The article by Picheny et al.(2013) is very interesting, and I believe that the methodologies developed here are innovative and should be useful for computer experiment practitioners. I congratulate the authors for writing such a nice article. Although I like most of the ideas in this article (especially the time allocation strategy), the formulation of the improvement function may need more justification, and this is the main focus of this discussion. To recall, the key assumptions of Picheny et al. are as follows:
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