  Alignments provide sophisticated diagnostics that pinpoint deviations in a
trace with respect to a process model and their severity. However, approaches
based on trace alignments use crisp process models as reference and recent
probabilistic conformance checking approaches check the degree of conformance
of an event log with respect to a stochastic process model instead of finding
trace alignments. In this paper, for the first time, we provide a conformance
checking approach based on trace alignments using stochastic Workflow nets.
Conceptually, this requires to handle the two possibly contrasting forces of
the cost of the alignment on the one hand and the likelihood of the model trace
with respect to which the alignment is computed on the other.
