cran
Y ~ Poisson(lambda)
lambda~Gamma(alpha,beta)
那么alpha 能有什么样的prior? 我用过uniform(0,10), cauchy等等，都不是很如意。说一下，我做的是count data with massive 0 and overdispersion的。
Gamma dist的likelihood
f(x) = beta^alpha * x^(alpha-1) *exp(-beta*x) / Gamma(alpha)
Gamma here means Gamma function
longoR
我也遇到了类似的问题，只不过是给normal的precision parameter一个gamma dist'n的时候碰到的。
如果假定alpha已知，beta的prior可以conjugate。
如果alpha未知，它和beta不独立，如果用joint conjugate，至少需要四个参数：
f(x,y|c,d,p,q) = (cy)^(x-1) y^p exp{-qy}/[gamma(x)]^d up to some multiplicative constant.
虽然不是完全不能做，不过看起来太复杂了，不如分别给alpha & beta prior容易。
cran
我作的是glmm with NegBin,
log(mu) = Xb,
beta=alpha/mu
至于variance component的prior,建议你看gelman在bayesian analysis的文章。
longoR
If the model is a simple poisson-gamma mixture, there is no need to specify any priors, because in such simple cases, usual likelihood-based analysis can easily find the MLE for alpha and beta.
But things are harder for GLMM.
longoR
I think if the prior choice has to be discussed case by case, the Bayesian approach loses one of its best property of being generally applicable and easy to implement.
Why do I need to be a Bayesian?
cran
我作的是用来忽悠ecologists的，不需要太多的理论。
revell
Sensitivity of Prior is an important part of a Bayesian analysis project.Bayesian approach provides numorous possibilities to her admirers, but requesting a careful heart of them.
