This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation framework, which employs a multi-time scale stochastic approximation algorithm. This approach effectively addresses the ratio bias that arises in both maximum likelihood estimation and posterior density estimation problems. The proposed algorithm enhances estimation accuracy and significantly reduces computational costs, as demonstrated through extensive numerical experiments. Our work extends the GSPE framework to handle complex models such as hidden Markov models and variational inference-based problems, offering a robust solution for parameter estimation in challenging stochastic environments.

翻译：本文针对随机模型中的参数校准挑战展开研究，特别关注似然函数无法以解析形式获取的场景。我们提出一种基于梯度的模拟参数估计框架，该框架采用多时间尺度的随机逼近算法。该方法有效解决了最大似然估计和后验密度估计中出现的比率偏差问题。如大量数值实验所示，所提算法在提升估计精度的同时显著降低了计算成本。我们的工作将GSPE框架扩展至隐马尔可夫模型和基于变分推断的复杂模型问题，为具有挑战性的随机环境中的参数估计提供了稳健解决方案。