I'm trying to sample from the normal distribution with a mean of .5 (like flipping a coin) and an arbitrary standard deviation using a markov chain (sequence of numbers where each number is dependent on the previous number of the sequence).
since this is a normal distribution under a markov chain, I expect the sampled values to fluctuate between 0 and 1 but mostly around .5 (like a random walk). I expect a result similar to this:
but when I try to do it my result looks like this:
I don't know why in that example the MCMC iteration never gets negative thetas or thetas greater than 1. all my plots are never contained between 0 and 1. if Normal(proposed_theta) outputs a value greater than 1 or is negative that is very problematic.