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

Saraiva, Erlandson Ferreira; Suzuki, Adriano K.; Milan, Luís Aparecido

doi:10.3390/e20090642

Cited by 10 publications

(4 citation statements)

References 27 publications

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“…Therefore, the Random Walk Metropolis (RWM) algorithm was utilized to generate random samples from an unknown distribution. Similar to acceptance-rejection sampling, the algorithm requires that the applied value has an acceptable probability for each iteration of the algorithm to ensure that the Markov chain converges for the goal density ( Saraiva & Suzuki, 2017 ). To use the RWM algorithm to update the shape parameter, the updated value is approved with probability min (1, A k ), where A k is defined by where c ′ ( t ) and k ( t ) , t =1 , 2, …, T are the Bayesian estimators of c ′ and k based on Gibbs’ sampling, respectively.…”

Section: Bayesian Confidence Intervalmentioning

confidence: 99%

Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

La-ongkaew

Niwitpong

2023

PeerJ

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The Weibull distribution has been used to analyze data from many fields, including engineering, survival and lifetime analysis, and weather forecasting, particularly wind speed data. It is useful to measure the central tendency of wind speed data in specific locations using statistical parameters for instance the mean to accurately forecast the severity of future catastrophic events. In particular, the common mean of several independent wind speed samples collected from different locations is a useful statistic. To explore wind speed data from several areas in Surat Thani province, a large province in southern Thailand, we constructed estimates of the confidence interval for the common mean of several Weibull distributions using the Bayesian equitailed confidence interval and the highest posterior density interval using the gamma prior. Their performances are compared with those of the generalized confidence interval and the adjusted method of variance estimates recovery based on their coverage probabilities and expected lengths. The results demonstrate that when the common mean is small and the sample size is large, the Bayesian highest posterior density interval performed the best since its coverage probabilities were higher than the nominal confidence level and it provided the shortest expected lengths. Moreover, the generalized confidence interval performed well in some scenarios whereas adjusted method of variance estimates recovery did not. The approaches were used to estimate the common mean of real wind speed datasets from several areas in Surat Thani province, Thailand, fitted to Weibull distributions. These results support the simulation results in that the Bayesian methods performed the best. Hence, the Bayesian highest posterior density interval is the most appropriate method for establishing the confidence interval for the common mean of several Weibull distributions.

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Section: Bayesian Confidence Intervalmentioning

confidence: 99%

Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

La-ongkaew

Niwitpong

2023

PeerJ

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“…(11) Aslam et al (2014) apresentam opções para a modelagem das prioris dos parâmetros de escala e forma da distribuição de Weibull; entre estas, o modelo gama-gama, no qual as prioris dos parâmetros de escala s e forma k são modeladas por distribuições gama independentes (Saraiva e Suzuki, 2017), cujas funções densidades de probabilidades são apresentadas a seguir:…”

Section: Inferência Bayesianaunclassified

Avaliação Da Produção Energética De Um Projeto Eólico Offshore No Litoral Fluminense

Pessanha,

Medrano,

Mendonça

et al. 2023

Anais Do Simpósio Brasileiro De Pesquisa Operacional

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“…Using the MCMC technique, we pursue generating (stationary) sequences of simulated values from the posterior distribution. The Metropolis-Hastings algorithm was developed by Metropolis et al [29] and generalized by Hastings [30], and it is now the most popular MCMC method (see [31][32][33], for example).…”

Section: Computation By Markov Chain Monte Carlomentioning

confidence: 99%

Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution

2020

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Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained by virtue of a posterior distribution using the random walk Metropolis–Hastings algorithm. Five different priors are considered. The properties of the Bayesian estimators are verified in a simulation study. The empirical Bayesian method turns out to work well. Our approach is then compared to the MLE and the method of the L-moments estimator by calculating the 20-year return level, the confidence interval, and various goodness-of-fit measures. It is also compared to modeling using the generalized extreme value distribution. We illustrate the usefulness of our approach in an application to the annual maximum wind speeds in Udon Thani, Thailand, and to the annual maximum sea-levels in Fremantle, Australia. In the latter example, non-stationarity is modeled through a trend in time on the location parameter. We conclude that Bayesian inference for K4D may be substantially useful for modeling extreme events.

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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

Cited by 10 publications

References 27 publications

Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

Avaliação Da Produção Energética De Um Projeto Eólico Offshore No Litoral Fluminense

Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution

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