  A key challenge in agent-based mobility simulations is the synthesis of
individual agent socioeconomic profiles. Such profiles include locations of
agent activities, which dictate the quality of the simulated travel patterns.
These locations are typically represented in origin-destination matrices that
are sampled using coarse travel surveys. This is because fine-grained trip
profiles are scarce and fragmented due to privacy and cost reasons. The
discrepancy between data and sampling resolutions renders agent traits
non-identifiable due to the combinatorial space of data-consistent individual
attributes. This problem is pertinent to any agent-based inference setting
where the latent state is discrete. Existing approaches have used continuous
relaxations of the underlying location assignments and subsequent ad-hoc
discretisation thereof. We propose a framework to efficiently navigate this
space offering improved reconstruction and coverage as well as linear-time
sampling of the ground truth origin-destination table. This allows us to avoid
factorially growing rejection rates and poor summary statistic consistency
inherent in discrete choice modelling. We achieve this by introducing joint
sampling schemes for the continuous intensity and discrete table of agent
trips, as well as Markov bases that can efficiently traverse this combinatorial
space subject to summary statistic constraints. Our framework's benefits are
demonstrated in multiple controlled experiments and a large-scale application
to agent work trip reconstruction in Cambridge, UK.
