Maximum entropy distributions with quantile information

Bajgiran, Amirsaman H.; Mardikoraem, Mahsa; Soofi, Ehsan S.

doi:10.1016/j.ejor.2020.07.052

Cited by 12 publications

(8 citation statements)

References 33 publications

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“…Wang and Lahiri (2021) avoided the discrete entropy and applied the information framework of Shoja and Soofi (2017) using entropies of beta and triangular distributions fitted to the histograms of the subjective probabilities. Bajgiran et al (2021) developed piecewise uniform ME models that only use the quantiles given by the forecasters' subjective probabilities. Quantile constraints can be represented in terms of the following expectations:…”

Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

“…This piecewise uniform PDF is a density histogram with unequal bins B k . Bajgiran et al (2021) observed that, unlike the ME with moment constraints, the ME model subject to the mixtures of the averagē p k = n i=1 p i p ik of the bin probabilities…”

Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

“…Table 3 shows implementation of the information framework for the quantilebase ME models and moment-based ME forecast models depicted in Figure 2. The information measures of the ME models with quantile constraints are given in Bajgiran et al (2021). Expressions for the entropy and KL divergence of normal distribution are well-known.…”

Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

See 2 more Smart Citations

Variants of Mixtures: Information Properties and Applications

Ardakani

Asadi

Ebrahimi

et al. 2021

JIRSS

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In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function.

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Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

Section: Uncertainty and Disagreement Of Forecastersmentioning

confidence: 99%

See 1 more Smart Citation

Variants of Mixtures: Information Properties and Applications

Ardakani

Asadi

Ebrahimi

et al. 2021

JIRSS

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“…(1996) studied elaboration by including a prior distribution for θ and embedding

F_{0}

in the Dirichlet process prior where θ represents the degree of belief (dispersion) parameter and

F_{0}

is given by θ 0 = lim θ→∞ Bajgiran et al . (2021) derived the minimum information elaboration by including an additional constraint to a maximum entropy model, where θ is the Lagrange multiplier and

θ_{0} = 0

.…”

Section: Introductionmentioning

confidence: 99%

Elaboration Models with Symmetric Information Divergence

Asadi

Devarajan

Ebrahimi

et al. 2022

Int Statistical Rev

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Summary Various statistical methodologies embed a probability distribution in a more flexible family of distributions. The latter is called elaboration model, which is constructed by choice or a formal procedure and evaluated by asymmetric measures such as the likelihood ratio and Kullback–Leibler information. The use of asymmetric measures can be problematic for this purpose. This paper introduces two formal procedures, referred to as link functions, that embed any baseline distribution with a continuous density on the real line into model elaborations. Conditions are given for the link functions to render symmetric Kullback–Leibler divergence, Rényi divergence and phi‐divergence family. The first link function elaborates quantiles of the baseline probability distribution. This approach produces continuous counterparts of the binary probability models. Examples include the Cauchy, probit, logit, Laplace and Student's t links. The second link function elaborates the baseline survival function. Examples include the proportional odds and change point links. The logistic distribution is characterised as the one that satisfies the conditions for both links. An application demonstrates advantages of symmetric divergence measures for assessing the efficacy of covariates.

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“…This quantity measures the average surprisal of the random vector [17]. Finding the distribution that maximizes the continuous entropy given some restrictions is a highly studied field, some examples can be found in [1,4,29]. Given the variances and some of the covariances between a collection of variables, the GMRF distribution (over the graph where the nodes are adjacent if and only if the covariance is specified) maximizes the continuous entropy, since the resultant covariance matrix maximizes the determinant [6].…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Order for Graphs Based on the Continuous Entropy of Gaussian Markov Random Fields

Baz¹,

Dı́az

Montes

et al. 2021

Atlantis Studies in Uncertainty Modelling

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Gaussian Markov Random Fields over graphs have been widely used in the context of both theoretical and applied Statistics. In this paper, we study the influence of the graph on the continuous entropy of the distribution. In particular, since the continuous entropy is highly dependant on the correlations between adjacent nodes in the graph, we consider the particular case of Gaussian Markov Random Fields with uniform correlation, i.e., Gaussian Markov Random Fields in which such correlations are equal. We define a partial order relation on the set of graphs that orders the graphs according to their contribution to the continuous entropy. We also present a graded version of this order relation that allows to compare incomparable graphs with respect to the original order relation. Finally, an example for the illustration of the graded order relation is provided.

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Maximum entropy distributions with quantile information

Cited by 12 publications

References 33 publications

Variants of Mixtures: Information Properties and Applications

Variants of Mixtures: Information Properties and Applications

Elaboration Models with Symmetric Information Divergence

A Fuzzy Order for Graphs Based on the Continuous Entropy of Gaussian Markov Random Fields

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