A blocking scheme for dimension-robust Gibbs sampling in large-scale image deblurring

Adams, Jesse; Morzfeld, Matthias; Joyce, Kevin; Howard, Michael; Luttman, Aaron

doi:10.1080/17415977.2021.1880398

Cited by 2 publications

(1 citation statement)

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“…The basic MCMC technique is the Gibbs sampler algorithm which frequently used in Bayesian inference. More detail about Gibbs sampler see the Gupta and Singh [15], Papanikolaou et al [16], Amin [17], Zhang et al [18],Luengo et al [19], Adams et al [20], Gearhart [21] and the references therein. To apply the Gibbs algorithm, the full conditional distributions of the parameters and are constructed from (14).…”

Section: Markov Chain Monte Carlo Techniquementioning

confidence: 99%

Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

Liu¹,

Arslan²,

Khan³

et al. 2021

Preprint

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The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

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