Autoregressive hidden Markov model with missing data for modelling functional MR imaging data

Functional Magnetic Resonance Imaging (fMRI) has opened ways to look inside active human brain. However, fMRI signal is an indirect indicator of underlying neuronal activity and has low-temporal resolution due to acquisition process. This paper proposes autoregressive hidden Markov model with missing data (AR-HMM-md) framework which aims at addressing aforementioned issues while allowing accurate capturing of fMRI time series characteristics. The proposed work models unobserved neuronal activity over time as sequence of discrete hidden states, and shows how exact inference can be obtained with missing fMRI data under the "Missing not at Random" (MNAR) mechanism. This mechanism requires explicit modelling of the missing data along with the observed data. The performance is evaluated by observing convergence characteristic of log-likelihoods and classification capability of the proposed model over existing models for two fMRI datasets. The classification is performed between real fMRI time series from a task-based experiment and randomly-generated time series. Another classification experiment is performed between children and elder subjects using fMRI time series from resting-state data. The proposed model captured the fMRI characteristics efficiently and thus converged to better posterior probability resulting into higher classification accuracy over existing models for both the datasets.