Approximate Bayesian Computation: A Nonparametric Perspective
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近似贝叶斯计算的非参数视角
- 研究问题
- 近似贝叶斯计算通过摘要统计量近似后验时，拒绝采样及回归调整各有何偏差与方差，哪些关系下调整可能改善表现？
- 方法与思路
- 作者从条件密度估计角度分析拒绝采样与线性调整，提出二次调整，并通过变换摘要统计量使其与参数的关系更接近同方差。
- 材料陈述的贡献
- 摘要称，二次调整的偏差项比线性调整更少；调整方法并非普遍更优，但在参数与摘要统计量关系近同方差时可能改善。
- 阅读关注点
- 应核对偏差方差展开的条件、摘要统计量与参数的维度、二次调整和变换规则，以及示例中同方差程度与评价指标。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；更少偏差项不保证更小总误差，具体正则条件及各示例的改善幅度未说明。
原文摘要
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics sobs from the data and simulating summary statistics for different values of the parameter Θ. The posterior distribution is then approximated by an estimator of the conditional density g(Θ|sobs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment and of the transformations of the summary statistics. Supplemental materials containing the details of the proofs are available online.