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In the Poisson-Gamma model (data follows iid Poisson distribution with mean and prior of this parameter is a Gamma (, ) random variable), if the

In the Poisson-Gamma model (data follows iid Poisson distribution with mean and prior of this parameter is a Gamma (, ) random variable), if the sample size of observed data, n, is approaching positive infinity, what would happen to the point estimation of , the Poisson mean parameterand prediction of a future observation?

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