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The article examines slice sampling — an adaptive MCMC algorithm that automatically adjusts its sampling parameters. Its effectiveness is demonstrated using Bayesian linear and logistic regression models, and the results are compared with classical frequentist methods.

Markov chain Monte Carlo (MCMC) methods are widely used for sampling from complex multidimensional distributions, particularly in Bayesian statistics. Classical algorithms, such as Gibbs sampling or the Metropolis algorithm, often require careful fine-tuning. In the first case, it is necessary to derive analytical expressions for all full conditional distributions, and in the second, to painstakingly select the scale and shape of the proposal distribution. This makes it difficult to use them quickly and effectively in everyday practice.

This article examines slice sampling — an adaptive variant of MCMC. Its key advantage is that it automatically adapts to the characteristics of the target distribution, eliminating the need to manually adjust parameters such as step width.

After providing a detailed description of the algorithm and its implementation in the MQL5 environment, we will test it using the examples of Bayesian linear and logistic regression, comparing the results with classical frequentist methods that provide point estimates of the parameters.

Author: Evgeniy Chernish