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Title: Signal compression and Bayesian functional regressions in presence of hybrid principal component: An EEG-fMRI Dataset Authors:  Mohammad Fayaz - Shahid Beheshti University of Medical Sciences (Iran) [presenting]
Alireza Abadi - Shahid Beheshti University of Medical Sciences (Iran)
Soheila Khodakarim - Shahid Beheshti University of Medical Sciences (Iran)
Abstract: In some situations that exist both scalar and functional data, called mixed and hybrid data, the hybrid PCA (HPCA) was introduced. Among the regression models for the hybrid data, we can count covariate-adjusted HPCA, the Semi-functional partial linear regression, FOF regression with signal compression, and functional additive regression, models. We study the effects of HPCA decomposition of hybrid data on the prediction accuracy of the two functional regression models: Bayesian scalar-on-function with Markov Chain Month Carlo (MCMC) sampler and function-on-function with signal compressions. We stated a two-step procedure for incorporating the HPCA in the functional regressions. The first step in reconstructing the data based on the HPCAs and the second step is merging data on the other dimensions and calculate the point-wise average of the desired functional dimension. We choose the number of HPCA based on the DIC, LPML, and deviance in the Bayesian settings and MSE and MPE for both of them. In the three simulations, we show that the regression models with the first HPCA have the best accuracy prediction and model fit summaries among no HPCA and all HPCAs with training/testing approach. Finally, we applied our methodology to the EEG-fMRI dataset.