标题： 期望传播用于贝叶斯经验似然推断 显示英文标题

标题： Expectation-propagation for Bayesian empirical likelihood inference

摘要： 贝叶斯推断通常依赖于指定一个近似数据生成过程的参数模型。 然而，错误设定的模型可能导致收敛速度缓慢和后验校准不可靠。 贝叶斯经验似然通过用通过矩约束定义的轮廓经验似然代替参数似然，提供了一种半参数替代方法，从而避免了显式的分布假设。 尽管有这些优势，贝叶斯经验似然面临显著的计算挑战，包括每次似然评估都需要解决一个约束优化问题，以及在小样本情况下非凸后验支持的困难。 本文引入了一种基于期望传播的变分方法来近似贝叶斯经验似然后验，无需通过伪观测等调整来改变目标后验，从而在计算成本和准确性之间取得平衡。 实证上，我们展示了我们的方法相对于现有方法（包括哈密顿蒙特卡洛和变分贝叶斯）可以实现更优的成本-精度权衡。 理论上，我们证明了近似结果和贝叶斯经验似然后验是渐近等价的。 显示英文摘要

摘要： Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical likelihood offers a semi-parametric alternative by replacing the parametric likelihood with a profile empirical likelihood defined through moment constraints, thereby avoiding explicit distributional assumptions. Despite these advantages, Bayesian empirical likelihood faces substantial computational challenges, including the need to solve a constrained optimization problem for each likelihood evaluation and difficulties with non-convex posterior support, particularly in small-sample settings. This paper introduces a variational approach based on expectation-propagation to approximate the Bayesian empirical-likelihood posterior, balancing computational cost and accuracy without altering the target posterior via adjustments such as pseudo-observations. Empirically, we show that our approach can achieve a superior cost-accuracy trade-off relative to existing methods, including Hamiltonian Monte Carlo and variational Bayes. Theoretically, we show that the approximation and the Bayesian empirical-likelihood posterior are asymptotically equivalent.