Slice sampling

Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution. The method is based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function.

To visualize this motivation, imagine printing out a simple bell curve and throwing darts at it. Assume that the darts are uniformly distributed around the board. Now take off all of the darts that are outside the curve (i.e. perform rejection sampling). The x-positions of the remaining darts will be distributed according to the bell curve. This is because there is the most room for the darts to land where curve is highest and thus the probability density is greatest.

Slice sampling, in its simplest form, samples uniformly from underneath the curve f(x) without the need to reject any points, as follows: