The paper introduces slice sampling, a Markov chain Monte Carlo (MCMC) method that adaptively samples from complex, multivariate distributions. Slice sampling involves sampling uniformly from the region under the density function of the distribution, and then selecting points based on horizontal coordinates. This method can be applied to univariate and multivariate distributions, and it is particularly useful for sampling from distributions where Gibbs sampling or Metropolis-Hastings algorithms are difficult to implement or inefficient. Slice sampling can adaptively choose the scale of changes, making it easier to tune compared to Metropolis methods and avoiding the inefficiencies of random walks. The paper discusses various methods for finding intervals and sampling within them, including the stepping-out and doubling procedures. It also proves the correctness of single-variable slice sampling, showing that it leaves the desired distribution invariant. Slice sampling is advantageous for routine and automated use, as it is simpler to implement and more efficient than other MCMC methods in many cases.The paper introduces slice sampling, a Markov chain Monte Carlo (MCMC) method that adaptively samples from complex, multivariate distributions. Slice sampling involves sampling uniformly from the region under the density function of the distribution, and then selecting points based on horizontal coordinates. This method can be applied to univariate and multivariate distributions, and it is particularly useful for sampling from distributions where Gibbs sampling or Metropolis-Hastings algorithms are difficult to implement or inefficient. Slice sampling can adaptively choose the scale of changes, making it easier to tune compared to Metropolis methods and avoiding the inefficiencies of random walks. The paper discusses various methods for finding intervals and sampling within them, including the stepping-out and doubling procedures. It also proves the correctness of single-variable slice sampling, showing that it leaves the desired distribution invariant. Slice sampling is advantageous for routine and automated use, as it is simpler to implement and more efficient than other MCMC methods in many cases.