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    $\begingroup$ was just thinking - is there a mathematically precise way you can define "over fitting"? if you can, it is likely you can also build features into a likelihood function or a prior to avoid it happening. my thinking is that this notion sounds similar to "outliers". $\endgroup$
    – probabilityislogic
    Commented May 5, 2019 at 13:49
  • $\begingroup$ Your example of a posterior "reverting" to the prior is known as posterior collapse. It's not a bug of the Bayesian method but rather an indication of insufficient information in your sample (at least for parts of your model). In a non-Bayesian setting your model would simply be unidentified. $\endgroup$
    – Durden
    Commented Mar 5 at 17:17