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Two-way layout factorial experiments of spatial point pattern responses in mineral flotation

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Abstract

Factorial experiments are well-understood when the given observations are outcomes of random variables. However, when we observe spatial point patterns in each combination of factors cells, the methodology is much less developed. Motivated by a real problem of locations of bubbles in a mineral flotation experiment where the interest is analysing if the spatial distribution might be affected by frother concentrations and volumetric airflow rates, we develop an approach for statistical testing of two-way factorial experiments for spatial point patterns. We describe the point patterns through the K-function, a second-order summary statistic, and develop a set of new Fisher-based statistics using weighted means. For inference by Monte Carlo, we use random permutations of weighted residuals depending on the null hypothesis. We conduct simulation experiments to demonstrate the performance of the new test statistics and present the results of the real problem.

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Acknowledgements

We are indebted to Dr Aila Särkkä and Dr Edith Gabriel for their careful comments on an earlier draft. We would like to thank Project CORFO, SMI-ICE-CHILE 13CE12-21844-F1-L1-P3, “Frother Roles Characterization in a Laboratory Mechanical Flotation Cell”, for their kindness in providing the data set analysed. Jonatan A. González and Jorge Mateu are partially funded by Grant MTM2016-78917-R from the Spanish Ministry of Science and Education. Bernardo Lagos-Álvarez thanks VRID Grant 216.014.026-1.0, from University of Concepción.

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Authors and Affiliations

  1. Department of Mathematics, University Jaume I, Castellón, Spain

    Jonatan A. González & Jorge Mateu

  2. Department of Statistics, University of Concepción, Concepción, Chile

    Bernardo M. Lagos-Álvarez

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  1. Jonatan A. González
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  2. Bernardo M. Lagos-Álvarez
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  3. Jorge Mateu
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Correspondence to Jonatan A. González.

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González, J.A., Lagos-Álvarez, B.M. & Mateu, J. Two-way layout factorial experiments of spatial point pattern responses in mineral flotation. TEST 30, 1046–1075 (2021). https://doi.org/10.1007/s11749-021-00768-w

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