I have a question im trying to work through, but im not too sure how to start it off.
the question is related to scientists studying populations of fish by tagging them. We are told that the scientists believe that they have tagged no more than 20% of the entire population, but that it is much more likely that the true proportion is about 5%. We dicide to take a random sample of the fish to determine the true proportion that have been tagged.
We are asked to give the appropriate beta proior distribution. Then go on to give the posterior distribution, mean, variance and the credible interval. I can do those last question no worries, it is just getting the prior beta distribution that i am having troube with.
Any help getting started as to how i can work out this distribution would be much appreciated.
Given that if you multiply two Beta PDF's you get a new Beta PDF for the posterior, what can you say about the parameters of the combined posterior and the connection between the prior distribution?
You are going to have a posterior PDF that is a beta with two parameters, a likelihood with its own form and a prior that is a beta. You know the posterior and the likelihood which means you can use that to get the parameters for the prior.