To understand global climate prior to the availability of widespread instrumental data, we need to reconstruct temperatures using natural proxies such as tree rings. For reconstructions of a temperature field with multiple proxies, the currently preferred method is RegEM (Schneider, 2001). However, this method has problems with speed, convergence, and interpretation.
In this thesis we show how one variant of RegEM can be replaced by the monotone EM algorithm (Liu, 1999). This method is much faster, especially in suitably designed pseudoproxy simulation experiments.
Multi-proxy reconstructions can be large, with thousands of variables and millions of parameters. We describe how monotone EM can be implemented efficiently for problems on this scale.
RegEM has been interpreted in a Bayesian context as a multivariate normal model with an inverse Wishart prior. We extend this interpretation, noting the empirical Bayesian aspects, the implications of the prior for the variance loss problem, and using posterior predictive checks for model criticism.
The Bayesian interpretation leads us to suggest a novel prior. Simulated reconstructions with this prior show promising performance against the usual prior, particularly in terms of low sensitivity to the tuning parameter.
