Bayesian estimation, Exponentiated Weibull distribution, Linex loss function, Lindley approximation, Maximum likelihood estimator, Progressive Type II censoring, Squared error loss function,
We propose a new estimation method for 3D object reconstruction using photon-counting integral imaging. Earlier studies used maximum likelihood estimation (MLE) as a classical statistical method to reconstruct 3D images from photon-counting elemental images. We use an alternative statistical method known as the Bayesian method, which is more flexible and may perform better than MLE in terms of the mean square error (MSE) metric. The performance of the new reconstruction method is illustrated and compared with MLE by using the MSE. To the best of our knowledge, this is the first report to use the Bayesian method for 3D reconstruction of photon-counting integral imaging.
In this paper, we consider Bayesian estimation and prediction problem for the parameters and unobserved lifetimes of exponentiated Weibull distribution based on a progressively type II censored samples. By using an extended likelihood function and informative joint prior distributions, the joint posterior density for the parameters and unobserved lifetimes of units censored at the failure time is obtained. Since the closed form of Bayes estimators does not exist, we use Markov Chain Monte Carlo (MCMC) method such as Gibbs sampling and Metropolis-Hastings algorithm to generate the posterior conditional probabilities of interest. Monte Carlo simulations and real data analysis are conducted to observe the behaviour of the proposed method.
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