Fast approximate inverse Bayesian inference in non-parametric multivariate regression with application to palaeoclimate reconstruction - Salter-Townshend, Michael (Trinity College (Dublin, Ireland). School of Computer Science & Statistics, 2009)
Bayesian statistical methods often involve computationally intensive inference procedures. Sampling algorithms represent the current standard for fitting and testing models. Such methods, while flexible, are computationally intensive and suffer from long run times and high potential sampling error. New methods for fitting non-parametric approximations offer a fast and accurate alternative. Essentially, a multivariate Gaussian distribution is used to approximate the posterior of the model parameters. Cross-validation is a useful tool in model validation which is an important aspect of statistical inference. Sampling based methods require many re-runs and are impractical for this task. A new method is developed in this thesis that performs fast cross-validation using the Gaussian approximations. Study of the palaeoclimate provides insight into long-term climate variability. This represents the motivating problem for the work in this thesis. A probabilistic forward model for vegetation given climate is fitted to modern training data using Bayesian methods. The model is then inverted and inference on climate given fossil pollen counts may be performed; this is referred to as the inverse model and crossvalidation is preferred in this context. Highly multivariate models may sometimes be broken down into a sequence of independent smaller problems, which may then be dealt with more easily in parallel. Procedures for assessing the performance of this approach are developed for the inverse problem via fast cross-validation. Spatial models for counts data with an over-abundance of zeros are developed and synergy with the Gaussian approximation method is demonstrated. Finally, the novel inference methods and new counts models are applied to the palaeoclimate training dataset and progress over the existing methods is demonstrated.
Keywords: Statistics, Ph.D.; Ph.D. Trinity College Dublin