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Change simplex sampler to be one vs all instead of one vs next
Let p_1, p_2, p_n denote the simplex being sampled. Right now a slice sampler is used where two coordinates p_i and p_j are picked, and one is moved by the slicer while the other one stays fixed.
Some alternatives:
- Pick a bi-partition of the p_i's, transfer mass between the two
- Important special case: one versus all: p_i vs p_1, p_2, .., p_{i-1}, p_{i+1}, p_n
- Other ideas in https://cran.r-project.org/web/packages/walkr/vignettes/walkr.pdf
Hypothesis: in high dimensions, 2 should be easy to implement and already much better than the existing. There might be some better alternatives out there too.