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Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data

1
Instituto de Matemática, Universidade Federal de Mato Grosso do Sul, Campo Grande 79070-900, Brazil
2
Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, São Carlos 13566-590, Brazil
3
Departamento de Estatística, Universidade de São Carlos, São Carlos 13565-905, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(9), 642; https://doi.org/10.3390/e20090642
Received: 27 June 2018 / Revised: 20 August 2018 / Accepted: 23 August 2018 / Published: 27 August 2018
(This article belongs to the Special Issue Foundations of Statistics)
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Abstract

In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set. View Full-Text
Keywords: Bayesian inference; Ali–Mikhail–Haq copula; MCMC; Metropolis-Hastings; slice sampling Bayesian inference; Ali–Mikhail–Haq copula; MCMC; Metropolis-Hastings; slice sampling
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Saraiva, E.F.; Suzuki, A.K.; Milan, L.A. Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data. Entropy 2018, 20, 642.

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