A multi-state idea for slice sampling Investigate the followingmulti-state method for slice sampling. As in Skilling"s multi-state leapfrog method (section 30.4), maintain a set of S state vectors...

A multi-state idea for slice sampling

 Investigate the followingmulti-state method for slice sampling. As in Skilling"s multi-state leapfrog method (section 30.4), maintain a set of S state vectors Update one state vector x(s) by one-dimensional slice sampling in a direction

y determined by picking two other state vectors and x(w)at random and setting Investigate this method on toy problems such as a highly-correlated multivariate Gaussian distribution. Bear in mind that if S ?? 1 is smaller than the number of dimensions N then this method will not be erotic by itself, so it may need to be mixed with other methods. Are there classes of problems that are better solved by this slice-sampling method than by the standard methods for picking y such as cycling through the coordinate axes or picking u at random from a Gaussian distribution?