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Abstract:
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In recent research on Bayesian functional regression, point-wise and joint credible intervals are often used to conduct posterior functional inference, but there are disadvantages to using such intervals including inflated false discovery rates and over-coverage. To address this, we propose the use of two novel approaches: a Functional Boxplot-based interval and a robust joint interval, when constructing posterior credible intervals in Bayesian Function-on-scalar Regression Models fit using penalized splines. We conduct a comprehensive simulation study to compare the different posterior interval estimation approaches under both Gaussian and Bernoulli functional outcome settings. In general, we show that the functional boxplot-based intervals provide closer to nominal coverage under varying true covariance structures while the robust joint intervals provide similar results to the commonly implemented joint credible intervals. We also explore the false discovery rate and sensitivity of all four approaches. Finally, we present an application of the intervals to several data examples.
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