本篇論文提出貝氏階層模型去分析功能性磁振影像資料。功能性磁振影像資料通常具有巨大的資料量且同時存在時間與空間的特性。一些研究指出，空間的相依性不只存在於信號變化的大小，同時也發生在時間相關上。然而，在現有大多數研究中為了計算效率而不考慮時間相關上的空間相依性。本篇論文應用空間隨機效果模型(spatial random effect model) 同時考慮信號和時間相關的空間相依性。透過模擬，我們發現提出的方法可以增加識別大腦區域對刺激反應的準確率。最後，我們透過模擬的結果及一個實際的事件相關功能性磁振影像資料來探討模型的特性。

A spatial Bayesian hierarchical model is proposed to analyze functional magnetic resonance imaging (fMRI) data. Typical fMRI experiments generate massive datasets with complex spatial and temporal structures. Several studies have found that the spatialdependence not only appears in signal changes but also in temporal correlations among voxels; however, current statistical approaches ignore the spatial dependence of temporal correlations to gain computational efficiency. We incorporated the spatial random effects model to simultaneously model spatial dependence arising from both signal changes and temporal correlations. Through simulation studies to demonstrate that the proposed approach increases the accuracy of the detection of brain activities while keeping computationally feasible. Finally, we apply a real event-related fMRI data to further illustrate the usefulness of the proposed model.

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