Browsing by Author "Ramos, Eduardo"

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    Objective Bayesian analysis for the differential entropy of the Gamma distribution
    (2024) Ramos, Eduardo; Egbon, Osafu A.; Ramos, Pedro L.; Rodrigues, Francisco A.; Louzada, Francisco
    The paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.
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    On Posterior Properties of the Two Parameter Gamma Family of Distributions
    (2021) Ramos, Pedro L.; Dey, Dipak K.; Louzada, Francisco; Ramos, Eduardo
    The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors Lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.
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    On the posterior property of the Rician distribution
    (2024) Achire, Enrique; Ramos, Eduardo; Ramos, Pedro Luiz
    The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles - Sustainable, Accurate, Fair, and Explainable - ensuring robustness, fairness, and transparency in predictive modelling.
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    POWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS
    (2023) Ramos, Pedro Luiz; Rodrigues, Francisco A.; Ramos, Eduardo; Dey, Dipak K.; Louzada, Francisco
    Using objective priors in Bayesian applications has become a common way of analyzing data without using subjective information. Formal rules are usually used to obtain these prior distributions, and the data provide the dominant infor-mation in the posterior distribution. However, these priors are typically improper, and may lead to an improper posterior. Here, for a general family of distribu-tions, we show that the objective priors obtained for the parameters either follow a power law distribution, or exhibit asymptotic power law behavior. As a result, we observe that the exponents of the model are between 0.5 and 1. Understand-ing this behavior allows us to use the exponent of the power law directly to verify whether such priors lead to proper or improper posteriors. The general family of distributions we consider includes essential models such as the exponential, gamma, Weibull, Nakagami-m, half-normal, Rayleigh, Erlang, and Maxwell Boltzmann dis-tributions, among others. In summary, we show that understanding the mechanisms that describe the shape of a prior provides essential information that can be used to understand the properties of posterior distributions.