# Accept-Reject Sampling

October 29, 2013 - 11:26 am by Joss Whittle Matlab PhD UniversityContinuing 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.