I have used Bayesian statistics in classes but what I am trying to do now is different than anything I have done in class. Previously, I was given information and certain numbers adn I could calculate the the posterior value in Baye's theorem.
What I am working on now is parameter estimation. I have a long list of values and these values can be found using an equation. There is a term in the equation that is typically looked up on a chart that was determined from experiments. I am trying to uses Baye's rule to estimate this term based on data instead of looking it up. I know baye's rule is
posterior = (likelihood)(prior)/(marginal likelihood)
For my prior I have a distribution of values with the peak being on the value that I would expect from looking it up on chart. I am having trouble coming up with the likelihood. I thought I had to fit my data to a certain distribution but I don't know how to determine what distribution to use. How do I determine the likelihood based off my data?