Approximate Confidence Distribution Computing
Approximate Confidence Distribution Computing
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DOI：
10.51387/23-nejsds38
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
S. Thornton;Wentao Li;Min‐ge Xie
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文献类型：
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作者：
S. Thornton;Wentao Li;Min‐ge Xie
近似置信分布计算（ACDC）提供了一个新的采取迅速发展的领域的似然自由推断从频率论的框架。这种统计推断的计算方法的吸引力取决于置信分布的概念，这是一种特殊类型的估计量，是相对于重复抽样原则定义的。ACDC方法为未知或难以处理的可能性问题中的计算推理提供了频率论验证。这项工作的主要理论贡献是识别的频率有效性从这种方法的推断所需的匹配条件。除了提供一个例子，如何现代理解的置信分布理论可以用来连接贝叶斯和频率论推理范式，我们提出了一个案例，扩大目前的范围，所谓的近似贝叶斯推理，包括非贝叶斯推理的目标是一个置信分布，而不是后验。这项工作的主要实际贡献是开发了一种数据驱动的方法，在贝叶斯或频率论的背景下驱动ACDC。ACDC算法通过选择依赖于数据的建议函数来进行数据驱动，该建议函数的结构非常通用并且适用于许多设置。我们探讨了三个数值例子，既验证了ACDC的发展中的理论论点，并建议ACDC优于近似贝叶斯计算方法的计算实例。
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 three 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.