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Measurement Invariance, Entropy, and Probability

2010
*
Entropy
*

Incorporating information about

doi:10.3390/e12030289
fatcat:g3a2wla3azh33crgenlhydctje
*measurement*scale into maximum*entropy*provides a general approach to the relations between*measurement*, information*and**probability*. ... Our approach extends the method of maximum*entropy*to use*measurement*scale as a type of information constraint. ...*Measurement*, Information*Invariance*,*and**Probability*We derive most likely*probability*distributions. Our method follows the maximum*entropy*approach [4, 7, 8] . ...##
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Φ-Entropy Inequality and Invariant Probability Measure for SDEs with Jump
[article]

2013
*
arXiv
*
pre-print

The semigroup Φ-

arXiv:1309.0942v2
fatcat:wsjpv43qsvfjxdhj3r2rmvcoya
*entropy*inequality for SDEs driven by Poisson point processes as well as a sharp result on the existence of*invariant**probability**measures*are also presented. ... By using the Φ-*entropy*inequality derived in Wu, Ch for Poisson*measures*, the same type of inequality is established for a class of stochastic differential equations driven by purely jump Lévy processes ... Next, partly for the proof of Theorem 1.1(2), we consider the existence of*invariant**probability**measures*for the following more general SDE: Although the existence of*invariant**probability**measures*for ...##
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Distribution-Invariant Risk Measures, Entropy, and Large Deviations

2007
*
Journal of Applied Probability
*

For distribution-

doi:10.1017/s0021900200002692
fatcat:at6ck5evx5f2zp7tpyj5qmrohq
*invariant*risk*measures*which are continuous on compacts, we employ the theory of large deviations to study the*probability*of large errors. ... If the approximate risk*measurements*are based on the empirical distribution of independent samples, then the rate function equals the minimal relative*entropy*under a risk*measure*constraint. ... Acknowledgements I would like to thank Boris Buchmann, Hans Föllmer,*and*Ulrich Horst for helpful discussions. I am very grateful for the useful comments of an anonymous referee. ...##
###
Distribution-Invariant Risk Measures, Entropy, and Large Deviations

2007
*
Journal of Applied Probability
*

For distribution-

doi:10.1239/jap/1175267161
fatcat:6jron4zkizfa7byblbejh7qsue
*invariant*risk*measures*which are continuous on compacts, we employ the theory of large deviations to study the*probability*of large errors. ... If the approximate risk*measurements*are based on the empirical distribution of independent samples, then the rate function equals the minimal relative*entropy*under a risk*measure*constraint. ... Acknowledgements I would like to thank Boris Buchmann, Hans Föllmer,*and*Ulrich Horst for helpful discussions. I am very grateful for the useful comments of an anonymous referee. ...##
###
Invariant probability and entropy measures for multidimensional maps of chaotic attractors

1996
*
Computers and Mathematics with Applications
*

we define

doi:10.1016/s0898-1221(96)00182-4
fatcat:yfeq3iflirde7h7pdywzb3h4fa
*and*calculate the*probability*density in phase spsce*and*the information*entropy*of Poincare' maps describing the chaotic, stationary behaviour of deterministic dynamical systems with many degrees ... By partitioning the phsse spsce into cells*and*computing the*probability*of finding points of the map in each cell, a numeric approximation of the two statistical*measures*is derived,*and*the results are ...*INVARIANT**PROBABILITY*DENSITY*AND**ENTROPY*OF POINCARE' MAPS Given a Poincare' map representing an attractor of a dynamical system in a volume V of a &dimensional phase space, let US cover V by a number ...##
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Probability distribution and entropy as a measure of uncertainty

2008
*
Journal of Physics A: Mathematical and Theoretical
*

The relationship between three

doi:10.1088/1751-8113/41/6/065004
fatcat:rqhxauojqzfhbfsbpcxrdqvnmm
*probability*distributions*and*their optimal*entropy*forms is discussed without postulating*entropy*property as usual. ... For this purpose, the*entropy*I is defined as a*measure*of uncertainty of the*probability*distribution p(x) of a random variable x by a variational relationship dx , a definition assuring the optimization ... Tsobnang*and*Professor S. Abe for very useful discussion*and*comments. ...##
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Predictability, topological entropy and invariant random orders
[article]

2019
*
arXiv
*
pre-print

On route, we investigate

arXiv:1812.10833v2
fatcat:7xikjnaz3bc5fco5sqy45ishia
*invariant*random orders*and*formulate a unified Kieffer-Pinsker formula for the Kolmogorov-Sinai*entropy*of*measure*preserving actions of amenable groups. ... We prove that a topologically predictable action of a countable amenable group has zero topological*entropy*, as conjectured by Hochman. ... We will denote by Prob(X) the (compact, convex) space of Borel*probability**measures*on X,*and*by Prob Γ (X) the subset of Γ-*invariant*Borel*probability**measures*. ...##
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Entropy computing via integration over fractal measures

