Generate new points with slice sampling

Create new samples for the live set by evolving a current point in the set through slice sampling within a bounding hyperrectangle, shrinking the rectangle when proposals are rejected.

Usage

slice_rectangle(enlarge = 1)

Arguments

enlarge: [double(1)]
Factor by which to inflate the hyperrectangle's volume before sampling (see Details). Optional, and must be greater or equal to 1 if provided; if left NA, sampling is initially bounded by the unit hypercube at each iteration.

Value

[slice_rectangle], a named list that inherits from [ernest_lrps].

Details

The slice LRPS generates proposals by uniformly sampling within a bounding hyperrectangle that contains regions of the parameter space satisfying the likelihood criterion. Sampling begins by selecting a known live point \(\theta\) that satisfies the criterion. Each iteration proposes a new point within this rectangle via uniform sampling and compares it against the criterion; if rejected, a new hyperrectangle is drawn such that the proposed point is on its boundary and \(\theta\) is in its interior. This continues until either a valid proposal is found or the rectangle has shrunk to the point where no further clamping operations can be performed.

By default, the hyperrectangle spans the extreme values of the current live set in each dimension. This may risk excluding valid regions of the parameter space, particularly where the posterior is multimodal or highly non-Gaussian. To mitigate this, set enlarge > 1, which inflates the hyperrectagle's volume by the specified factor before sampling. Setting enlarge to NA disables this behaviour, instead slicing from the unit hypercube at each iteration.

References

Neal, R. M. (2000). Slice Sampling (Version 1). arXiv. doi:10.48550/ARXIV.PHYSICS/0009028

Examples

# Basic usage with default parameters
lrps <- slice_rectangle()

# More patient sampler for complex posteriors
patient_lrps <- slice_rectangle(enlarge = 1.25)