Normalized Measures of Entropy

Heterogeneity within psychiatric disorders is both theoretically and practically problematic: For many disorders, it is possible for 2 individuals to share very few or even no symptoms in common yet share the same diagnosis. Polythetic diagnostic criteria have long been recognized to contribute to this heterogeneity, yet no unified theoretical understanding of the coherence of symptom criteria sets currently exists. A general framework for analyzing the logical and mathematical structure, coherence, and diversity of Diagnostic and Statistical Manual diagnostic categories (DSM-5 and DSM-IV-TR) is proposed, drawing from combinatorial mathematics, set theory, and information theory. Theoretical application of this framework to 18 diagnostic categories indicates that in most categories, 2 individuals with the same diagnosis may share no symptoms in common, and that any 2 theoretically possible symptom combinations will share on average less than half their symptoms. Application of this framework to 2 large empirical datasets indicates that patients who meet symptom criteria for major depressive disorder and posttraumatic stress disorder tend to share approximately three-fifths of symptoms in common. For both disorders in each of the datasets, pairs of individuals who shared no common symptoms were observed. Any 2 individuals with either diagnosis were unlikely to exhibit identical symptomatology. The theoretical and empirical results stemming from this approach have substantive implications for etiological research into, and measurement of, psychiatric disorders.

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“…Shannon entropy may be normalized on the interval [0, 1] by dividing by the maximum possible entropy (Kumar, Kumar, & Kapur, 1986):…”

Section: Diversity Measures For Empirical Datamentioning

confidence: 99%

Quantifying heterogeneity attributable to polythetic diagnostic criteria: Theoretical framework and empirical application.

Olbert¹,

Gala²,

Tupler³

2014

Journal of Abnormal Psychology

143

102

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“…It is the weighted linear average of normalized expected utility and entropy. The definition of risk is based on Yang and Qiu [12], Golan et al [15], Kumar et al [16] and Soofi [17]. It is founded on the fact that the decision maker wishes less uncertainty and bigger expected utility.…”

Section: Normalized Expected Utility-entropy Measure Of Riskmentioning

confidence: 99%

“…This leads to standardized measures which can be compared with one another [16]. An analog measure 1 ( ) a NH   , called the information index, serves to measure the reduction in uncertainty [17].…”

Section: Normalized Expected Utility-entropy Measure Of Riskmentioning

confidence: 99%

Normalized Expected Utility-Entropy Measure of Risk

Yang

Wan-hua

2014

Entropy

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Yang and Qiu proposed an expected utility-entropy (EU-E) measure of risk, which reflects an individual's intuitive attitude toward risk. Luce et al. have derived the numerical representations under behavioral axioms about preference orderings among gambles and their joint receipt, which further demonstrates the reasonability of the EU-E decision model as a normative one. In the paper, combining normalized expected utility and entropy together, we improve the EU-E measure of risk and decision model, and then propose the normalized EU-E measure of risk and decision model. The normalized EU-E measure of risk has some normative properties under certain conditions. Moreover, the normalized EU-E decision model can be a proper descriptive model to some extent. Using this model, two cases of common ratio effect and common consequence effect, which are the examples of certainty effects, can be explained in an intuitive way.

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“…Entropy has traditionally been used as a measure of disorder and complexity within random signals [38,39] and has found application in fields as diverse as medicine, engineering and geophysics, to name but a few. Entropy, for instance, has been used to quantify nonlinearities and complexity in electroencephalogram (EEG) signals [40], event-related potentials in neuroelectrical signals [41,42], structural damage identification [43] and characterization of complexity in random processes [44][45][46].…”

Section: Wavelet-tsallis Q-entropymentioning

confidence: 99%

Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals

Ramírez-Pacheco

Rizo-Dominguez

Cortez

2015

Entropy

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Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well.

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Normalized Measures of Entropy

Cited by 51 publications

References 2 publications

Quantifying heterogeneity attributable to polythetic diagnostic criteria: Theoretical framework and empirical application.

Quantifying heterogeneity attributable to polythetic diagnostic criteria: Theoretical framework and empirical application.

Normalized Expected Utility-Entropy Measure of Risk

Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals

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