Suppose we have no idea what the value of the Poisson intensity parameter 1 is prior to looking at the data. In that cas

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Suppose We Have No Idea What The Value Of The Poisson Intensity Parameter 1 Is Prior To Looking At The Data In That Cas 1 (17 KiB) Viewed 30 times

Suppose we have no idea what the value of the Poisson intensity parameter 1 is prior to looking at the data. In that case, we would consider that we should give all positive values of equal weight. So we let the positive uniform prior density be pm) = 1 for a>0, an improper prior since its integral over all possible values is infinite. Show that the posterior distribution of 1 given the yı: Ya..., yn - Poisson() is a proper distribution, ie. Gamma 1 Vi, n).