Accept-Reject Sampling

Continuing on from experiments last week with Metropolis Hastings sampling for probability distributions I decided to implement Accept-Reject sampling. Accept-Reject seems to deliver well distributed results faster than Metropolis Hastings does but in the long run can easily introduce biased samples if the proposal distribution q(x) is not well tuned to the specific probability distribution function. MH on the other hand, is far more resilient to an improperly chosen proposal distribution as it will still converge to an unbiased result in most cases, albeit by taking a longer time to converge than it normally would. Accept-Reject also seems to have issues towards the truncations of it’s function causing under-sampling of values close to the lower and upper bounds.

Tags Accept-Reject, Bayesian Statistics, Matlab, Metropolis-Hastings, Monte Carlo Integration