Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation
Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation
复制标题
用于近似贝叶斯计算的马尔可夫链蒙特卡洛核的方差有界和几何遍历性
DOI：
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Krzysztof Latuszynski
中科院分区：
文献类型：
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作者：
Anthony Lee;Krzysztof Latuszynski
近似贝叶斯计算已经成为一个标准的计算工具时，处理棘手的似然函数的贝叶斯推理。我们发现，许多常见的马尔可夫链蒙特卡罗内核，以方便在这种情况下的推理可能无法方差边界，因此几何遍历，这可能会产生后果的可靠性估计在实践中。这种现象通常与近似中公差的选择无关。我们证明，最近推出的马尔可夫核可以继承其棘手的Metropolis-Hastings对应的方差界和几何遍历的属性，在合理的弱条件下。我们表明，这种替代内核的计算成本是有界的，只要事先是适当的，并提出指示性的结果的一个例子，其中可以计算谱间隙和渐近方差，以及一个例子，涉及部分和离散观察，时间齐次，纯跳马尔可夫过程的推断。我们还提供了两个一般定理，一个提供了一个简单的充分条件，缺乏可逆内核的方差界和其他提供了一个积极的结果，关于继承的方差界和几何遍历的混合物的可逆内核。
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.
DOI：
10.1214/14-aap1022
发表时间：
2015
期刊：
The Annals of Applied Probability
影响因子：
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作者：
Andrieu C
通讯作者：
Andrieu C
影响因子：
10.7
作者：
Pritchard, JK;Seielstad, MT;Feldman, MW
通讯作者：
Feldman, MW