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鞅后验分布AI 解读

Abstract The prior distribution is the usual starting point for Bayesian uncertainty. In this paper, we present a different perspective that focuses on missing observations as the source of statistical uncertainty, with the parameter of interest being known precisely given the entire population. We argue that the foundation of Bayesian inference is to assign a distribution on missing observations conditional on what has been observed. In the i.i.d. setting with an observed…

频数的频数分布与依赖总体规模的可交换随机划分AI 解读

Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this article introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions. A cluster structure, naturally arising from a completely random measure mixed Poisson process, allows the probability distribution of the random partitions of a subset of a population to be…

贝叶斯密度估计中非参数正态混合的一致性AI 解读

The past decade has seen a remarkable development in the area of Bayesian nonparametric inference from both theoretical and applied perspectives. As for the latter, the celebrated Dirichlet process has been successfully exploited within Bayesian mixture models, leading to many interesting applications. As for the former, some new discrete nonparametric priors have been recently proposed in the literature that have natural use as alternatives to the Dirichlet process in a…

利用辅助变量构造平稳时间序列模型及其应用AI 解读

Here we present a novel method for modeling stationary time series. Our approach is to construct the model with a specified marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. We construct models that parallel existing structures, namely state-space models, autoregressive conditional heteroscedasticity (ARCH) models, and generalized ARCH models. We use Bayesian techniques to…