  Sequential traces of user data are frequently observed online and offline,
e.g., as sequences of visited websites or as sequences of locations captured by
GPS. However, understanding factors explaining the production of sequence data
is a challenging task, especially since the data generation is often not
homogeneous. For example, navigation behavior might change in different phases
of browsing a website, or movement behavior may vary between groups of users.
In this work, we tackle this task and propose MixedTrails, a Bayesian approach
for comparing the plausibility of hypotheses regarding the generative processes
of heterogeneous sequence data. Each hypothesis is derived from existing
literature, theory or intuition and represents a belief about transition
probabilities between a set of states that can vary between groups of observed
transitions. For example, when trying to understand human movement in a city
and given some observed data, a hypothesis assuming tourists to be more likely
to move towards points of interests than locals, can be shown to be more
plausible than a hypothesis assuming the opposite. Our approach incorporates
such hypotheses as Bayesian priors in a generative mixed transition Markov
chain model, and compares their plausibility utilizing Bayes factors. We
discuss analytical and approximate inference methods for calculating the
marginal likelihoods for Bayes factors, give guidance on interpreting the
results, and illustrate our approach with several experiments on synthetic and
empirical data from Wikipedia and Flickr. Thus, this work enables a novel kind
of analysis for studying sequential data in many application areas.
