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loldrup comments on How do I make sample size matter? - Less Wrong Discussion
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If only the mean if the likelihood distribution is involved, not the variance, then truly the sample size used when creating the likelihood distribution has no influence on the Bayesian update.
Then the next question is: is it a problem? If I understand you correctly then your answer is: "not really, because <something>".
Then it's only the <something> part I don't get.
You ask me if it's clear to me why only the mean if the likelihood distribution is involved in the Bayesian update. Well, it isn't currently, but I'll read the article "Continuous Bayes" and see if it then becomes more clear to me:
http://www.sidhantgodiwala.com/blog/2015/03/14/continuous-bayes/