How should I find the likelihood function of a Bayesian Model?
For example, if I'm given a coin, I can use the Bernoulli Distribution as the likelihood function (because I know in advance that the outputs are 0 or 1 and it fits that distribution).
What if I'm given some data that I don't know the underlying distribution but it seems to follow a gamma distribution? (gamma is just for the example here, it could be normal, exponential, or some weird distribution).
- Should I just estimate the parameters of that Gamma (ie fitdist in R) and use these parameters along the likelihood function? (and if that is the case, it wouldn't work with the weird distribution)
- Use bayesian modeling to estimate the likelihood function. If that is the case, how can I achieve that? (I'm not expecting a printed code here but more like an explanation that puts me in the right direction)