Spatial preferential sampling occurs when the choice of sampling locations depends stochastically on the process of interest. Ignoring this dependence leads to inaccurate inferences. Our framework models experimenter preferences jointly with the spatial process to adjust for this. We dispense with the unrealistic assumption (required by existing methods) of conditional independence of sampling locations by defining a whole design distribution proportional to a utility function on the space of designs. The proposed model likelihood is generally intractable. We provide fitting techniques based on the noisy Markov chain Monte Carlo and demonstrate their usage on a data set of spatially distributed ammonia concentrations.

Original languageEnglish
Article numberqlad040
Pages (from-to)1041-1063
Number of pages23
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number4
Early online date30 Jun 2023
Publication statusPublished - 31 Aug 2023

Bibliographical note

Funding Information:
Elizabeth Gray was supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/L015684/1


  • intractable likelihood
  • noisy Monte Carlo
  • preferential sampling
  • reparameterisation
  • space-filling design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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