In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time and/or space, in order to practically work with the probability of interest. Given access only to these discretizations, we consider the construction of unbiased Monte Carlo estimators of expectations w.r.t. such target probability distributions. It is shown how to obtain such estimators using a novel adaptation of randomization schemes and Markov simulation methods. Under appropriate assumptions, these estimators possess finite variance and finite expected cost. There are two important consequences of this approach: (i) unbiased inference is achieved at the canonical complexity rate, and (ii) the resulting estimators can be generated independently, thereby allowing strong scaling to arbitrarily many parallel processors. Several algorithms are presented, and applied to some examples of Bayesian inference problems, with both simulated and real observed data.

中文翻译：

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离散模型的无偏估计

在本文中，我们考虑计算带有离散化误差的概率测度的期望值。示例包括部分观察到的扩散过程或逆问题，其中可能必须离散化时间和/或空间，以便实际以感兴趣的概率工作。如果仅获得这些离散化，我们将考虑使用此类目标概率分布的期望的无偏蒙特卡洛估计量的构造。它显示了如何使用新颖的随机化方案和马尔可夫仿真方法获得此类估计量。在适当的假设下，这些估计量具有有限的方差和有限的预期成本。这种方法有两个重要的后果：（i）以规范的复杂度实现无偏推论，（ii）可以独立生成结果估计器，从而可以对任意多个并行处理器进行强大的缩放。提出了几种算法，并将其应用于贝叶斯推理问题的一些示例，包括模拟数据和实际观测数据。