Abstract: Traditional independent vector analysis resolves permutation ambiguity using the higher-order dependency among the whole frequency band. Researchers have shown that neighboring frequencies have stronger dependency and using frequency bands partition can improve the separation result. Firstly, in this work, the overlapping cliques independent vector analysis based on natural gradient was extended to a fast algorithm using Newton gradient. Secondly, multivariate generalized Gaussian distribution and multivariate Student t distribution were introduced as source distribution priors in overlapping cliques or overlapping bands partition fast independent vector analysis algorithms because they were more suitable to model the heavy-tailed property of speech signals. Finally, a non-overlapping bands partition scheme was proposed in the fast independent vector analysis with heavy-tailed distributions. Power ratio correlation was introduced to avoid the block permutation ambiguity between frequency bands. Both simulation and real recording experimental results show that the proposed algorithm is better than the traditional fast independent vector analysis and other overlapping bands partition algorithms.