摘要：This paper presents a methodology for cross-validation in the context of Bayesian
modelling of situations we loosely refer to as `inverse problems'. It is motivated by
an example from palaeoclimatology in which scientists reconstruct past climates
from fossils in lake sediment. The inverse problem is to build a model with which
to make statements about climate, given sediment. One natural aspect of this is to
examine model t via `inverse' cross-validation. We discuss the advantages of in-
verse cross-validation in Bayesian model assessment. In high-dimensional MCMC
studies the inverse cross-validation exercise can be computationally burdensome.
We propose a fast method involving very many low-dimensional MCMC runs, us-
ing Importance Re-sampling to reduce the dimensionality. We demonstrate that,
in addition, the method is particularly suitable for exploring multimodal distri-
butions. We illustrate our proposed methodology with simulation studies and the
complex, high-dimensional, motivating palaeoclimate problem.
关键词：Cross-validation, Inverse, Importance Re-sampling, Model t, Re-use
