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  • $\begingroup$ This sounds like a case where you really need a Bayesian approach. $\endgroup$ Commented Mar 13, 2017 at 22:27
  • $\begingroup$ Ironically, I am asking this question because I need to know the likelihood, so that I can code it in Stan. If you could give guidance on how I could implement it in a probabilistic programming language, I would definitely find that an acceptable answer. $\endgroup$ Commented Mar 13, 2017 at 22:44