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Sparse partitioning: nonlinear regression with binary or tertiary predictors, with application to association studies. (English) Zbl 1232.62049

Summary: This paper presents sparse partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or tertiary predictors and allows the number of predictors to exceed the size of the sample, two properties which make it well suited for association studies.
Sparse partitioning differs from other regression methods by placing no restrictions on how the predictors may influence the response. To compensate for this generality, parse partitioning implements a novel way of exploring the model space. It searches for high posterior probability partitions of the predictor set, where each partition defines groups of predictors that jointly influence the response.
The result is a robust method that requires no prior knowledge of the true predictor-response relationship. Testing on simulated data suggests that sparse partitioning will typically match the performance of an existing method on a data set which obeys the existing method’s model assumptions. When these assumptions are violated, sparse partitioning will generally offer superior performance.

MSC:

62F15 Bayesian inference
62J02 General nonlinear regression
62F35 Robustness and adaptive procedures (parametric inference)
65C60 Computational problems in statistics (MSC2010)

Software:

SSS; BayesDA; LogicReg
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References:

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