Can likelihood be changed when the prior changes?

Question

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

•Data∼Gamma(α,β)

•Parameters

α∼Gamma(kα,θα)

β∼Gamma(kβ,θβ)

I used Winbugs (code below).

model{
  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)

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)

Question

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?

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.