Adaptive Slice Sampling for Bayesian Regression Models

Summary

This article explains slice sampling, an MCMC method that can draw from a target distribution using its unnormalized density. For a one-dimensional update, it samples a height beneath the density at the current point, finds an interval around that point by stepping outward, then draws within the interval and shrinks it until the new point lies inside the slice. Coordinate-wise updates extend the procedure to multidimensional parameters. The method adapts to the target distribution and avoids manually tuning a proposal step size as in Metropolis sampling.

The article describes an MQL5 implementation and applies it to Bayesian linear and logistic regression. It reports that posterior estimates and credible intervals were close to ordinary least squares and iteratively reweighted least squares results, with trace plots, autocorrelation checks, and posterior histograms used to assess sampling. Logistic regression showed some bias attributed to approximating the sigmoid. Slice sampling still requires appropriate implementation and diagnostics; the reported examples do not establish performance for every model or target distribution.

Key ideas

• Slice sampling defines a horizontal slice beneath the target density and samples within it.
• Stepping-out and shrinkage procedures adapt the sampling interval around the current point.
• Coordinate-wise slice sampling can update parameters in a multidimensional target distribution.
• The article compares Bayesian regression estimates with frequentist methods and uses sampling diagnostics.
• The logistic regression example has a reported bias related to sigmoid approximation.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.