Maximum entropy methods for generating simulated rainfall

Julia Piantadosi, Phil Howlett, Jonathan Borwein, John Henstridge
2012 Numerical Algebra, Control and Optimization  
We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. • Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. • The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration.
more » ... • Finally, we discuss the numerical for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall. Checkerboard copula An m-dimensional checkerboard copula is a distribution with a corresponding density defined almost everywhere by a step function on an m-uniform subdivision of the hypercube [0, 1] m . Example Simple 2-D example with 3 subdivisions Of course we expect a better solution if we increase the number of subdivisions in the checkerboard.
doi:10.3934/naco.2012.2.233 fatcat:lzieo7dcm5dxrcznyxjbiloy5u