Search results for "differential entropy"

showing 3 items of 3 documents

Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation

2016

This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on "most trials" (meaning that the convergence holds on a fraction of trials that converge…

Statistics and ProbabilityAsymptotic analysisMathematical optimizationPosterior probabilityBayesian probabilityMathematics - Statistics TheoryStatistics Theory (math.ST)050105 experimental psychologydifferential entropyDifferential entropyactive data selection03 medical and health sciences0302 clinical medicineactive learningFOS: Mathematics0501 psychology and cognitive sciencescost of observationdecision theoryMathematicsD-optimalityBayes estimatorSequential estimation05 social sciencesBayesian adaptive estimationAsymptotically optimal algorithmConvergence of random variablesasymptotic optimalitysequential estimation030217 neurology & neurosurgery
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Extropy: Complementary Dual of Entropy

2015

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a complementary dual function which we call "extropy." The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of distinct measures for any quantity that is not merely an event indicator. As with entropy, the maximum extropy distribution is also the uniform distribution, and both measures are invariant with respect to permutations of their mass functions. However, they behave quite differently in their assessments…

Bregman divergenceFOS: Computer and information sciencesStatistics and ProbabilitySettore MAT/06 - Probabilita' E Statistica MatematicaKullback–Leibler divergenceComputer Science - Information TheoryGeneral MathematicsFOS: Physical sciencesBinary numberMathematics - Statistics TheoryStatistics Theory (math.ST)Kullback–Leibler divergenceBregman divergenceproper scoring rulesGini index of heterogeneityDifferential entropyBinary entropy functionFOS: MathematicsEntropy (information theory)Statistical physicsDual functionAxiomMathematicsdifferential and relative entropy/extropy Kullback- Leibler divergence Bregman divergence duality proper scoring rules Gini index of heterogeneity repeat rate.Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniDifferential and relative entropy/extropyInformation Theory (cs.IT)Probability (math.PR)repeat ratePhysics - Data Analysis Statistics and ProbabilitydualityStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaMathematics - ProbabilityData Analysis Statistics and Probability (physics.data-an)Statistical Science
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Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

2020

A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x &isin

General MathematicsReliability (computer networking)Context (language use)02 engineering and technologystochastic ordersLifetime distribution01 natural sciencesMeasure (mathematics)differential entropyDifferential entropy010104 statistics & probabilitystochastic neuronal modelFixed time0202 electrical engineering electronic engineering information engineeringComputer Science (miscellaneous)Applied mathematicsreliability; replacement model; stochastic orders; differential entropy; stochastic neuronal modelreplacement model0101 mathematicsEngineering (miscellaneous)Mathematicsreliabilitylcsh:Mathematicslcsh:QA1-939020201 artificial intelligence & image processingReplacement procedureRandom variableMathematics
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