Search Results (16)

In longitudinal studies, a terminal event such as death typically halts data collection, and patients may exhibit marked changes as they approach the event. Existing methods face three related challenges: interpreting the effect of residual life on the longitudinal response, accommodating time-varying covariates and coefficients, and retaining information from censored individuals. We propose a joint model that addresses these challenges in a unified likelihood framework. The longitudinal submodel includes an explicit residual-life effect $g(T_i-t,\mathit{\xi })$, time-varying covariates ${\mathbf{X}}_i\left(t\right)$ with time-varying coefficients $\mathit{\beta }\left(t\right)$, and shared random effects. Exponential-decay and Gaussian-kernel specifications are considered for $g(·)$. The survival submodel depends on the latent state $m_i\left(t\right)={\mathbf{X}}_i{\left(t\right)}^{\top }\mathit{\beta }\left(t\right)+{\mathbf{Z}}_i{\left(t\right)}^{\top }{\mathbf{b}}_i$. The coefficient functions are approximated by B-splines, and the full observed-data likelihood is maximized numerically with random-effects integrals evaluated by Gauss–Hermite quadrature. Under the stated regularity conditions, we establish consistency, root-n asymptotic normality of the finite-dimensional parameters, and the sieve convergence rate of the time-varying coefficient functions. Simulation studies demonstrate accurate recovery of the coefficient and residual-life functions. In the MADIT application, the fitted hazard ratio for ICD implantation is 0.433, and the residual-life effect indicates an increase in medical costs approximately three weeks before death. Full article

Modeling count data using generalized linear mixed models (GLMMs) is a common practice in ecological research. However, datasets such as bird vocalization counts often display overdispersion, where the variance exceeds the mean, violating Poisson assumptions and potentially leading to biased inference. This study investigates the call counts of owl nestlings by comparing Poisson and Negative Binomial (NB) GLMMs to assess the impact of overdispersion on model performance. The models incorporate a random intercept for nest identity, thereby accounting for the hierarchical structure of the data and the correlation among observations within the same nest. Parameter estimation was performed using the Laplace approximation and the Adaptive Gauss–Hermite Quadrature (AGHQ) method to evaluate likelihood-based inference under different estimation approaches. Although the overdispersion diagnostic indicated extra-Poisson variation, model comparison based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and log-likelihood showed that the Poisson GLMM provided a better overall fit than the NB-GLMM. These findings demonstrate that the presence of overdispersion alone does not necessarily justify replacing a Poisson GLMM with a NB-GLMM and highlight the importance of combining distributional diagnostics with likelihood-based model selection when analyzing hierarchical ecological count data. Full article

Nonlinear state estimation plays an important role in aerospace sensing applications, where estimation accuracy must be balanced against computational efficiency. In this paper, a sparse-grid Gaussian kernel quadrature Kalman filter (SGKQKF) is proposed for discrete-time nonlinear state estimation by combining Gaussian kernel quadrature (GKQ) weighting with a Smolyak sparse-grid construction. The univariate GKQ rule is constructed on scaled Gauss–Hermite nodes through a truncated Mercer eigendecomposition of the Gaussian kernel and is then extended to multivariate cases via the Smolyak construction to alleviate the curse of dimensionality associated with tensor-product rules. The proposed method is positioned within the established sparse-grid filtering framework, with the specific contribution of integrating kernel-adapted quadrature weights into sparse-grid structures for discrete-time nonlinear Gaussian filtering. For fixed nodes, the exact kernel-quadrature weights minimize the worst-case integration error in the reproducing kernel Hilbert space (RKHS) induced by the Gaussian kernel, whereas the closed-form weights used in the implementation are interpreted as a Mercer-based practical approximation to this exact rule, with the approximation error characterized through the Mercer spectral-tail expression of the Gaussian kernel. For sparse grids, where a closed-form RKHS optimality result is not available, numerical maximum mean discrepancy (MMD) evaluations are presented as empirical diagnostics in the tested configurations. Numerical experiments demonstrate that the proposed filter achieves a favorable accuracy–efficiency trade-off compared with conventional deterministic Gaussian filters. Full article

