Statistical Validation of Mutual Information Calculations: Comparisons of Alternative Numerical Algorithms

Cellucci, C. J.; Albano, A. M.; Rapp, P. E.

doi:10.21236/ada445843

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…ANOVA‐like interpretations have also been suggested for MI‐based dependence [ Brillinger , 2004]. Cellucci et al [2005] compared MI‐based dependence with traditional measures of dependence, such as Pearson linear correlation coefficient, Spearman rank order correlation, and Kendall's tau.…”

Section: Methodsmentioning

confidence: 99%

Nonlinear statistics reveals stronger ties between ENSO and the tropical hydrological cycle

Khan

Ganguly

Bandyopadhyay

et al. 2006

Geophysical Research Letters

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[1] Cross-spectrum analysis based on linear correlations in the time domain suggested a coupling between large river flows and the El Niño-Southern Oscillation (ENSO) cycle. A nonlinear measure based on mutual information (MI) reveals extrabasinal connections between ENSO and river flows in the tropics and subtropics, that are 20-70% higher than those suggested so far by linear correlations. The enhanced dependence observed for the Nile, Amazon, Congo, Paraná, and Ganges rivers, which affect large, densely populated regions of the world, has significant impacts on inter-annual river flow predictabilities and, hence, on water resources and agricultural planning.

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Section: Methodsmentioning

confidence: 99%

Nonlinear statistics reveals stronger ties between ENSO and the tropical hydrological cycle

Khan

Ganguly

Bandyopadhyay

et al. 2006

Geophysical Research Letters

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“…The time shifted self-information is a nonlinear measure of temporal decorrelation. Explanatory examples are given in Cellucci, et al [ 79 ]. If a message has strong temporal predictability then I(A I ,A I + K ) remains high as K is increased.…”

Section: Resultsmentioning

confidence: 99%

Communication patterns in a psychotherapy following traumatic brain injury: A quantitative case study based on symbolic dynamics

Rapp

Cellucci²,

Gilpin

et al. 2011

BMC Psychiatry

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BackgroundThe role of psychotherapy in the treatment of traumatic brain injury is receiving increased attention. The evaluation of psychotherapy with these patients has been conducted largely in the absence of quantitative data concerning the therapy itself. Quantitative methods for characterizing the sequence-sensitive structure of patient-therapist communication are now being developed with the objective of improving the effectiveness of psychotherapy following traumatic brain injury.MethodsThe content of three therapy session transcripts (sessions were separated by four months) obtained from a patient with a history of several motor vehicle accidents who was receiving dialectical behavior therapy was scored and analyzed using methods derived from the mathematical theory of symbolic dynamics.ResultsThe analysis of symbol frequencies was largely uninformative. When repeated triples were examined a marked pattern of change in content was observed over the three sessions. The context free grammar complexity and the Lempel-Ziv complexity were calculated for each therapy session. For both measures, the rate of complexity generation, expressed as bits per minute, increased longitudinally during the course of therapy. The between-session increases in complexity generation rates are consistent with calculations of mutual information. Taken together these results indicate that there was a quantifiable increase in the variability of patient-therapist verbal behavior during the course of therapy. Comparison of complexity values against values obtained from equiprobable random surrogates established the presence of a nonrandom structure in patient-therapist dialog (P = .002).ConclusionsWhile recognizing that only limited conclusions can be based on a case history, it can be noted that these quantitative observations are consistent with qualitative clinical observations of increases in the flexibility of discourse during therapy. These procedures can be of particular value in the examination of therapies following traumatic brain injury because, in some presentations, these therapies are complicated by deficits that result in subtle distortions of language that produce significant post-injury social impairment. Independently of the mathematical analysis applied to the investigation of therapy-generated symbol sequences, our experience suggests that the procedures presented here are of value in training therapists.

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“…Thus, we can compute the above probabilities ( and ) and hence ( ), by the Fraser and Swinney (1986) algorithm that is fully described by [42]. This algorithm can be directly applied to a given time series.…”

Section: Reconstruction Of Phase Space During Reconstructionmentioning

confidence: 99%

Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

Adediran

Kagamba

Alochukwu

2016

Mathematical Problems in Engineering

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In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.

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Statistical Validation of Mutual Information Calculations: Comparisons of Alternative Numerical Algorithms

Cited by 4 publications

References 19 publications

Nonlinear statistics reveals stronger ties between ENSO and the tropical hydrological cycle

Nonlinear statistics reveals stronger ties between ENSO and the tropical hydrological cycle

Communication patterns in a psychotherapy following traumatic brain injury: A quantitative case study based on symbolic dynamics

Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

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