Persistent obstruction theory for a model category of measures with applications to data merging

  title={Persistent obstruction theory for a model category of measures with applications to data merging},
  author={Abraham Smith and Paul Bendich and John Harer},
  journal={Transactions of the American Mathematical Society, Series B},
Collections of measures on compact metric spaces form a model category (“data complexes”), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on a product space that marginalizes to any measures on pairs of its factors. The homotopy and homology for this category allow measurement of obstructions to finding measures on larger and larger product spaces. The obstruction theory is compatible with a… 

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