Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2028 2022 2022 Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria. Nizar Altounji Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria. Mohamed Bisher Zeina Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria. Moustafa Mazhar Ranneh This research presents the concept of neutrosophic Bayesian estimation defining the neutrosophic loss function, neutrosophic risk function, neutrosophic posterior risk function and neutrosophic maximum a posteriori estimator. Minimization of the neutrosophic posterior risk of the estimator is also discussed. An algebraic isomorphism is used to simplify equations solving. As an application of the presented theorems, a sample drawn from a neutrosophic gamma distribution with a conjugate prior is discussed and studied and the parameter of the formulated distribution is successfully estimated using neutrosophic quadratic loss function which results an estimator that equals the posterior mean. 2023 2023 43 50 10.54216/GJMSA.070105 https://www.americaspg.com/articleinfo/33/show/2028