Using Bayesian inference to account for uncertainty in parameter estimates in modelled invasive flowering rush

Abstract

Quantification of uncertainty that arises from a number of sources can enhance our understanding of biophysical processes of invasive species and the use of effective techniques, which results in more informed decision-making. To predict invasive flowering rush (FR) (Butomus umbellatus L.) within high spatial resolution imagery (<20 cm) from Applanix 439 Digital Sensor System (DSS) (Applanix Corporation, Richmond Hill, ON, Canada) requires a statistical approach with inherent modelling uncertainty. This letter provides a preliminary assessment of Bayesian logistic regression that is used to represent complex relationships between covariates derived from DSS imagery and estimates of inherent uncertainty in FR distributions. The Markov Chain Monte Carlo technique was used to generate the results of posterior parameter estimates, which were used to compare the sensitivity and robustness of different posterior estimators such as mean, median and other statistical descriptors. Predicted scenario of FR from the simulated posterior distributions was assessed by receiver operating characteristic (ROC) curves and their corresponding area under the ROC curves (AUC). The numerical value of the AUC suggested that the highest overall quantitative index of accuracy corresponded to 0.777 (AUC), while the lowest overall quantitative index of accuracy corresponded to 0.696 (AUC). The potential of this approach is illustrated in a case study in Ottawa National Wildlife Refuge in Northwest Ohio.

Acknowledgements

I thank A. Droog and H. Michaels who helped with the fieldwork component of this research and R. Huffman and K. Huffman from the ONWR. I also thank the two anonymous reviewers, who provided helpful suggestions and excellent additions.