Reference no: EM132845643

In general, we want to maximize the acceptance probability when sampling a given probability distribu- tion using the rejection method. However, as we will later see in Markov chain Monte Carlo methods, when the idea of rejection is used in conjunction with complex computational algorithms, we may want to fix the probability of acceptance to optimize other aspects of an algorithm. Assume we want to sample the target random variable X ∼ Unif(-2,2) using a proposal random variable Y ∼ Unif(0,b), b > 0, and the symmetry of the uniform distribution. Find b so that the probability of acceptance is 0.4.