariate rate, and the joint paired individual exponentially weighted moving average and multivariate rate control charts. The simulation results show that the performance of the control charts is severely affected if control limits with known parameters are used, especially when only a few historical sample data are available. Mainly, the steady-state average time to signal was used as an evaluation index to analyze the affected degree of the three control charts, and the control limits were corrected. In addition, we evaluate the effect of model misspecification on the control charts. Finally, an example is given to illustrate the application of the proposed method.

HMM for discovering decision-making dynamics using reinforcement learning experiments.

Major depressive disorder (MDD), a leading cause of years of life lived with disability, presents challenges in diagnosis and treatment due to its complex and heterogeneous nature. Emerging evidence indicates that reward processing abnormalities may serve as a behavioral marker for MDD. To measure reward processing, patients perform computer-based behavioral tasks that involve making choices or responding to stimulants that are associated with different outcomes, such as gains or losses in the laboratory. Reinforcement learning (RL) models are fitted to extract parameters that measure various aspects of reward processing (e.g. reward sensitivity) to characterize how patients make decisions in behavioral tasks. Recent findings suggest the inadequacy of characterizing reward learning solely based on a single RL model; instead, there may be a switching of decision-making processes between multiple strategies. An important scientific question is how the dynamics of strategies in decision-making affect the reward learning ability of individuals with MDD. Motivated by the probabilistic reward task within the Establishing Moderators and Biosignatures of Antidepressant Response in Clinical Care (EMBARC) study, we propose a novel RL-HMM (hidden Markov model) framework for analyzing reward-based decision-making. Our model accommodates decision-making strategy switching between two distinct approaches under an HMM: subjects making decisions based on the RL model or opting for random choices. We account for continuous RL state space and allow time-varying transition probabilities in the HMM. We introduce a computationally efficient Expectation-maximization (EM) algorithm for parameter estimation and use a nonparametric bootstrap for inference. Extensive simulation studies validate the finite-sample performance of our method. We apply our approach to the EMBARC study to show that MDD patients are less engaged in RL compared to the healthy controls, and engagement is associated with brain activities in the negative affect circuitry during an emotional conflict task.

Evaluation of orthogonal composite designs for second‐order model in presence of missing observation

AbstractOrthogonal‐array composite designs (OACDs) and orthogonal‐uniform composite designs (OUCDs) are orthogonal composite designs that combine two‐level full or fractional factorial and three‐level orthogonal‐array/uniform designs for estimation of the linear, bilinear, and quadratic effects in a second‐order response surface model. In this study, the effects of missing one observation in the various design portions (factorial (f) axial (a) and center (c)), on the precision of parameter estimates, prediction variance and design efficiency of OACDs and OUCDs for 5 ≤ k ≤ 9 factors at different values of α (the distance of a non‐zero co‐ordinate in an additional design point from the center) are evaluated. The results showed that missing a factorial and an axial point have adverse effect on the precision of parameter estimates of OACDs and OUCDs, while missing a center point has little effect. Missing an axial point caused the highest effect on the prediction variance and design efficiencies. The FDS plots showed OACDs to be better designs for k ≤ 7 and OUCDs for k = 8 and 9 factors.

BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification

Data-driven inverse optimization (IO) aims to estimate unknown parameters in an optimization model from observed decisions. The IO problem is commonly formulated as a large-scale bilevel program that is notoriously difficult to solve. We propose a derivative-free optimization approach based on Bayesian optimization, BO4IO, to solve general IO problems. The main advantages of BO4IO are two-fold: (i) it circumvents the need of complex reformulations or specialized algorithms and can hence enable computational tractability even when the underlying optimization problem is nonconvex or involves discrete variables, and (ii) it allows approximations of the profile likelihood, which provide uncertainty quantification on the IO parameter estimates. Our extensive computational results demonstrate the efficacy and robustness of BO4IO to estimate unknown parameters from small and noisy datasets. In addition, the proposed profile likelihood analysis effectively provides good approximations of the confidence intervals on the parameter estimates and assesses the identifiability of the unknown parameters.

Modeling the co-circulation of influenza and COVID-19 in Hong Kong, China

BackgroundAfter abandoning the zero-case strategy for COVID-19 in December 2022 in mainland China, the Hong Kong Special Administrative Region of China (HKSAR) has undergone an anticipated surge of the prevalence of COVID-19, as well as other influenzas, such as influenza A/H1N1, influenza A/H3N2, and influenza B as well. Noteworthy, people are usually concerned about the mutual influences between two families of respiratory viruses, like co-circulation or co-infection.MethodsWe fitted a unified model to weekly reported severe COVID-19 cases and the confirmed influenza A laboratory cases in HKSAR, respectively, using the R package POMP to obtain the best fitting and parameter estimates. The reconstructed transmission rates of the COVID-19 (/influenza A) versus the weekly reported influenza A (/COVID-19) confirmations between April 2022 and April 2024 were also compared.ResultsOur numerical results suggest that influenza confirmations remained either at a very low level or were absent before 2023, while starting from 2023, the influenza epidemic re-emerged as expected because of the resumption of international travels and other social communications. Besides, the peak of influenza cases in April 2023 favored the form of the peak of COVID-19 between May–June, 2023.Additionally, during the sudden abolishment of the zero-case policy in mainland China (December 2022 to January 2023), we estimated that there were approximately 381 cases imported from mainland China into HKSAR.ConclusionsWe estimated the potential number of imported COVID-19 severe cases from mainland China to Hong Kong and revealed some potential population-level interference between the two families of respiratory viruses.

A General Framework for Generating Three-Components Heavy-Tailed Distributions with Application

AbstractThe estimation of a certain threshold beyond which an extreme value distribution can be fitted to the tail of a data distribution remains one of the main issues in the theory of statistics of extremes. While standard Peak over Threshold (PoT) approaches determine this threshold graphically, we introduce in this paper a general framework which makes it possible for one to determine this threshold algorithmically by estimating it as a free parameter within a composite distribution. To see how this threshold point arises, we propose a general framework for generating three-component hybrid distributions which meets the need of data sets with right heavy-tail. The approach involves the combination of a distribution which can efficiently model the bulk of the data around the mean, with an heavy-tailed distribution meant to model the data observations in the tail while using another distribution as a link to connect the two. Some special examples of distributions resulting from the general framework are generated and studied. An estimation algorithm based on the maximum likelihood method is proposed for the estimation of the free parameters of the hybrid distributions. Application of the hybrid distributions to the S &P 500 index financial data set is also carried out.

Statistical models of ballot truncation in ranked choice elections

We introduce and study two new statistical models of ballot truncation – the process wherein voters neglect to rank every candidate during ranked choice voting (RCV). These models allow the incorporation of ballot truncation into simulations of ranked choice elections, resulting in more realistic predictions of likely outcomes. Our Independent Truncation model is based on a survival analysis approach, while our Plackett-Luce Truncation model extends the classical Plackett-Luce ranking model. Using ballot data from Cambridge MA elections, we motivate our new models and fit them to obtain parameter estimates. We then demonstrate our models in a simulation study to measure the effect of ballot truncation on minority representation in a hypothetical multi-winner election.