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Random slice
Subset of the parameter space defined by all values of x such that the target probability density exceeds a value uniformly drawn between 0 and f(x₀).
Stepping-out algorithm
Iterative procedure that symmetrically extends an initial interval around the current state to guarantee that the slice is entirely contained within the sampling interval.
Shrinkage algorithm
Method of reducing the sampling interval when a drawn point falls outside the slice, by contracting the interval toward the previously accepted point.
Slice hyperrectangle
Multidimensional generalization of the slice interval, defined as the Cartesian product of intervals containing the multidimensional slice.
Distribution under the slice
Conditional probability distribution defined on the slice, used to determine the spatial extent of sampling at each iteration of the algorithm.
Elliptical slice sampling
Variant of slice sampling that uses ellipses instead of hyperrectangles for more efficient exploration in high-dimensional spaces with correlations.
Slice line
Horizontal line in the target density plot, randomly determined between 0 and the density value at the current point, defining the sampling bounds.
Slice acceptance criterion
Condition verifying that the proposed point belongs to the defined slice, thereby guaranteeing the preservation of the target stationary distribution.
Slice mixing
Algorithm's ability to efficiently explore the parameter space by using the local structure of the density to determine the range of moves between states.
Slice confidence interval
Probabilistic estimate of the region containing the complete slice, used to ensure that sampling does not miss any part of the high-probability region.
Double-slice variant
Extension of slice sampling using two levels of slices to improve efficiency in multimodal or heavy-tailed distributions.
Conditional rejection
Rejection mechanism in slice sampling where points outside the slice are systematically rejected without requiring a Metropolis ratio calculation.
Spatial uniformity
Property of uniform distribution of sampled points inside the slice, ensuring fair exploration of all regions with equal probability.