Bayesian statistics are becoming popular in ecological science. There are at least two major reasons for this popularity. First, statistical modeling tends to be more flexible in the Bayesian context; this allows ecologists to base analyses on models that more adequately reflect ecological complexities. Second, the Bayesian approach forces ecologists to explicitly account for uncertainty in every aspect of their statistical problems; this is particularly important in ecology where we are often quite uncertain about many aspects of our study systems. Despite these potential advantages, very little work has been done on Bayesian approaches to classical problems in multivariate statistical community ecology. Motivated by this research opportunity, I studied correspondence analysis (CA) from a Bayesian perspective.
Results/Conclusions
Community ecologists routinely use CA to analyze species-by-sites matrices when species abundances are assumed to be unimodally related to one or more environmental gradients. CA is used in this manner largely because it provides an approximation to the maximum likelihood estimate of some of the parameters in the Gaussian ordination model, which assumes unimodal relationships. I show that if a particular prior distribution is assumed, CA provides the exact solution to a Bayesian estimation problem under the Gaussian ordination model. This characterization of CA is more explicit than the approximate maximum likelihood approach. I show that this prior distribution is objective; it makes no assumptions about which species and sites are statistically associated with one another. I show, through an example, how this Bayesian approach provides a natural framework for quantifying uncertainty in inferences drawn from a CA. This work demonstrates the potential for a general Bayesian approach to multivariate statistical community ecology.
