论文标题
在高斯近似贝叶斯后分布上
On The Gaussian Approximation To Bayesian Posterior Distributions
论文作者
论文摘要
本文得出了将贝叶斯后验分布视为高斯所需的最小数字$ n $。提出了两个例子。在其中一个中，卡方分布，可观察的$ x $以及参数$ξ$在整个真实轴上定义，另一个是二项式分布，可观察的$ x $是整个数字，而参数$ξ$是在真实轴心的有限间隔下定义的。在第一种情况下，所需的最小$ n $在二项式模型中很高，较低。在这两种情况下，$ξ$的规模上的度量$μ$的精确定义至关重要。
The present article derives the minimal number $N$ of observations needed to consider a Bayesian posterior distribution as Gaussian. Two examples are presented. Within one of them, a chi-squared distribution, the observable $x$ as well as the parameter $ξ$ are defined all over the real axis, in the other one, the binomial distribution, the observable $x$ is an entire number while the parameter $ξ$ is defined on a finite interval of the real axis. The required minimal $N$ is high in the first case and low for the binomial model. In both cases the precise definition of the measure $μ$ on the scale of $ξ$ is crucial.
