Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference hinges upon the concept of a confidence distribution, a special type of estimator which is defined with respect to the repeated sampling principle. An ACDC method provides frequentist validation for computational inference in problems with unknown or intractable likelihoods. The main theoretical contribution of this work is the identification of a matching condition necessary for frequentist validity of inference from this method. In addition to providing an example of how a modern understanding of confidence distribution theory can be used to connect Bayesian and frequentist inferential paradigms, we present a case to expand the current scope of so-called approximate Bayesian inference to include non-Bayesian inference by targeting a confidence distribution rather than a posterior. The main practical contribution of this work is the development of a data-driven approach to drive ACDC in both Bayesian or frequentist contexts. The ACDC algorithm is data-driven by the selection of a data-dependent proposal function, the structure of which is quite general and adaptable to many settings. We explore two numerical examples that both verify the theoretical arguments in the development of ACDC and suggest instances in which ACDC outperform approximate Bayesian computing methods computationally.
翻译:近似信任分配计算(ACDC)提供了对经常现象框架内快速发展的无概率推断领域的新看法。这种统计推断计算方法的吸引力取决于信任分配的概念,即根据重复抽样原则界定的一种特殊类型的估计标准。ACDC方法为在未知或难解可能性问题中进行计算推断提供了常客验证。这项工作的主要理论贡献是确定一种必要的匹配条件,以便经常地从这一方法中得出无概率推断的有效性。除了提供一个例子说明如何利用现代的信任分配理论来连接贝叶西亚和常态推断模式,我们提出一个案例,以扩大所谓的近似巴伊西亚假设的当前范围,将非巴伊西亚人推断纳入非巴伊西亚人的推断。这项工作的主要实际贡献是发展一种数据驱动方法,在巴伊西亚或经常情况下驱动ACD的经常性推断。ACD算法的现代理解理论是如何利用现代信任分配理论将巴伊西亚人和常态推断模式联系起来的。我们用A类计算算算法的理论和A级算法中的许多数字参数选择了A的理论结构。我们从A级计算模型中推选出了A的理论模型。