Bayesian mixture models and their Big Data implementations with application to invasive species presence-only data

Due to their conceptual simplicity and flexibility, non-parametric mixture models are widely used to identify latent clusters in data. However, when it comes to Big Data, such as Landsat imagery, such model fitting is computationally prohibitive. To overcome this issue, we fit Bayesian non-parametric models to pre-smoothed data, thereby reducing the computational time from days to minutes, while disregarding little of the useful information. Tree based clustering is used to partition the clusters into smaller and smaller clusters in order to identify clusters of high, medium and low interest. The tree-based clustering method is applied to Landsat images from the Brisbane region, which were the actual sources of motivation for development of the method. The images are taken as a part of the red imported fire-ant eradication program that was launched in September 2001 and which is funded by all Australian states and territories, along with the federal government. To satisfy budgetary constraints, modelling is performed to estimate the risk of fire-ant incursion in each cluster so that the eradication program focuses on high risk clusters. The likelihood of containment is successfully derived by combining the fieldwork survey data with the results obtained from the proposed method.

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