Slice sampling

In mathematics and physics, Slice sampling is a type of Markov chain Monte Carlo sampling algorithm based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function.

Additional recommended knowledge

What is the Correct Way to Check Repeatability in Balances?

Safe Weighing Range Ensures Accurate Results

How to ensure accurate weighing results every day?

Implementation

To sample a random variable X with density f(x) we introduce an auxiliary variable Y and iterate as follows: Given a sample x we choose y uniformly at random from the interval [0,f(x)]; given y we choose x uniformly at random from the set f ^{− 1}[y,f(x)]. The sample of x is obtained by ignoring the y values.

Example

To sample from the normal distribution N(0,1) we first choose an initial x -- say 0. After each sample of x we choose y uniformly at random from ; after each y sample we choose x uniformly at random from [ − α,α] where .

An implementation in the Macsyma language is:
slice(x):=block([y,alpha],

  y:random( exp(-x^2/2.0)/sqrt(2.0*dfloat(%pi))),
  alpha:sqrt(-2.0*ln(y*sqrt(2.0*dfloat(%pi)))),
  x:signum(random())*random(alpha)

);

See also

• Sampling (statistics)
• Markov chain Monte Carlo

References

• Radford M. Neal, "Slice Sampling". The Annals of Statistics, 31(3):705-767, 2003.