rnd = slicesample(initial,nsamples,'pdf',pdf)
rnd = slicesample(initial,nsamples,'logpdf',logpdf)
[rnd,neval] = slicesample(initial,...)
[rnd,neval] = slicesample(initial,...,Name,Value)
rnd = slicesample(
nsamples random samples using the slice sampling method (see Algorithms).
initial is a row vector or scalar containing the initial value of the random sample sequences.
Initial point, a scalar or row vector. Set
Positive integer, the number of samples that
Handle to a function that generates the probability density function, specified with
Handle to a function that generates the logarithm of the probability density function, specified with
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
Nonnegative integer, the number of samples to generate and discard before generating the samples to return. The slice sampling algorithm is a Markov chain whose stationary distribution is proportional to that of the
Positive integer, where
Width of the interval around the current sample, a scalar or vector of positive values.
Scalar, the mean number of function evaluations per sample.
Generate Random Samples From a Multimodal Density
This example shows how to generate random samples from a multimodal density using
Define a function proportional to a multimodal density.
rng default % For reproducibility f = @(x) exp(-x.^2/2).*(1 + (sin(3*x)).^2).*... (1 + (cos(5*x).^2)); area = integral(f,-5,5);
Generate 2000 samples from the density, using a burn-in period of 1000, and keeping one in five samples.
N = 2000; x = slicesample(1,N,'pdf',f,'thin',5,'burnin',1000);
Plot a histogram of the sample.
[binheight,bincenter] = hist(x,50); h = bar(bincenter,binheight,'hist'); h.FaceColor = [.8 .8 1];
Scale the density to have the same area as the histogram, and superimpose it on the histogram.
hold on h = gca; xd = h.XLim; xgrid = linspace(xd(1),xd(2),1000); binwidth = (bincenter(2)-bincenter(1)); y = (N*binwidth/area) * f(xgrid); plot(xgrid,y,'r','LineWidth',2) hold off
The samples seem to fit the theoretical distribution well, so the
burnin value seems adequate.
There are no definitive suggestions for choosing appropriate values for
width. Choose starting values of
thin, and increase them, if necessary, to give the requisite independence and marginal distributions. See Neal  for details of the effect of adjusting
At each point in the sequence of random samples,
slicesample selects the next point by “slicing” the density to form a neighborhood around the previous point where the density is above some value. Consequently, the sample points are not independent. Nearby points in the sequence tend to be closer together than they would be from a sample of independent values. For many purposes, the entire set of points can be used as a sample from the target distribution. However, when this type of serial correlation is a problem, the
thin parameters can help reduce that correlation.
slicesample uses the slice sampling algorithm of Neal . For numerical stability, it converts a
logpdf function. The algorithm to resize the support region for each level, called “stepping-out” and “stepping-in,” was suggested by Neal.
 Neal, Radford M. "Slice Sampling." Ann. Stat. Vol. 31, No. 3, pp. 705–767, 2003. Available at Project Euclid.