65 research outputs found
Conditions for swappability of records in a microdata set when some marginals are fixed
We consider swapping of two records in a microdata set for the purpose of
disclosure control. We give some necessary and sufficient conditions that some
observations can be swapped between two records under the restriction that a
given set of marginals are fixed. We also give an algorithm to find another
record for swapping if one wants to swap out some observations from a
particular record. Our result has a close connection to the construction of
Markov bases for contingency tables with given marginals
Minimal and minimal invariant Markov bases of decomposable models for contingency tables
We study Markov bases of decomposable graphical models consisting of
primitive moves (i.e., square-free moves of degree two) by determining the
structure of fibers of sample size two. We show that the number of elements of
fibers of sample size two are powers of two and we characterize primitive moves
in Markov bases in terms of connected components of induced subgraphs of the
independence graph of a hierarchical model. This allows us to derive a complete
description of minimal Markov bases and minimal invariant Markov bases for
decomposable models.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ207 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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