In this study, the Monte Carlo (MC) method is employed to generate the diameter and relative positional distributions of carbon nanotubes (CNTs). Based on this, we develop a three-layer thermal model for a copper-carbon nanotube (Cu-CNT) through-silicon via (TSV). By integrating Gauss–Hermite quadrature with the Law of Large Numbers (LLN), an analytical expression for thermal conductivity is derived, enabling efficient and accurate estimation of the thermal conductivity of Cu-CNT-filled TSV. Contrary to expectations, the thermal conductivity of TSV does not increase significantly with CNT volume fraction, primarily due to the interfacial thermal resistance at Cu-CNT and CNT-CNT junctions. Through calibration against previously reported experimental data, the effective Cu-CNT interfacial thermal resistance is estimated to be on the order of 10⁻⁷ m²K/W. Comparison with previously reported effective thermal conductivity data of Cu-CNT composites shows that the model maintains an error below 2% when the CNT volume fraction is below 10%. The model is therefore most suitable for low CNT volume fractions, where the assumed spatial distribution and structural simplifications remain physically valid. Furthermore, this study investigates the influence of TSV length on thermal performance, predicts the variation in thermal conductivity of Cu-CNT composites under different volume fractions, and the extracted thermal conductivity values are further used as material inputs for device-level electro-thermal COMSOL 6.1 simulations. Full article

We introduce Causal Incentive Design (CID), a framework that applies causal inference to canonical single-stage principal–agent problems (PAPs) characterized by bilateral private information. Within CID, the operating rules of PAPs are formalized using an additive-noise causal graphical model (CGM). Incentives are modeled as interventions on a function space variable, $\Gamma$, which correspond to policy interventions in the principal–follower causal relation. The causal inference target estimand $V(\Gamma )$ is defined as the expected value of the principal’s utility variable under a specified policy intervention in the post-intervention distribution. In the context of additive-Gaussian independent noise, the estimand $V(\Gamma )$ decomposes into a two-layer expectation: (i) an inner Gaussian smoothing of the principal’s utility regression; and (ii) an outer averaging over the conditional probability of the follower’s action given the incentive policy. A Gauss–Hermite quadrature method is employed to efficiently estimate the first layer, while a policy-local kernel reweighting approach is used for the second. For offline selection of a single incentive policy, a Functional Causal Bayesian Optimization (FCBO) algorithm is introduced. This algorithm models the objective functional $\gamma \mapsto V\left(\gamma \right)$ using a functional Gaussian process surrogate defined on a Reproducing Kernel Hilbert Space (RKHS) domain and utilizes an Upper Confidence Bound (UCB) acquisition functional. Consequently, the policy value $V\left(\gamma \right)$ becomes an interventional query that can be answered using offline observational data under standard identifiability assumptions. High-probability cumulative-regret bounds are established in terms of differential information gain for the proposed FBO algorithm. Collectively, these elements constitute the central contributions of the CID framework, which integrates causal inference through identification and estimation with policy search in principal–agent problems under private information. This approach establishes a causal decision-making pipeline that enables commitment to a high-performing incentive in a single-shot game, supported by regret guarantees. Provided that the data used for estimation is sufficient, the resulting offline pipeline is appropriate for scenarios where adaptive deployment is impractical or costly. Beyond the methodological contribution, this work introduces a novel application of causal graphical models and causal reasoning to incentive design and principal–agent problems, which are central to economics and multi-agent systems. Full article

Beta regression models are a class of models used frequently to model response variables in the interval $(0, 1)$. Although there are articles in which these models are used to model clustered and longitudinal data, the prediction of random effects is limited, and residual analysis has not been implemented. In this paper, a random intercept beta regression model is proposed for the complete analysis of this type of data structure. We proposed some types of residuals and formulate a methodology to obtain the best prediction of random effects. This model is developed through the parameterisation of beta distribution in terms of the mean and dispersion parameters. A log-likelihood function is approximated by the Gauss–Hermite quadrature to numerically integrate the distribution of random intercepts. A simulation study is used to investigate the performance of the estimation process and the sampling distributions of the residuals. Full article

