论文标题
客观先验中的电力法分布
Power laws distributions in objective priors
论文作者
论文摘要
贝叶斯应用程序中的客观先验的使用已成为一种常见的实践，可以在没有主观信息的情况下分析数据。正式规则通常会获得这些先验分布，并且数据提供了后验分布中的主要信息。但是，这些先验通常是不适当的，可能导致后方不当。在这里，我们在这里表明，对于一般的分布家族，获得的参数获得的客观先验遵循幂律分布或具有渐近的幂律行为。结果，我们观察到该模型的指数在0.5到1之间。了解这些行为使我们可以轻松地验证此类先验是否直接从幂律的指数直接导致正确或不当的后代。我们的研究中考虑的一般家庭包括指数，伽玛，威布尔，中Nakagami-M，Haf-Normal，Rayleigh，Erlang和Maxwell Boltzmann分布等基本模型。总而言之，我们表明，理解描述先验的形状的机制提供了必不可少的信息，可以在提出额外复杂性的情况下使用。
The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the posterior distribution. However, these priors are typically improper and may lead to improper posterior. Here, we show, for a general family of distributions, that the obtained objective priors for the parameters either follow a power-law distribution or has an asymptotic power-law behavior. As a result, we observed that the exponents of the model are between 0.5 and 1. Understand these behaviors allow us to easily verify if such priors lead to proper or improper posteriors directly from the exponent of the power-law. The general family considered in our study includes essential models such as Exponential, Gamma, Weibull, Nakagami-m, Haf-Normal, Rayleigh, Erlang, and Maxwell Boltzmann distributions, to list a few. In summary, we show that comprehending the mechanisms describing the shapes of the priors provides essential information that can be used in situations where additional complexity is presented.
