Functional magnetic resonance imaging (fMRI) is one of the most popular neuroimaging technologies used in human brain studies. However, fMRI data analysis faces several challenges, including intensive computation due to the massive data size and large estimation errors due to a low signal-to-noise ratio of the data. A new statistical model and a computational algorithm are proposed to address these challenges. Specifically, a new multi-subject general linear model is built for stimulus-evoked fMRI data. The new model assumes that brain responses to stimuli at different brain regions of various subjects fall into a low-rank structure and can be represented by a few principal functions. Therefore, the new model enables combining data information across subjects and regions to evaluate subject-specific and region-specific brain activity. Two optimization functions and a new fast-to-compute algorithm are developed to analyze multi-subject stimulus-evoked fMRI data and address two research questions of a broad interest in psychology: evaluating every subject’s brain responses to different stimuli and identifying brain regions responsive to the stimuli. Both simulation and real data analysis are conducted to show that the new method can outperform existing methods by providing more efficient estimates of brain activity.

功能磁共振成像（fMRI）是在人脑研究中使用的最流行的神经成像技术之一。然而，fMRI数据分析面临数项挑战，包括由于海量数据大小而导致的密集计算以及由于数据信噪比低而导致的巨大估计误差。提出了一种新的统计模型和一种计算算法来应对这些挑战。具体来说，为刺激诱发的功能磁共振成像数据建立了一个新的多主体通用线性模型。新模型假设大脑对各种对象的不同大脑区域的刺激的反应属于低等级结构，可以用一些主要功能来表示。因此，新模型可以组合跨对象和区域的数据信息，以评估特定对象和特定区域的大脑活动。开发了两个优化功能和一种新的快速计算算法，以分析多对象刺激诱发的功能磁共振成像数据，并解决心理学界广泛关注的两个研究问题：评估每个受试者的大脑对不同刺激的反应，并确定响应于不同刺激的大脑区域刺激。进行模拟和真实数据分析均表明，通过提供更有效的大脑活动估计，该新方法可以胜过现有方法。