Temporal point processes are essential for modeling event dynamics in fields such as neuroscience and social media. The time rescaling theorem is commonly used to assess model fit by transforming a point process into a homogeneous Poisson process. However, this approach requires that the process be nonterminating and that complete (hence, unbounded) realizations are observed—conditions that are often unmet in practice. This article introduces a generalized time-rescaling theorem to address these limitations and, as such, facilitates a more widely applicable evaluation framework for point process models in diverse real-world scenarios.

Probabilistic neural networks (PNN) and general regression neural networks (GRNN) represent knowledge by simple but interpretable models that approximate the optimal classifier or predictor in the sense of expected value of the accuracy. These models require the specification of an important smoothing parameter, which is usually chosen by cross-validation or clustering. In this article, we demonstrate the problems with the cross-validation and clustering approaches to specify the smoothing parameter, discuss the relationship between this parameter and some of the data statistics, and attempt to develop a fast approach to determine the optimal value of this parameter. Finally, through experimentation, we show that our approach, referred to as a gap-based estimation approach, is superior in speed to the compared approaches, including support vector machine, and yields good and stable accuracy.