The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance depends on a key parameter, N, the number of iterations (or particles) used to approximate the target density. Larger values of N yield more accurate estimates but at increased running time. Previous studies has provided guidelines for selecting an optimal value of N to balance this tradeoff. However, this approach involves multiple steps and manual adjustments. To overcome these limitations, we introduce an adaptive version of the PM algorithm, where N is automatically adjusted during the iterative process toward its optimal value, thus eliminating the need for manual intervention. This algorithm ensures convergence under certain conditions. On two examples, including a real data problem on pulmonary infection in preschool children, the proposed algorithm compares favorably to the existing approach.

翻译：伪边际（PM）算法是一种常用的马尔可夫链蒙特卡洛（MCMC）方法，用于在目标分布密度函数不可直接获取但可通过非负无偏估计器近似时进行采样。其性能取决于一个关键参数N，即用于近似目标密度的迭代次数（或粒子数）。较大的N值能提供更精确的估计，但会显著增加运行时间。先前的研究已为选择最优N值以平衡此权衡提供了指导原则。然而，该方法涉及多个步骤且需人工调整参数。为克服这些限制，本文提出一种自适应版本的PM算法，该算法在迭代过程中自动将N调整至最优值，从而无需人工干预。该算法在特定条件下能保证收敛性。通过两个实例（包括一项关于学龄前儿童肺部感染的真实数据分析）的验证，本算法相较于现有方法表现出更优的性能。