Doubling slice sampling

Draw a slice height and randomly place an interval of width w around x0. While at least one endpoint is inside the slice and fewer than p doublings have occurred, choose left or right with probability one half and extend that side by the current interval width, even if the chosen endpoint was already outside the slice. Propose uniformly from the resulting interval and shrink rejected sides relative to x0. An in-slice x1 must also pass Figure 6: repeatedly bisect the original doubled interval toward x1, track whether x0 and x1 have entered different halves, and after such separation reject if both endpoints of a resulting interval lie outside the slice. Continue back to the original width, with the source’s round-off guard. This excludes candidates from which interval construction would have stopped earlier and preserves the required transition symmetry.