Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging. The multimodality of the likelihood function and the so called label switching problem contribute to the challenge. We propose extensions of the Approximate Bayesian Computation Population Monte-Carlo (ABC-PMC) algorithm as an alternative framework for inference on finite mixture models. There are several decisions to make when implementing an ABC-PMC algorithm for finite mixture models, including the selection of the kernel used for moving the particles through the iterations, how to address the label switching problem and the choice of informative summary statistics. Examples are presented to demonstrate the performance of the proposed ABC-PMC algorithm for mixture modeling.

中文翻译：

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有限混合模型的近似贝叶斯计算

有限混合模型用于统计学和其他学科，但混合模型的推理具有挑战性。似然函数的多峰性和所谓的标签切换问题促成了这一挑战。我们提出了近似贝叶斯计算种群蒙特卡罗 (ABC-PMC) 算法的扩展，作为对有限混合模型进行推理的替代框架。在为有限混合模型实现 ABC-PMC 算法时，需要做出几个决定，包括选择用于通过迭代移动粒子的内核、如何解决标签切换问题以及选择信息汇总统计。举例说明了所提出的用于混合建模的 ABC-PMC 算法的性能。