Lung tumor tracking for radiotherapy requires real-time, multiple-step ahead forecasting of a quasi-periodic time series recording instantaneous tumor locations. We introduce a location-mixture autoregressive (LMAR) process that admits multimodal conditional distributions, fast approximate inference using the EM algorithm and accurate multiple-step ahead predictive distributions. LMAR outperforms several commonly used methods in terms of out-of-sample prediction accuracy using clinical data from lung tumor patients. With its superior predictive performance and real-time computation, the LMAR model could be effectively implemented for use in current tumor tracking systems.
"A location-mixture autoregressive model for online forecasting of lung tumor motion." Ann. Appl. Stat. 8 (3) 1341 - 1371, September 2014. https://doi.org/10.1214/14-AOAS744