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基于三角密度混合的贝叶斯众数回归AI 解读

Bayesian semiparametric models for mean and median regressions abound, but a void for mode regressions exists. We fill this gap by nonparametrically modeling the error distribution in such regressions that entails constructing prior distributions on densities which exhibit flexibility, while fixing the mode at 0. Such priors exist when constraining the mean and median but, to our knowledge, there is none for the mode. Our solution with mixtures of triangular distributions…

贝叶斯一致性的新方法AI 解读

We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback–Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.

论贝叶斯一致性AI 解读

Summary We consider a sequence of posterior distributions based on a data-dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.

通过扩展 Johnson 充分性公设刻画右中性先验AI 解读

In this paper we present a new characterization and perspective on a neutral to the right prior. This characterization is based on a sequence of predictive laws which provides explicitly the posterior parameters and Bayes estimators for such a prior.

贝叶斯自助法与可交换抽球方案族的扩展AI 解读

Summary A Bayesian bootstrap for a finite population with censored observations is introduced. It is shown to reduce to the finite population Bayesian bootstrap if there is no censoring and to reduce to the censored data Bayesian bootstrap for a large population. A class of general urn schemes for simulating exchangeable sequences of variables is introduced which is connected to the bootstrap method.