A Universal Generator for Bivariate Log-Concave Distributions
Different universal (also called automatic or black-box) methods
have been suggested to sample from univariate log-concave distributions.
The description of a universal generator for bivariate distributions has
not been published up to now. The new algorithm for bivariate log-concave
distributions is based on the method of transformed density rejection.
In order to construct a hat function for a rejection algorithm the bivariate
density is transformed by the logarithm into a concave function. Then it
is possible to construct a dominating function by taking the minimum of
several tangent planes which are by exponentiation transformed back into
the original scale. The choice of the points of contact is automated using
adaptive rejection sampling. This means that a point that is rejected
by the rejection algorithm is used as additional point of contact until
the maximal number of points of contact is reached. The paper describes
how this main idea can be used to construct Algorithm ULC2D that
can generate random pairs from bivariate log-concave distribution
with a computable density.
Mathematics Subject Classification:
65C10 (Random Number Generation)
CR Categories and Subject Descriptors:
G.3 [Probability and Statistics]: Random number generation
random number generation, rejection method, bivariate log-concave distributions,
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Trans. Math. Softw. 26(1), 201 - 219.