A Wavelet-Based Bayesian Approach to Regression Models with Long Memory Errors and Its Application to fMRI Data

作者：Jeong Jaesik; Vannucci Marina^*; Ko Kyungduk

来源：Biometrics, 2013, 69(1): 184-196.

DOI：10.1111/j.1541-0420.2012.01819.x

• Bayesian inference
• fMRI Data
• Long memory errors
• Regression models
• Wavelets

This article considers linear regression models with long memory errors. These models have been proven useful for application in many areas, such as medical imaging, signal processing, and econometrics. Wavelets, being self-similar, have a strong connection to long memory data. Here we employ discrete wavelet transforms as whitening filters to simplify the dense variancecovariance matrix of the data. We then adopt a Bayesian approach for the estimation of the model parameters. Our inferential procedure uses exact wavelet coefficients variances and leads to accurate estimates of the model parameters. We explore performances on simulated data and present an application to an fMRI data set. In the application we produce posterior probability maps (PPMs) that aid interpretation by identifying voxels that are likely activated with a given confidence.

• 出版日期2013-3