# slice sampling

(1.2 hours to learn)

## Summary

Slice sampling is a method for sampling from a one-dimensional probability distribution by doing Gibbs sampling in an auxiliary variable model. A major virtue is that it doesn't require specifying a step size. For this reason, it's a useful tool for constructing MCMC samplers which don't require tuning step size parameters.

## Context

This concept has the prerequisites:

- Gibbs sampling (Slice sampling is a special case of Gibbs sampling)
- Metropolis-Hastings algorithm (When it's intractable to sample exactly from a slice, we need to use a more general M-H update.)

## Core resources (read/watch one of the following)

## -Free-

→ Information Theory, Inference, and Learning Algorithms

A graudate-level textbook on machine learning and information theory.

→ Machine learning summer school: Markov chain Monte Carlo (2009)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Bayesian Reasoning and Machine Learning

A textbook for a graudate machine learning course.

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 11.4, pages 546-548

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 24.5.2, pages 864-866

## See also

- Other auxiliary variable sampling methods include:
- The Swendsen-Wang algorithm is a powerful sampling method for Ising models.
- Hamiltonian Monte Carlo (HMC) uses gradient information to sample from a continuous model

- elliptical slice sampling , for models with a multivariate Gaussian prior
- the No-U-Turn Sampler (NUTS) , a parameter-free version of Hamiltonian Monte Carlo