TY - JOUR
T1 - Transfer Entropy as a Log-likelihood Ratio
AU - Barnett, L
AU - Bossomaier, Terence
N1 - Imported on 12 Apr 2017 - DigiTool details were: month (773h) = September, 2012; Journal title (773t) = Physical Review Letters. ISSNs: 0031-9007;
PY - 2012/9
Y1 - 2012/9
N2 - Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic '2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.
AB - Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic '2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.
KW - Data analysis
KW - Probability
KW - Statistics
U2 - 10.1103/PhysRevLett.109.138105
DO - 10.1103/PhysRevLett.109.138105
M3 - Article
VL - 109
SP - 1
EP - 10
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 13
ER -