We propose a new approach to anomaly detection from multivariate noisy sensor data. We address two major challenges: To provide variable-wise diagnostic information and to automatically handle multiple operational modes. Our task is a practical extension of traditional outlier detection, which is to compute a single scalar for each sample. To consistently define the variable-wise anomaly score, we leverage a predictive conditional distribution. We then introduce a mixture of Gaussian Markov random field and its Bayesian inference, resulting in a sparse mixture of sparse graphical models. Our anomaly detection method is capable of automatically handling multiple operational modes while removing unwanted nuisance variables.We demonstrate the utility of our approach using real equipment data from the oil industry.