论文检索

多元高斯累积分布函数与对偶贝叶斯 probit 模型的边际似然AI 解读

Summary The computation of multivariate Gaussian cumulative distribution functions is a key step in many statistical procedures, often representing a crucial computational bottleneck. Over the past few decades, efficient algorithms have been proposed to address this problem, mainly using Monte Carlo solutions. This work highlights a connection between the multivariate Gaussian cumulative distribution function and the marginal likelihood of a tailored dual Bayesian probit…

Catalano等对《网络潜在生长过程的根与社群推断》的讨论AI 解读

We congratulate the authors for their methodological and theoretical contribution to the statistical literature on networks. A natural extension of the proposed PAPER model is included, with K communities growing simultaneously and where new nodes are either assigned to an existing community or elected as a new root. The employed assignment rule is of Pólya-urn type, which leads to a logarithmic growth of the number of communities (Korwar & Hollander, 1973) and is known to…

Catalano、Fasano 与 Rebaudo 对《鞅后验分布》的讨论AI 解读

We congratulate the authors for an insightful foundational contribution to the statistical literature. This work builds on well-established methodologies, such as predictive inference, Doob’s theorem, and conditional independent sequences, providing a unifying framework and a novel understanding of Bayesian uncertainty. A central role is played by the predictive characterisation of the random parameter in terms of observable (yet unobserved) quantities, which are regarded as…

Probit、Tobit、多项 Probit 及扩展模型的贝叶斯共轭性：综述与新结果AI 解读

A broad class of models that routinely appear in several fields can be expressed as partially or fully discretized Gaussian linear regressions. Besides including classical Gaussian response settings, this class also encompasses probit, multinomial probit and tobit regression, among others, thereby yielding one of the most widely-implemented families of models in routine applications. The relevance of such representations has stimulated decades of research in the Bayesian…

高维二元回归中可扩展且准确的变分贝叶斯方法AI 解读

Summary Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed in recent literature, bypassing such a trade-off is still an open problem even in routine binary regression models, and there is limited theory on the quality of variational approximations in high-dimensional settings. To address this gap, we study the approximation accuracy of routinely used…