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The slowly varying drift poses a major problem in the analysis of functional magnetic resonance imaging (fMRI) data. In this paper, based on the observation that noise in fMRI is long memory fractional noise and the slowly varying drift resides in a subspace spanned only by large scale wavelets, we examine a modified general linear model (GLM) in wavelet domain under Bayesian framework. This modified model estimates the activation parameters at each scale of wavelet decomposition. Then, a model selection criterion based on the results from the modified scheme is proposed to model the drift. Results obtained from simulated as well as real fMRI data show that the proposed Bayesian estimator can accurately capture the noise structure, and hence, result in robust estimation of the parameters in GLM. Besides, the proposed model selection criterion works well and could efficiently remove the drift.