In recent years, simulation-based inferences have garnered significant attention due to the inherent challenges in directly computing likelihood functions for many real-world problems. Iterated filtering (Ionides et al., 2006, 2011b) has emerged as a method to maximize likelihood functions by perturbing models and approximating the gradient of log-likelihood through sequential Monte Carlo filtering. Using Stein’s identity, Doucet et al. (2013) devised a second-order approximation of the gradient of log-likelihood using sequential Monte Carlo smoothing. In this paper, we first generalize Stein’s identity for normal distribution to p-generalized Gaussian distribution, enabling more flexible perturbation with different tail behaviors. Building upon these gradient approximations, we introduce a novel weighted average algorithm for maximizing likelihood through the two-time-scale stochastic approximation. We integrate the algorithm into the iterated filtering framework, relaxing the requirement for an unbiased and bounded variance of the two-time-scale stochastic approximation. We demonstrate the potential of this algorithm in fitting both linear and non-linear complex scientific problems.
