We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise constant or piecewise linear functions, that differ for the specific situations at hand. Posterior consistency and in most cases contraction rates for the estimators are presented. Numerical studies on simulated and real data accompany the theoretical results.

翻译：本文综述了我们在多种随机过程的贝叶斯非参数推断方面的一些最新研究成果。其共同特征是，在所考虑的情形中，先验分布均定义在适当的分段常数或分段线性函数集合上，且这些集合因具体场景而异。我们给出了后验一致性以及多数情况下估计量的收缩速率。伴随理论结果，还提供了基于模拟和真实数据的数值研究。