We develop algorithms for sampling from a probability distribution on a submanifold embedded in R n . Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory.
We suggest a simple algorithm for Monte Carlo generation of uniformly distributed variables on a compact group. Example include random permutations, Rubik's cube positions, orthogonal, unitary, and symplectic matrices, and elements of GLn over a finite field. the algorithm reduces to the “standard” fast algorithm when there is one, but many new example are included.
Abstract. Projection pursuit algorithms approximate a function of p variables by a sum of nonlinear functions of linear combinations'We develop some approximation theory, give a necessary and sufficient condition for equality in (1), and discuss nonuniqueness of the representation.
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