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Abstract:
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Reparametrizations, or variable transformations, are known to be key to efficient implementation of MCMC algorithms. However, the majority of proposals to date focus on either a single transformation or straightforward combinations of several transformations. Here, we demonstrate that by interweaving two specific kinds of (one-to-one) transformations, we can gain considerable speed in convergence and simplicity in construction. Simplicity is due to choosing transformations via sufficiency and ancillarity, two familiar classical concepts. In addition, by using conditional sufficiency and ancillarity, we can interweave different transformations for different steps (e.g., Gibbs steps) within each iteration, and thereby the proposed strategy provides a fairly general recipe for constructing a new generation of efficient algorithms for complicated applications.
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