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Entropy 2014, 16(5), 2839-2849; doi:10.3390/e16052839

Exact Test of Independence Using Mutual Information

1,*  and 2
1 Army RDECOM, RDMR-WDS-WO, Redstone Arsenal, AL 35898, USA 2 Torch Technologies, Inc., Huntsville, AL 35802, USA
* Author to whom correspondence should be addressed.
Received: 18 February 2014 / Revised: 15 May 2014 / Accepted: 20 May 2014 / Published: 23 May 2014
(This article belongs to the Special Issue Information in Dynamical Systems and Complex Systems)
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Using a recently discovered method for producing random symbol sequences with prescribed transition counts, we present an exact null hypothesis significance test (NHST) for mutual information between two random variables, the null hypothesis being that the mutual information is zero (i.e., independence). The exact tests reported in the literature assume that data samples for each variable are sequentially independent and identically distributed (iid). In general, time series data have dependencies (Markov structure) that violate this condition. The algorithm given in this paper is the first exact significance test of mutual information that takes into account the Markov structure. When the Markov order is not known or indefinite, an exact test is used to determine an effective Markov order.
Keywords: mutual information; significance test; surrogate data mutual information; significance test; surrogate data
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Pethel, S.D.; Hahs, D.W. Exact Test of Independence Using Mutual Information. Entropy 2014, 16, 2839-2849.

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