In David Robinson's blog:Understanding empirical Bayes estimation (using baseball statistics) he used the hit ratio to fit the beta distribution as a prior distribution,Where hit rate = hits/total. The estimated parameter is:$α_0=78.661$ and $β_0=224.875$. So far so good ... But my question is:The estimated parameters are close to the order of magnitude of the player data. But if the hits and total of 4-5 digit, the hit rate remains the same, so does the estimated beta distribution.

If new players always hit the ball tens of thousands of times,The estimated prior distribution has little effect, as if $α_0$ and $β_0$ imply the order of magnitude of the data. Why is the estimated parameter not $α_0=7866.1$ $β_0=22487.5$? Or an order of magnitude larger to match the order of magnitude of the data itself? how should I understand?

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    $\begingroup$ As the eminent Bayesian, D.V. Lindley, famously said, There's no one less Bayesian than an empirical Bayesian. $\endgroup$ – Mark L. Stone Feb 16 at 4:11
  • $\begingroup$ Yes it is called empirical Bayes not experience Bayes. $\endgroup$ – Michael Chernick Feb 16 at 4:15
  • $\begingroup$ @MichaelChernick Our Dear Michael,I edited it as you asked。Help me $\endgroup$ – abraxas Feb 16 at 4:38
  • $\begingroup$ @MarkL.Stone But the prior distribution is hard to pick $\endgroup$ – abraxas Feb 16 at 4:39
  • $\begingroup$ @MarkL.Stone Bradley Efron in his book large-scale Inference, Bradley Efron expounds the estimation of james-stein from the perspective of empirical bayes, which makes me believe that empirical bayes is feasible $\endgroup$ – abraxas Mar 6 at 3:48

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