This study introduces the Lindley Stochastic Frontier Analysis—LSFA model, a novel approach that incorporates the Lindley distribution to enhance the flexibility and accuracy of efficiency estimation. The LSFA model is compared against traditional SFA models, including the half-normal, exponential, and gamma models, using advanced numerical methods such as the Gauss–Hermite Quadrature, Monte Carlo Integration, and Simulated Maximum Likelihood Estimation for parameter estimation. Simulation studies revealed that the LSFA model outperforms in scenarios involving small sample sizes and complex, skewed distributions, particularly those characterized by gamma distributions. In contrast, traditional models such as the half-normal model perform better in larger samples and simpler settings, while the gamma model is particularly effective under exponential inefficiency distributions. Among the numerical techniques, the Gauss–Hermite Quadrature demonstrates a strong performance for half-normal distributions, the Monte Carlo Integration offers consistent results across models, and the Simulated Maximum Likelihood Estimation shows robustness in handling gamma and Lindley distributions despite higher errors in simpler cases. The application to a banking dataset assessed the performance of 12 commercial banks pre-COVID-19 and during COVID-19, demonstrating LSFA’s superior ability to handle skewed and intricate data structures. LSFA achieved the best overall reliability in terms of the root mean square error and bias, while the gamma model emerged as the most accurate for minimizing absolute and percentage errors. These results highlight LSFA’s potential for evaluating efficiency during economic shocks, such as the COVID-19 pandemic, where data patterns may deviate from standard assumptions. This study highlights the advantages of the Lindley distribution in capturing non-standard inefficiency patterns, offering a valuable alternative to simpler distributions like the exponential and half-normal models. However, the LSFA model’s increased computational complexity highlights the need for advanced numerical techniques. Future research may explore the integration of generalized Lindley distributions to enhance model adaptability with enriched numerical optimization to establish its effectiveness across diverse datasets. Full article

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. Full article

Uncertain variables, such as electric power system parameters, have significant impacts on dynamic simulations of power systems. As traditional uncertainty analysis methods for power system dynamic simulations, both the simulation method and the approximation methods are difficult to balance the model complexity, computational efficiency, and simulation accuracy. In order to balance the model complexity, computational efficiency, and simulation accuracy, this paper proposes a method for uncertainty analysis for power system dynamic simulation based on the Nataf transformation and Gaussian-Hermite quadrature. Firstly, the samples on the normal distribution space are determined according to the Gaussian-Hermite quadrature points and the Nataf transformation. Secondly, obtain the simulation samples by inverse Nataf transformation, and perform power system dynamic simulation. Thirdly, the random output is approximated as a linear combination of a single random input, and the mean and standard deviation of the random output under the impact of a single random input are calculated by Gaussian-Hermite quadrature. Then, calculate the mean and standard deviation of the random output under the impact of all random input. Finally, the effectiveness of the proposed method is validated on the IEEE 9-bus system and IEEE 39-bus system. Compared with Monte Carlo simulation and Latin Hypercube sampling, the proposed method can greatly reduce the simulation time for uncertain dynamic simulations while maintaining high accuracy. Full article

As convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadamard inequality, the importance of this paper lies in providing some new improvements for convex functions and new directions in studying new variants of the Hermite–Hadamard inequality. The first part of the article includes some known concepts regarding convex functions and related inequalities. In the second part of the study, a derivation of the Hermite–Hadamard inequality for convex functions of higher order is given, emphasizing the purpose and importance of some quadrature formulas. In the third section, the applications of the main results are presented by obtaining Hermite–Hadamard-type estimates for various classical quadrature formulas such as the Gauss–Legendre two-point quadrature formula and the Gauss–Chebyshev two-point quadrature formulas of the first and second kind. Full article