2000
*
Chaos
*

We discuss the properties of

doi:10.1063/1.166492
pmid:12779373
fatcat:2oi23gbwvrgpzoadpmgpy2iflu
*invariant**measures*corresponding to iterated function systems (IFSs) with place-dependent*probabilities**and*compute their Renyi*entropies*, generalized dimensions,*and*multifractal ... This provides a new method of computing*entropy*for some classical*and*quantum dynamical systems. Numerical techniques are based on integration over the fractal*measures*. ... It is easy to prove that the IFS F q satisfies our general assumption,*and*hence, a unique*invariant**probability**measure*µ q exists. ...##
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Invariance in ecological pattern
[article]

2019
*
arXiv
*
pre-print

First,

arXiv:1906.06979v2
fatcat:slyucxhcq5cxhfu4ro5blsciom
*invariance*provides a simpler*and*more fundamental maximum*entropy*derivation of the log series distribution. ... Common answers include maximum*entropy*, neutrality,*and*convergent outcome from different underlying biological processes. ... Acknowledgments The Donald Bren Foundation (SAF)*and*the Swiss National Science Foundation (grant 31003A_169671 to JB) support our research. ...##
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Invariance in ecological pattern

2019
*
F1000Research
*

First,

doi:10.12688/f1000research.21586.1
pmid:32089829
pmcid:PMC7008606
fatcat:vjkikqnpwnbtzl7iemx6rsqukm
*invariance*provides a simpler*and*more fundamental maximum*entropy*derivation of the log series distribution. ... Common answers include maximum*entropy*, neutrality,*and*convergent outcome from different underlying biological processes. ... That scale provided a much simpler analysis, in which r is the incremental scale with respect to*invariance**and*the*measurement*scale with respect to*entropy*. ...##
###
Invariance in ecological pattern
[article]

2019
*
bioRxiv
*
pre-print

First,

doi:10.1101/673590
fatcat:mluuk3nnnvedrbrotwc4rsflju
*invariance*provides a simpler*and*more fundamental maximum*entropy*derivation of the log series distribution. ... Common answers include maximum*entropy*, neutrality,*and*convergent outcome from different underlying biological processes. ... Acknowledgments The Donald Bren Foundation (SAF)*and*the Swiss National Science Foundation (grant 31003A_169671 to JB) support our research. ...##
###
Self-deprivation: A review

1984
*
Psychological bulletin
*

Particular biological processes set the relation between the information in observations

doi:10.1037/0033-2909.96.2.384
fatcat:o5me5fk7ejf53fgpn2m4od4bii
*and*magnitude, the basis for information*invariance*, symmetry*and**measurement*scale. ... The*measurement*scale, in turn, determines the most likely*probability*distributions*and*observed patterns associated with particular processes. ... Intuitive description of*measurement**and**probability*Intuitively, one can think of the symmetry of information*invariance**and**measurement*scale in the following way. ...##
###
Self-deprivation: A review

1984
*
Psychological bulletin
*

Particular biological processes set the relation between the information in observations

doi:10.1037//0033-2909.96.2.384
fatcat:wm4sai47ezcbjfwr6kp5642zue
*and*magnitude, the basis for information*invariance*, symmetry*and**measurement*scale. ... The*measurement*scale, in turn, determines the most likely*probability*distributions*and*observed patterns associated with particular processes. ... Intuitive description of*measurement**and**probability*Intuitively, one can think of the symmetry of information*invariance**and**measurement*scale in the following way. ...##
###
A simple derivation and classification of common probability distributions based on information symmetry and measurement scale

2011
*
Journal of Evolutionary Biology
*

Second, different problems associate magnitude to information in different ways, an association we describe in terms of the relation between information

doi:10.1111/j.1420-9101.2010.02204.x
pmid:21265914
fatcat:bkdluwvmuvfcvn5v3ud4anczay
*invariance**and**measurement*scale. ... Our framework relates the different continuous*probability*distributions through the variations in*measurement*scale that change each family of maximum*entropy*distributions into a distinct family. ... Intuitive description of*measurement**and**probability*Intuitively, one can think of the symmetry of information*invariance**and**measurement*scale in the following way. ...##
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Ruelle's inequality in negative curvature

2018
*
Discrete and Continuous Dynamical Systems. Series A
*

As an application, we prove Ruelle's inequality

doi:10.3934/dcds.2018119
fatcat:fcgcvvlisbhwzdnew2dokb7tfm
*and*Pesin's*entropy*formula for the geodesic flow in manifolds with pinched negative sectional curvature. ... In this paper we study different notions of*entropy*for measurepreserving dynamical systems defined on noncompact spaces. ... I would also like to thank Samuel Tapie for his inspiring remarks on some results of this paper, Godofredo Iommi for some nice suggestions that improved the presentation of this work,*and*the referee of ...
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