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Partially observable Markov decision processes (POMDPs) have received significant interest in research on spoken dialogue systems, due to among many benefits its ability to naturally model the dialogue strategy selection problem under unreliable automated speech recognition. However, the POMDP approaches are essentially model-based, and as a result, the dialogue strategy computed from POMDP is still subject to the correctness of the model. In this paper, we extend some of the previous MDP user models to POMDPs, and evaluate the effects of user models on the dialogue strategy computed from POMDPs. We experimentally show that the strategies computed from POMDPs perform better than those from MDPs, and the strategies computed from poor user models fail severely when tested on different user models. This paper further investigates the evaluation methods for dialogue strategies, and proposes a method based on the bias-variance analysis for reliably estimating the dialogue performance.