I made inference with a Bayesian linear model. The following is my posterior predictive check result. The figure of mean looks good. But for max and min, the T(yrep) is too far from T(y), it may because the range of parameters are too wide. It seems to me that the model is fitting data poorly, so is there any way to imporve the ppc for max and min?

I find the problem. I used y= beta*x +alphe+normal(0,lognormal(0,1)). The prior of the lognormal(0,1) is too far from its real value. I change the prior based on my data can fix the problem.

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