The Variational Bayes Method For Inverse Regression Problems With an Application To The Palaeoclimate Reconstruction

The palaeoclimate reconstruction problem is described as an example of inverse regression problems. In the reconstruction problem, past climate is inferred using pollen data. Modern data is used to build a regression model of how pollen responds to climate. The inverse problem is to infer climate from data on ancient pollen prevalence. The inverse inference presents a challenging and computationally intensive problem. It is demonstrated that Variational Bayes (VB), that assumes conditional independence, provides quick solutions to the reconstruction problem. The advantage of the use of the VB method is that many more climate variables can be included in the estimation without imposing a huge burden to the reconstruction problem. We explore the accuracy of the VB method, and comment on its usefulness more generally in inverse inference problems.