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind. Full article

In this study, singular integral solutions were studied to investigate scattering of Rayleigh waves by subsurface cracks. Defining a wave scattering model by objects, such as cracks, still can be quite a challenge. The model’s analytical solution uses five different numerical integration methods: (1) the Gauss–Legendre quadrature, (2) the Gauss–Chebyshev quadrature, (3) the Gauss–Jacobi quadrature, (4) the Gauss–Hermite quadrature and (5) the Gauss–Laguerre quadrature. The study also provides an efficient dynamic finite element analysis to demonstrate the viability of the wave scattering model with an optimized model configuration for wave separation. The obtained analytical solutions are verified with displacement variation curves from the computational simulation by defining the correlation of the results. A novel, verified model, is proposed to provide variations in the backward and forward scattered surface wave displacements calculated by different frequencies and geometrical crack parameters. The analytical model can be solved by the Gauss–Legendre quadrature method, which shows the significantly correlated displacement variation with the FE simulation result. Ultimately, the reliable analytic model can provide an efficient approach to solving the parametric relationship of wave scattering. Full article

This paper introduces an estimation procedure for a random effects probit model in presence of heteroskedasticity and a likelihood ratio test for homoskedasticity. The cases where the heteroskedasticity is due to individual effects or idiosyncratic errors or both are analyzed. Monte Carlo simulations show that the test performs well in the case of high degree of heteroskedasticity. Furthermore, the power of the test increases with larger individual and time dimensions. The robustness analysis shows that applying the wrong approach may generate misleading results except for the case where both individual effects and idiosyncratic errors are modelled as heteroskedastic. Full article

Errors in the extracted key parameters directly influence the errors in the temperature and strain measured by fiber Brillouin distributed sensors. Existing key parameter extraction algorithms for Brillouin gain spectra are mainly based on simplified models, therefore, the extracted parameters may have significant errors. To ensure high accuracy in the extracted key parameters in different cases, and consequently to measure temperature and strain with high accuracy, a key parameter extraction algorithm based on the exact Voigt profile is proposed. The objective function is proposed using the least-squares method. The Levenberg-Marquardt algorithm is used to minimize the objective function and consequently extract the key parameters. The optimization process is presented in detail, at the same time the initial values obtainment method and the convergence criterion are given. The influences of the number of sample points in Gauss-Hermite quadrature on the accuracy and the computation time of the algorithm are investigated and a suggestion about the selection of the number of sample points is given. The direct algorithm, the random algorithm and the proposed algorithm are implemented in Matlab and are used to extract key parameters for abundant numerically generated and measured Brillouin gain spectral signals. The results reveal that the direct algorithm requires less computation time, but its errors are considerably larger than that of the proposed algorithm. The convergence rate of the random algorithm is about 80~90%. The proposed algorithm can converge in all cases. Even for the convergence cases, the computation time and the fitting error of the random algorithm are 1~2 times larger than those of the proposed algorithm. Full article

Multi-Unmanned Aerial Vehicle (UAV) Doppler-based target tracking has not been widely investigated, specifically when using modern nonlinear information filters. A high-degree Gauss–Hermite information filter, as well as a seventh-degree cubature information filter (CIF), is developed to improve the fifth-degree and third-degree CIFs proposed in the most recent related literature. These algorithms are applied to maneuvering target tracking based on Radar Doppler range/range rate signals. To achieve this purpose, different measurement models such as range-only, range rate, and bearing-only tracking are used in the simulations. In this paper, the mobile sensor target tracking problem is addressed and solved by a higher-degree class of quadrature information filters (HQIFs). A centralized fusion architecture based on distributed information filtering is proposed, and yielded excellent results. Three high dynamic UAVs are simulated with synchronized Doppler measurement broadcasted in parallel channels to the control center for global information fusion. Interesting results are obtained, with the superiority of certain classes of higher-degree quadrature information filters. Full article