We propose an interdisciplinary framework, Bayesian formal predictive model
checking (Bayes FPMC), which combines Bayesian predictive inference, a well
established tool in statistics, with formal verification methods rooting in the
computer science community.
Bayesian predictive inference allows for coherently incorporating uncertainty
about unknown quantities by making use of methods or models that produce
predictive distributions which in turn inform decision problems. By formalizing
these problems and the corresponding properties, we can use spatio-temporal
reach and escape logic to probabilistically assess their satisfaction. This
way, competing models can directly be ranked according to how well they solve
the actual problem at hand.
The approach is illustrated on an urban mobility application, where the
crowdedness in the center of Milan is proxied by aggregated mobile phone
traffic data. We specify several desirable spatio-temporal properties related
to city crowdedness such as a fault tolerant network or the reachability of
hospitals. After verifying these properties on draws from the posterior
predictive distributions, we compare several spatio-temporal Bayesian models
based on their overall and property-based predictive performance