摘要：In recent times, complex computer models have received wide attention
in scienti c research. However, in order to make conventional statistical statements
regarding the scienti c 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 de nes
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.
