Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation
近似贝叶斯计算 MCMC 核的方差有界性与几何遍历性AI 解读 ↓
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近似贝叶斯计算 MCMC 核的方差有界性与几何遍历性
- 研究问题
- 似然难以计算时，近似贝叶斯计算常用的 MCMC 核是否具有方差有界性与几何遍历性，替代核又能否继承理想核的性质？
- 方法与思路
- 作者分析常用核失去遍历性质的机制，研究一种替代核从不可计算的 Metropolis–Hastings 核继承性质的条件，并讨论计算成本。
- 材料陈述的贡献
- 摘要称常用核的性质失效通常不取决于容差；替代核可在条件下继承相关性质，并给出可逆核及其混合的两个一般定理。
- 阅读关注点
- 应核对方差有界性与几何遍历性的逻辑关系、继承性质的条件、计算成本有界的含义，以及谱隙和渐近方差例子的范围。
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- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未列出定理条件或成本界，不能认定适当先验足以保证所有 ABC 算法高效可靠。
原文摘要
Approximate Bayesian computation has emerged as a standard computational tool when dealing with intractable likelihood functions in Bayesian inference. We show that many common Markov chain Monte Carlo kernels used to facilitate inference in this setting can fail to be variance bounding and hence geometrically ergodic, which can have consequences for the reliability of estimates in practice. This phenomenon is typically independent of the choice of tolerance in the approximation. We prove that a recently introduced Markov kernel can inherit the properties of variance bounding and geometric ergodicity from its intractable Metropolis–Hastings counterpart, under reasonably weak conditions. We show that the computational cost of this alternative kernel is bounded whenever the prior is proper, and present indicative results for an example where spectral gaps and asymptotic variances can be computed, as well as an example involving inference for a partially and discretely observed, time-homogeneous, pure jump Markov process. We also supply two general theorems, one providing a simple sufficient condition for lack of variance bounding for reversible kernels and the other providing a positive result concerning inheritance of variance bounding and geometric ergodicity for mixtures of reversible kernels.