Through the application of process mining, organisations can improve their business processes by leveraging data recorded as a result of the performance of these processes. Over the past two decades, the field of process mining evolved considerably, offering a rich collection of analysis techniques with different objectives and characteristics. Despite the advances in this field, a solid statistical foundation is still lacking. Such a foundation would allow analysis outcomes to be found or judged using the notion of statistical significance, thus providing a more objective way to assess these outcomes. This paper contributes several statistical tests and association measures that treat process behaviour as a variable. The sensitivity of these tests to their parameters is evaluated and their applicability is illustrated through the use of real-life event logs. The presented tests and measures constitute a key contribution to a statistical foundation for process mining.

In this article, we propose two novel experimental design techniques for designing maximally informative experiments to estimate the parameters of nonlinear dynamical vehicle models. The two techniques include a batch design and a sequential design technique that seek to maximize the expected Shannon information gain of the parameter distribution using either an online or offline approach (respectively). We apply and compare the techniques in both simulation and real-world experiments with a wheeled vehicle. In our simulation experiments, both of our proposed designs provide superior Shannon information gains relative to an unoptimized benchmark technique. In our real-world experiments, our sequential design technique achieves superior expected Shannon information gains relative to our batch design technique and the benchmark technique.