Maximum Likelihood Estimation
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Related Articles from SNS
Lagrange multipliers in Maximum likelihood estimations and Least squares problems with Constraints
Announce Type: cross Abstract: This study investigates a statistical property of Lagrange multipliers in constrained Maximum Likelihood Estimation (MLE) and Least Squares (LS) problems from the perspective of numerical optimization. Building on large-sample theory, we show that the associated Lagrange multipliers converge to zero as the sample size increases, provided the distribution is correctly specified in MLE or the residuals are normally distributed in LS. Although this asymptotic...
A Counting Process View of Relational Event Models: Practical Asymptotics
arXiv:2606.07680v1 Announce Type: cross Abstract: Relational Event Models (REMs) provide a rigorous framework for analyzing dyadic interactions observed in continuous time, capturing history-dependent dynamics such as triadic closure and reciprocity. Framing REMs through the lens of counting processes embeds the model in a rich theoretical foundation, facilitating its mathematical analysis. While Maximum Likelihood Estimation (MLE) is standard practice for estimating these models, the...
Estimating Bidirectional Causal Effects with Large Scale Online Kernel Learning
Announce Type: replace-cross Abstract: In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on unidirectional effects, overlooking the common bidirectional relationships in real-world phenomena. Building on heteroskedasticity-based identification, the proposed method integrates a quasi-maximum likelihood estimator for...
Detecting Cyber Attacks in Power System AGC Using a Drifted Ornstein-Uhlenbeck Process
arXiv:2606.02075v1 Announce Type: new Abstract: The Automatic Generation Control (AGC) system, reliant on real-time measurements over communication networks, is susceptible to stealthy false data injection attacks (FDIAs), risking equipment damage and economic losses. We propose a robust FDIA detection method using maximum likelihood estimation (MLE) of a drifted multivariate Ornstein-Uhlenbeck (OU) process.
Improving the Accuracy of Forensic Age Estimation Through Bias Reduction
Chronological age estimation can provide supporting information in forensic casework when traditional identification methods are limited. DNA methylation, a stable epigenetic mark, has emerged as a promising tool for predicting chronological age from trace samples. However, many existing age estimation models rely on linear regression approaches, which often yield biased prediction errors across the age distribution (i.e. model residuals show a significant age dependence).
Magnetometry with Broadband Microwave Fields in Nitrogen-Vacancy Centers in Diamond
arXiv:2510.11720v2 Announce Type: replace-cross Abstract: Nitrogen-vacancy (NV) centers in diamond are optically addressable and versatile light-matter interfaces with practical application in magnetic field sensing, offering the ability to operate at room temperature and reach sensitivities below pT/$\sqrt{\mathrm{Hz}}$. We propose an approach to simultaneously probe all of the magnetically sensitive states using a broadband microwave field and demonstrate that it can be used to measure the...
Gene ancestries reveal diverse microbial associations during eukaryogenesis
Abstract The origin of eukaryotes remains a central enigma in biology1. Continuing debates agree on the pivotal role of a symbiosis between an alphaproteobacterium and an Asgard archaeon2,3. However, the nature, timing and contributions of other potential bacterial partners4,5,6 and the role of interactions with viruses7,8,9 remain contentious.
Generalized TV--$\ell_p$ Structured Priors for Bayesian $T_1$ Mapping
arXiv:2606.05381v1 Announce Type: new Abstract: We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with $\ell_p$ norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in $T_1$ mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV--$\ell_p$ construction is proven to constitute a well-defined family of prior distributions,...
Deep learning four decades of human migration
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Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps
Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density....