Sampling from a distribution is an active problem in statistics. When the distribution is easy to sample from, methods like Monte Carlo are applicable. But when the distribution is complex, of non-standard form or multivariate, more complicated algorithms are required. The well-known Markov Chain Monte Carlo method using the Metropolis-Hastings (MH) algorithm can perform very well to sample the complicated distributions in many situations. But it has the drawback of being sensitive to the scale of the proposal distribution used. Recently, some algorithms have been introduced in the literature to avoid some of the problems of the MH algorithm. These include Graves method, Sliced sampling, and Equi-energy sampling. In this project, a simulation study is done to compare the performance of these algorithms under various settings of their tuning parameters when applied to various types of distributions.
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