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

Jonatan A. González*, Bernardo M. Lagos-Álvarez, Jorge Mateu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1046-1075
Number of pages30
JournalTest
Volume30
Issue number4
DOIs
StatePublished - Dec 2021

Bibliographical note

Funding Information:
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.

Funding Information:
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.

Publisher Copyright:
© 2021, Sociedad de Estadística e Investigación Operativa.

Keywords

  • Flotation bubble data
  • Frother concentration
  • K-function
  • Permutation test
  • Replicated point patterns
  • Volumetric airflow rate

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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