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：本文综述了我们近期在多种随机过程贝叶斯非参数推断方面取得的若干成果。其共同特征在于，所考虑情形中的先验分布均定义于适当的分段常数或分段线性函数集上，这些函数集因具体场景而异。我们给出了后验相合性，并在大多数情形下给出了估计量的收缩率。伴随理论结果，我们还提供了基于模拟数据和真实数据的数值研究。