Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable, with the notable exception of Gaussian processes. Inference of models with non-Gaussian errors typically involves estimation of a high-dimensional latent variable. We propose two methods that use iterated posterior linearization followed by Hamiltonian Monte Carlo to sample the posterior distributions of such latent models with a particular focus on log-Gaussian gamma processes. The proposed methods are validated with two synthetic datasets generated from the log-Gaussian gamma process and a multiscale biocomposite stiffness model. In addition, we apply the methodology to an experimental Raman spectrum of argentopyrite.

翻译：随机过程是统计建模中一类灵活且广泛应用的模型族。尽管随机过程具备诸如包含不确定性特性等吸引人的性质，但其推断通常难以处理，高斯过程是显著的例外。具有非高斯误差的模型推断通常涉及对高维潜变量的估计。我们提出了两种方法，它们采用迭代后验线性化并结合哈密顿蒙特卡洛，来对此类潜模型的后验分布进行采样，并特别关注对数-高斯伽马过程。所提方法通过两个由对数-高斯伽马过程生成的人工数据集以及一个多尺度生物复合材料刚度模型进行了验证。此外，我们将该方法应用于实验获得的硫银铁矿拉曼光谱。