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Abstract:
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Astronomers often deal with data where the covariates and the dependent variable are measured with heteroskedastic, non-normal error. While techniques have been developed for estimating regression parameters for data with heteroskedasticity and measurement errors, most methods lack procedures for checking method assumptions and constructing prediction intervals. To address these issues, we consider using non-conformity scores and their corresponding conformal prediction sets for model validation. We empirically demonstrate that these conformal prediction sets give finite sample control over type 1 error probabilities under a variety of assumptions on the measurement errors in the observed data and model misspecification, while other prediction intervals do not. We further demonstrate how our conformal prediction approach can be used for testing structural assumptions of proposed models from the literature that relate planet mass and planet radius.
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