Statistics in ecological modeling; presence -only data and boosted MARS

摘要

The research presented in this thesis was primarily motivated by current problems in ecological modeling. One such major problem is the so-called presence-only problem, the analysis of which forms the core of this thesis. The remainder of the thesis introduces boosted MARS, a new flexible modeling procedure.;In ecological modeling of the habitat of a species, it can be prohibitively expensive to determine species absence. Presence-only data consists of a sample of locations with known presences and a separate group of locations sampled from the population, with unknown presences. We propose four different approaches, all of which estimate an underlying presence-absence model for presence-only data. In the first, an application of the EM algorithm can be used with almost any off-the-shelf logistic model. In the other three models, gradient boosted regression trees are used to maximize different loss functions arising from different model assumptions. Simulations and analyses based on sampling from presence-absence records of fish in New Zealand rivers illustrates that these new procedures can reduce both deviance and the shrinkage of marginal effect estimates that occur in the naive model often used in practice. It is shown that the population prevalence of a species is only identifiable when there is some unrealistic constraint on the structure of the logistic model. In practice, it is strongly recommended that an estimate of population prevalence be provided.;Boosted MARS is a modeling procedure which aims to mimic the flexibility and performance of gradient boosted trees, but while providing a smoother fitted model. Refitting the boosted MARS basis functions using L1 regularization sometimes improves predictive performance. However, boosted regression trees usually outperform either boosted MARS mdoel. We also investigate the effects of smoothing and thresholding the MARS basis functions on predictive and descriptive performance.