The paper introduces slice sampling, a method for Markov chain sampling that adaptively chooses the magnitude of changes made to the sampled variables. Slice sampling is based on the principle that one can sample from a distribution by uniformly sampling from the region under its density function. The method involves alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position. This approach is particularly useful for univariate distributions and can be extended to multivariate distributions by updating each variable in turn. Slice sampling is more efficient than Gibbs sampling and simpler than Metropolis updates, as it adaptively chooses the scale of changes, avoiding the need to tune parameters for each variable. The paper also discusses methods to suppress random walks, such as overrelaxation and reflection, to further improve sampling efficiency. Slice sampling is shown to be effective for a wide range of distributions, including those typical in Bayesian inference, and is suitable for routine and automated use. The paper concludes with a comparison of slice sampling to other Markov chain methods and highlights its advantages in terms of implementation and efficiency.The paper introduces slice sampling, a method for Markov chain sampling that adaptively chooses the magnitude of changes made to the sampled variables. Slice sampling is based on the principle that one can sample from a distribution by uniformly sampling from the region under its density function. The method involves alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position. This approach is particularly useful for univariate distributions and can be extended to multivariate distributions by updating each variable in turn. Slice sampling is more efficient than Gibbs sampling and simpler than Metropolis updates, as it adaptively chooses the scale of changes, avoiding the need to tune parameters for each variable. The paper also discusses methods to suppress random walks, such as overrelaxation and reflection, to further improve sampling efficiency. Slice sampling is shown to be effective for a wide range of distributions, including those typical in Bayesian inference, and is suitable for routine and automated use. The paper concludes with a comparison of slice sampling to other Markov chain methods and highlights its advantages in terms of implementation and efficiency.