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后验分布的偏斜对称近似AI 解读

Abstract Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric families, often taken to be Gaussian. This choice facilitates optimization and inference, but typically affects the quality of the approximation. In fact, even in basic parametric models, posterior distributions often display asymmetries that yield bias and reduced accuracy when considering…

基于 Rademacher 复杂度的差异型近似贝叶斯计算后验集中理论AI 解读

There has been an increasing interest on summary-free solutions for approximate Bayesian computation (abc) that replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these strategies has motivated theoretical studies on the limiting properties of the induced posteriors. However, there is still the lack of a theoretical framework for…

偏斜 Bernstein–von Mises 定理与偏斜模态近似AI 解读

Gaussian deterministic approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. Although these approximations are justified, in asymptotic regimes, by Bernstein-von Mises type results, in practice the expected Gaussian behavior might poorly represent the actual shape of the target posterior, thus affecting approximation accuracy. Motivated by these considerations, we derive an improved class of closed-form and…

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…

无限分解的贝叶斯累积收缩AI 解读

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing…

通过统一偏斜正态分布实现 probit 回归的共轭贝叶斯推断AI 解读

Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the…

网络总体的贝叶斯非参数建模AI 解读

Replicated network data are increasingly available in many research fields. For example, in connectomic applications, interconnections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued…