I thought the mean of the gamma distribution is Alpha/beta, so shouldn't our results be (sum xi + alpha) / (1 ( n + 1/beta)) instead of multiplying them?
There's two ways to write the gamma distribution: one uses the "shape" parameter and the other uses the "rate" parameter. Essentially one has exp(-x * beta) and (beta)^alpha while the other has exp(-x/beta) and (1/beta)^alpha. The former has mean alpha/beta while the latter has mean alpha * beta.
Thanks, but why are you sure you can derive the posterior with proportionality? i.e. are you sure the constant term will be the same as if you would calculate it all the way (without dropping the constant terms)?
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I'm happy to hear it! Good luck with your studies.
I thought the mean of the gamma distribution is Alpha/beta, so shouldn't our results be (sum xi + alpha) / (1 ( n + 1/beta)) instead of multiplying them?
There's two ways to write the gamma distribution: one uses the "shape" parameter and the other uses the "rate" parameter. Essentially one has exp(-x * beta) and (beta)^alpha while the other has exp(-x/beta) and (1/beta)^alpha. The former has mean alpha/beta while the latter has mean alpha * beta.
I can replicate it, but I've no idea what the hell I'm doing
I think if you start doing some Bayesian statistical analysis, this will be better motivated and you'll see why you're doing it.
Thanks, but why are you sure you can derive the posterior with proportionality? i.e. are you sure the constant term will be the same as if you would calculate it all the way (without dropping the constant terms)?
Yup, I'm sure. Look in any Bayesian book.