Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions

Kuo, Kun-Lin; Song, Chwan-Chin; Jiang, T.

doi:10.1016/j.jmva.2017.03.005

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…Analogous to CRE, conditional FCRE can be computed using the fractional CRE of empirical data [30][31][32][33].…”

Section: Empirical Fractional Conditional Cumulative Residual Entropymentioning

confidence: 99%

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Dong

2022

Fractal Fract

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Fractional cumulative residual entropy is a powerful tool for the analysis of complex systems. In this paper, we first provide some properties of fractional cumulative residual entropy (FCRE). Secondly, we generate cumulative residual entropy (CRE) to the case of conditional entropy, named fractional conditional cumulative residual entropy (FCCRE), and introduce some properties. Then, we verify the validity of these properties with randomly generated sequences that follow different distributions. Moreover, we give the definition of empirical fractional conditional accumulative residual entropy and prove that it can be used to approximate FCCRE. Finally, the empirical analysis of the aero-engine gas path data is carried out. The results show that FCRE and FCCRE can effectively capture complex information in the gas path system.

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“…Analogous to CRE, conditional FCRE can be computed using the fractional CRE of empirical data [30][31][32][33].…”

Section: Empirical Fractional Conditional Cumulative Residual Entropymentioning

confidence: 99%

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Dong

2022

Fractal Fract

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“…Various methods have been proposed for doing this when the random variables concerned can only take a finite number of different values, which means of course that we need to refer to the probability mass rather than density functions of these variables, see for example Arnold, Castillo and Sarabia (2002), Chen, Ip and Wang (2011), Chen and Ip (2015) and Kuo, Song and Jiang (2017). Similar to what was done earlier, here we will again focus attention on a more widely applicable method, in particular the method that simply consists in making the assumption that the joint density of the parameters θ that most closely corresponds to the set of full conditional densities in equation ( 2) is equal to the limiting density function of a Gibbs sampling algorithm that is based on these conditional densities with some given fixed or random scanning order of the parameters concerned.…”

Section: Finding Compatible Approximations To Incompatible Full Condi...mentioning

confidence: 99%

Integrated organic inference (IOI): A reconciliation of statistical paradigms

Bowater¹

2020

Preprint

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It is recognised that the Bayesian approach to inference can not adequately cope with all the types of pre-data beliefs about population quantities of interest that are commonly held in practice. In particular, it generally encounters difficulty when there is a lack of such beliefs over some or all the parameters of a model, or within certain partitions of the parameter space concerned. To address this issue, a fairly comprehensive theory of inference is put forward called integrated organic inference that is based on a fusion of Fisherian and Bayesian reasoning.Depending on the pre-data knowledge that is held about any given model parameter, inferences are made about the parameter conditional on all other parameters using one of three methods of inference, namely organic fiducial inference, bispatial inference and Bayesian inference. The full conditional post-data densities that result from doing this are then combined using a framework that allows a joint post-data density for all the parameters to be sensibly formed without requiring these full conditional densities to be compatible. Various examples of the application of this theory are presented. Finally, the theory is defended against possible criticisms partially in terms of what was previously defined as generalised subjective probability.

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“…Accordingly, the problem of efficiently determining whether a given system of conditionals is compatible has received considerable attention over the years. Kuo et al [22], after listing previous attempts, provide probably the best solution to date. Their idea relies on the Structural Ratio Matrix which contains ratios between conditional distributions.…”

Section: Introductionmentioning

confidence: 99%

Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging

Muré

2019

ESAIM: PS

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Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a "pseudo-Gibbs sampler". We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.Résumé. Les modèles statistiques sont souvent définis par lois de probabilité conditionnelles plutôt que jointes. Il peut cependant être difficile de contrôler la compatibilité des lois conditionnelles, i.e. l'existence d'une loi jointe qui les engendre. Quand les lois conditionnelles sont compatibles, un échantillonneur de Gibbs peut être utilisé pour échantillonner selon la loi jointe dont elles procèdent. Dans le cas contraire, l'algorithme de l'échantillonneur de Gibbs peut parfois tout de même être appliqué. Une telle procédure est appelée « pseudo-échantillonneur de Gibbs ». Nous montrons que sa distribution stationnaire est le compromis optimal entre les lois conditionnelles, au sens où elle minimise un écart quadratique moyen entre elles et ses propres lois conditionnelles. Cela permet une analyse bayésienne objective des paramètres de corrélation de modèles de krigeage : nous utilisons des lois a posteriori de Jeffreys univariées conditionnelles plutôt que la très usitée loi a posteriori de Jeffreys multivariée. Cette stratégie rend la procédure pleinement bayésienne abordable. Des exemples numériques montrent que ses performances fréquentistes en termes de taux de couverture des intervalles prédictifs sont quasi-optimales.

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Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions

Cited by 7 publications

References 19 publications

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Integrated organic inference (IOI): A reconciliation of statistical paradigms

Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging

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