Estimating the errors on measured entropy and mutual information

被引：218

作者：

Roulston, MS ^{[1
]}

机构：

[1] CALTECH, Div Geol & Planetary Sci, Pasadena, CA 91125 USA

来源：

PHYSICA D | 1999年 / 125卷 / 3-4期

关键词：

entropy; mutual information;

D O I：

10.1016/S0167-2789(98)00269-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems. Expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics. In this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists. Their validity is demonstrated by numerical experiment. For illustration the formulae are then used to evaluate the errors on the time-lagged mutual information of the logistic map. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：285 / 294

页数：10

共 18 条

[11] INFORMATION THEORETIC TEST FOR NONLINEARITY IN TIME-SERIES [J].

PALUS, M ;

ALBRECHT, V ;

DVORAK, I .

PHYSICS LETTERS A, 1993, 175 (3-4) :203-209

[12] SINGULAR-VALUE DECOMPOSITION IN ATTRACTOR RECONSTRUCTION - PITFALLS AND PRECAUTIONS [J].

PALUS, M ;

DVORAK, I .

PHYSICA D-NONLINEAR PHENOMENA, 1992, 55 (1-2) :221-234

[13] Detecting nonlinearity in multivariate time series [J].

Palus, M .

PHYSICS LETTERS A, 1996, 213 (3-4) :138-147

[14] Coarse-grained entropy rates for characterization of complex time series [J].

Palus, M .

PHYSICA D-NONLINEAR PHENOMENA, 1996, 93 (1-2) :64-77

[15] TESTING FOR NONLINEARITY USING REDUNDANCIES - QUANTITATIVE AND QUALITATIVE ASPECTS [J].

PALUS, M .

PHYSICA D-NONLINEAR PHENOMENA, 1995, 80 (1-2) :186-205

[16] MEASURING STATISTICAL DEPENDENCES IN A TIME-SERIES [J].

POMPE, B .

JOURNAL OF STATISTICAL PHYSICS, 1993, 73 (3-4) :587-610

[17] Significance testing of information theoretic functionals [J].

Roulston, MS .

PHYSICA D, 1997, 110 (1-2) :62-66

[18] Extraction of delay information from chaotic time series based on information entropy [J].

Tian, YC ;

Gao, FR .

PHYSICA D, 1997, 108 (1-2) :113-118

← 1 2 →