Abstract
Generalized linear models (GLM) are discussed in this paper, which are used widely in the field of robust parameter design involving non-normal response variables. As for the estimation problems such as data over-dispersion which exist generally in robust parameter design, the Markov chain Monte Carlo (MCMC) approach based on adaptive rejection metropolis sampling algorithm is brought forward to simulate dynamically the Markov chain of the parameter's posterior distribution of the GLM. Furthermore, the parameters' Bayesian estimation and significant factors of the GLM will be given when relative objective Jeffreys' prior distribution is used for the parameters of the GLM. Practical industrial experiment data is utilized to simulate and analyze the Bayesian GLM by the SAS software. The results demonstrate that the Bayesian GLM performs more reliable and valid in parameter robust estimation and significant factors identification than the conventional GLM.
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