Papers › Nonparametric FBST for Validating Linear Models
Nonparametric FBST for Validating Linear Models
Rodrigo F. L. Lassance, Julio M. Stern, Rafael B. Stern
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The Full Bayesian Significance Test (FBST) possesses many desirable aspects, such as dismissing the need for hypotheses to have positive prior probability and providing a measure of evidence against H₀. Still, few attempts have been made to bring the FBST to nonparametric settings, with the main drawback being the need to obtain the highest posterior density (HPD) in a function space. In this work, we use a Gaussian processes prior to derive the FBST for hypotheses of the type H₀: g(x) = b(x)β, ∀x ∈𝒳, β ∈ℝᵏ, where g(·) is the regression function, b(·) is a vector of linearly independent linear functions -- such as b(x) = x′ -- and 𝒳 is the covariates' domain. We also make use of pragmatic hypotheses to verify if the data might be compatible with a linear model when factors such as measurement errors or utility judgments are accounted for. This contribution extends the theory of the FBST, allowing its application in nonparametric settings and providing a procedure that easily tests if linear models are adequate for the data and that can automatically perform variable selection.
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