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Application of Bayesian Mixture Models to Satellite Images and Estimating the Risk of Fire-Ant Incursion in the Identified Geographical Cluster

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Case Studies in Applied Bayesian Data Science

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2259))

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Abstract

Bayesian non-parametric mixture models have found great success in the statistical practice of identifying latent clusters in data. However, fitting such models can be computationally intensive and of less practical use when it comes to tall datasets, such as Landsat imagery. To overcome this issue, we propose to obtain multiple samples from data using stratified random sampling to enforce adequate representation in each sample from sub-populations that may exist in data. The non-parametric model is then fitted to each sample dataset independently to obtain posterior estimates. Label correspondence across multiple estimates is achieved using multivariate component densities of a chosen reference partition followed by pooling multiple posterior estimates to form a consensus posterior inference. The labels for pixels in the entire image are inferred using the conditional posterior distribution given pooled estimates, thereby substantially reducing the computational time and memory requirement.

The method is tested on Landsat images from the Brisbane region in Australia, which were compiled as a part of the national program for the eradication of the imported red fire-ant that was launched in September 2001 and which continues to the present date. The aim is to estimate the risk of fire-ant incursion in each of the identified geographical cluster so that the eradication program focuses on high risk areas.

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Acknowledgements

This research was supported by an ARC Australian Laureate Fellowship for project, Bayesian Learning for Decision Making in the Big Data Era under Grant no. FL150100150. The authors also acknowledge the support of the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) and the support of QUT’s high-performance computing and Research Support (HPC) group.

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Authors and Affiliations

  1. School of Mathematical Sciences, ARC Centre of Mathematical and Statistical Frontiers, Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD, Australia

    Insha Ullah & Kerrie L. Mengersen

Authors
  1. Insha Ullah
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  2. Kerrie L. Mengersen
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Correspondence to Insha Ullah .

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Editors and Affiliations

  1. Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia

    Kerrie L. Mengersen

  2. I2M, CNRS, Centrale Marseille, Aix-Marseille University, Marseille, France

    Pierre Pudlo

  3. CEREMADE, Université Paris Dauphine, Paris, France

    Christian P. Robert

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Ullah, I., Mengersen, K.L. (2020). Application of Bayesian Mixture Models to Satellite Images and Estimating the Risk of Fire-Ant Incursion in the Identified Geographical Cluster. In: Mengersen, K., Pudlo, P., Robert, C. (eds) Case Studies in Applied Bayesian Data Science. Lecture Notes in Mathematics, vol 2259. Springer, Cham. https://doi.org/10.1007/978-3-030-42553-1_17

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