I am trying to learn about Bayesian parameter estimation and found some really good tutorial over here (Tutorial 1 & 2). Just to test my understanding I am trying to implement MCMC approach for estimating probability of getting head based on a give dataset. The input dataset has 8 heads and 2 tails. Assuming the prior follows Beta(2,2), analytically probability of getting head = (8+2)/(10+2+2) = 0.71. However I am getting very different answer when trying to use metropolis-hastings algorithm. Can anyone checkout my implementation over here and explain what I am missing
http://nbviewer.ipython.org/github/ragrawal/meetup/blob/master/notebook/MCMC.ipynb
I think your answer is 0.717147231334, and it is not a problem. It can be little bit different even though you have analytic answer 0.71.
Actually, the analytic answer 0.71 is a posterior mean of the posterior distribution, and your answer is numerical approximation of it (sample mean).