I have a data which follows gamma distribution and want to know the uncertainty of the parameters of this data.





I used Winbugs (code below).

  for (i in 1:N){
    Y[i] ~ dgamma(k, theta)

k ~ dgamma(0.1, 0.1)
theta ~ dgamma(0.1, 0.1)

1.To plot the likelihood, first, I used a uniform prior then divided the posterior by the prior which makes the posterior same as the likelihood. (Figure1)

enter image description here

2.Next I changed the prior several times and looked what happens, but the problem is when I plotted the likelihood by dividing the posterior by the prior, likelihood changes which shouldn’t, whenever I change the prior. (Figure 2, 3)

enter image description here

enter image description here


Is it possible that the likelihood changes when the prior changes? If the prior is too narrow, is there a possibility that the posterior might be wrong? Can somebody help me what the problem is?

  • $\begingroup$ Why do you think the likelihood would remain constant when you change the prior? As you pointed out, it is proportional to the quotient of the posterior by the prior, so if the prior changes it seems reasonable that the likelihood would as well. $\endgroup$
    – Matt
    Mar 26, 2014 at 18:43
  • $\begingroup$ I'm not good at statistics but in my understanding the likelihood is dependent on data not the prior. Am I wrong? $\endgroup$
    – moon
    Mar 26, 2014 at 20:25
  • $\begingroup$ I think this is a Bayesian/frequentist divide. If you use a classical statistical test, then the likelihood does not depend on anything except the data. If you use a prior, then it does and is equal to the other case with a uniform prior (as your graph shows). $\endgroup$
    – Matt
    Mar 26, 2014 at 20:37

1 Answer 1


I have not inspected the code (i unfortunately don't use WinBUGS), but i would agree with @moon that there must be an error here, potentially because the observed data is not independently modelled? The likelihood is simply the probability that we be observe a given set of data (e.g. see maximum likelihood estimation) - none of the inputs in this formula / estimation is dependent on prior or posterior.


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