Abstract
In this paper a Markov chain for contingency tallies with two lows is defined. The chain is shown to be rapidly mixing using the path coupling method. The mixing time of the chain is quadratic in the number of columns and linear in the logarithm of the table sum. Two extensions of the new chain are discussed: one for three-rowed contingency tables and one for m-rowed contingency tables. We show that, unfortunately, it is not possible to prove rapid mixing for these chains by simply extending the path coupling approach used in the two-rowed case.
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Dyer, M., Greenhill, C. (1998). A genuinely polynomial-time algorithm for sampling two-rowed contingency tables. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055065
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DOI: https://doi.org/10.1007/BFb0055065
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