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All N win probabilities of a factor-structured Gaussian race (multinomial probit with covariance VV’ + diag(D)) in one shared-lattice pass, and the inverse: calibrating abilities from observed shares.
nodes <- hermite_nodes(2)
p <- win_probabilities_factor(mu, V, D, nodes) # min wins; negate mu for argmax
a <- abilities_from_probabilities_factor(p, V, D, nodes)Why not N calls to mvtnorm::pmvnorm? That computes the same numbers (agreement to ~1e-6 at N = 5, verified in the test suite) but pays for N separate (N-1)-dimensional integrals; the shared survival field prices every alternative from one O(Q N L) pass. At N = 200 the difference is seconds versus minutes; at N = 1000, seconds versus hours.
Pure base R, no dependencies (mvtnorm suggested for the cross-check tests only). The Python/Rust implementations, benchmarks, and the paper live in the parent repository.
CRAN preparation checklist: roxygenize man pages, add vignette, R CMD check –as-cran, submit.
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