文章基本信息

标题：A Simulation Approach to Bayesian Emulation of Complex Dynamic Computer Models
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作者：Sourabh Bhattacharya
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2007
卷号：2
期号：4
页码：783-816
出版社：International Society for Bayesian Analysis
摘要：In recent times, complex computer models have received wide attention in scientic research. However, in order to make conventional statistical statements regarding the scientic research, many expensive runs of the computer model are usually needed. New statistical theories, making their appearances, hold promise to alleviate the technical challenges. However, in cases where the underlying com- plex system is evolving with time, an e ective theory for statistical analyses is lacking. In this paper, we propose a novel Bayesian methodology that extends the existing methodologies to the case of complex dynamic systems. The approach described in the paper exploits the recursive nature of dynamic simulation models to give a more ecient and accurate emulator. The motivating example, although not a real model for any physical process, may be thought of as a proxy for a model representing climate change, where it is of interest to predict, over time t, the four-dimensional proxy time series yt = (temperature; ice melting rate, barren land, CO2 emission). Also available are proxy observations on deforestation, recorded over time; hence treated as known. The latter is known as forcing input, denoted by zt. The computer model is treated as a black box. Typically, Gaussian processes are used to model unknown computer models, which we adopt in our article. In order to exploit the recursive nature of dynamic computer models, we introduce a grid within the range of the unknown function where the entire dynamic sequence is expected to lie. This grid essentially denes a look-up table. Our proposed method then assumes that conditional on the response surface on the grid, and the available training data, the future responses are approximately independent. Exploiting the properties of Gaussian process, we justify our proposal theoretically and with ample simulation studies. We also apply our proposed methodology to the motivating example.
关键词：Gaussian process; Latin hypercube sampling; Markov property; matrix normal; parallel computing; spatial interpolation