Algorithm 802: An Automatic Generator for Bivariate Log-Concave Distributions

Different automatic (also called universal or black-box) methods have been suggested to sample from univariate log-concave distributions. Our new automatic 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 points that are rejected by the rejection algorithm can be used as additional points of contact. The paper describes the details how this main idea can be used to construct Algorithm ALC2D that can generate random pairs from all bivariate log-concave distributions with known domain, computable density and computable partial derivatives.