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Postulating monotonicity in nonparametric Bayesian regression

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In situations where it can be applied, an assumed monotonicity property of the regression function with respect to covariates has a strong stabilizing effect on the estimates. Because of this, other parametric or structural assumptions may not be needed at all. Although monotonic regression in one dimension is well studied, the question remains whether one can find computationally feasible generalizations to multiple dimensions. We propose a nonparametric monotonic regression model for one or more covariates and a Bayesian estimation procedure. The monotonic construction is based on marked point processes, where the random point locations and the associated marks (function levels) together form piecewise constant realizations of the regression surfaces. The actual inference is based on model averaged results over the realizations. The proposed model and estimation procedure is the first of its kind to combine the monotonicity postulate with multiple covariates, nonparametric model formulation, and probability based inference.

(The talk is based on joint work with Olli Saarela)

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