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Trajectory prediction is one of the key capabilities for robots to safely navigate and interact with pedestrians. Critical insights from human intention and behavioral patterns need to be integrated to effectively forecast long-term pedestrian behavior. Thus, we propose a framework incorporating a Mutable Intention Filter and a Warp LSTM (MIF-WLSTM) to simultaneously estimate human intention and perform trajectory prediction. The Mutable Intention Filter is inspired by particle filtering and genetic algorithms, where particles represent intention hypotheses that can be mutated throughout the pedestrian motion. Instead of predicting sequential displacement over time, our Warp LSTM learns to generate offsets on a full trajectory predicted by a nominal intention-aware linear model, which considers the intention hypotheses during filtering process. Through experiments on a publicly available dataset, we show that our method outperforms baseline approaches and demonstrate the robust performance of our method under abnormal intention-changing scenarios. Code is available at https://github.com/tedhuang96/mifwlstm.