共轭先验分布下逆伽马分布尺度参数的Bayes分析

doi:10.16088/j.issn.1001-6600.2025112801

Abstract

Abstract: The forms and properties of the Bayesian estimation for the scale parameter in the inverse gamma distribution with known the shape parameter were investigated under the gamma conjugate prior distribution and the weighted p,q symmetric entropy loss function. Firstly, the exact form of the Bayesian estimation for the scale parameter is derived, and its admissibility and minimaxity are proved. Secondly, the forms of multi-layer Bayesian estimation, E-Bayesian estimation, and knife-cut Bayesian estimation for the scale parameter of the inverse gamma distribution are investigated based on the derived Bayesian estimation. Finally, numerical simulations with MCMC algorithm are conducted to discuss the robustness and precision of the obtained Bayesian, E-Bayesian, and knife-cut Bayesian estimation. Results indicatethat all three estimations exhibit high robustness and precision, while knife-cut Bayesian estimation has the highest precision specially.

Key words: weighted p, q symmetric entropy loss function, inverse gamma distribution, prior distribution, Bayesian estimation, MCMC algorithm

CLC Number: O212.8

Sun Ying, Xu Bao. Bayesian analysis of scale parameter in inverse gamma distribution under conjugate prior distributions[J].Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(5): 112-121.

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Bayesian analysis of scale parameter in inverse gamma distribution under conjugate prior distributions

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