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高维贝叶斯模型中 Metropolis-within-Gibbs 方案的可扩展性AI 解读

Abstract We study general coordinate-wise Markov chain Monte Carlo schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding (potentially not implementable) random scan Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate…

Ascolani、Lijoi 与 Prünster 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 timely and insightful contribution, which introduces a novel Bayesian approach to inferring the latent structure (early history and community detection) given a current observation of a network with n nodes. The Bayesian component of the model is summarized through a uniform prior on the random relabelling associated to the observed network. The methodological innovation is remarkably complemented by strong theoretical (frequentist)…

贝叶斯层级模型中 Gibbs 采样器的维度无关混合时间AI 解读

Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performance, however, there are still relatively few quantitative results on their convergence properties, for example, much less than for gradient-based sampling methods. In this work, we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from…

Ascolani、Lijoi与Prünster对《鞅后验分布》的讨论AI 解读

We would like to congratulate the authors on their fine and insightful contribution, which provides an original perspective on Bayesian inference and opens up new exciting research directions. The key point is a novel interpretation of the role of prediction: in a Bayesian framework all the uncertainty lies in the unobserved data Yn+1,∞ and, once they are imputed through the predictive distributions, inference is straightforward. Therefore, prediction rules, besides allowing…