I am an IT guy writing my masters thesis on MCMC methods for use in predicting the outcome of football(soccer) matches. Right now I am trying to wrap my head around MCMC and Metropolis-Hastings in particular. Coming from software development I don't really have the understanding of probability and statistics needed. I do understand how and why the acceptance function of Metropolis-Hastings work, but I can't really wrap my head around how to calculate the acceptance probability
$ min(1, \frac{P(X')}{P(X)} * \frac{Q(X|X')}{Q(X'|X)}) $
Were $X$ is my previous sample and $X'$ is my randomly generated sample from the proposal distribution $Q$
In trying to understand the algorithm i have created the toy problem where my goal is to estimate a target density $P(X) \sim N(0,1)$, using the proposal distribution $Q(X) \sim N(.,0.25)$
I know this must seem like a really stupid question, but do you actually evaluate the density in $X$ for $P(X)$, and how do you calculate the transition probability $Q(X|X')$?
I know this is stupid since $Q$ is symmetric and would cancel out the transition probability (and that this can be done using the Metropolis algorithm), but I need to know how to calculate it correctly. Thanks!