Bayesian Procrustes analysis with applications to hydrology

Abstract

In this paper, we introduce Procrustes analysis in a Bayesian framework, by treating the classic Procrustes regression equation from a Bayesian perspective, while modeling shapes in two dimensions. The Bayesian approach allows us to compute point estimates and credible sets for the full Procrustes fit parameters. The methods are illustrated through an application to radar data from short-term weather forecasts (nowcasts), a very important problem in hydrology and meteorology.

Keywords:

• Bayesian computation and estimation
• complex normal distribution
• full Procrustes fit
• Procrustes analysis
• shape analysis

Acknowledgements

We are grateful to Professor Christopher K. Wikle for some helpful comments and suggestions. We are also thankful to two referees for some helpful comments and suggestions regarding an earlier version of the manuscript. This research was made possible by National Science Foundation MSPA-CSE Grant ATM-0434213.