Bayesian residual analysis for spatially correlated data

R., Lobo, Viviana G.; Fonseca, Thaís C. O.

doi:10.1177/1471082x18811529

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…The approach can be used for GRFs with stationary and nonstationary covariances and to data observed at regular or irregularly spaced locations. More recently, Lobo and Fonseca (2020) use a cross-validation approach to assess goodness-of-fit of spatial models. These approaches, however, consider only spatial data.…”

Section: Introductionmentioning

confidence: 99%

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Morris

Sibanda

2022

Environ Ecol Stat

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Within the field of geostatistics, Gaussian processes are a staple for modelling spatial and spatio-temporal data. Statistical literature is rich with estimation methods for the mean and covariance of such processes (in both frequentist and Bayesian contexts). Considerably less attention has been paid to developing goodness-of-fit tests for assessment of model adequacy. Jun et al. (Environmetrics 25(8):584–595, 2014) introduced a statistical test that uses pivotal discrepancy measures to assess goodness-of-fit in the Bayesian context. We present a modification and generalization of their statistical test. The initial method involves spatial partitioning of the data, followed by evaluation of a pivotal discrepancy measure at each posterior draw to obtain a posterior distribution of pivotal statistics. Order statistics from this distribution are used to obtain approximate p-values. Jun et al. (Environmetrics 25(8):584–595, 2014) use arbitrary partitions based on pre-existing spatial boundaries. The partitions are made to be of equal size. Our contribution is two-fold. We use K-means clustering to create the spatial partitions and we generalise Jun et al.’s approach to incorporate unequal partition sizes. Observations from a spatial or spatio-temporal process are partitioned using an appropriate feature vector that incorporates the geographic location of the observations into subsets (not necessarily of the same size). The method’s viability is illustrated in a simulation study, and in an application to hoki (Macruronus novaezelandiae) catch data from a survey of the sub-Antarctic region.

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Section: Introductionmentioning

confidence: 99%

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Morris

Sibanda

2022

Environ Ecol Stat

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Bayesian cross-validation of geostatistical models

Fonseca

Moura

2020

Spatial Statistics

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The problem of validating or criticising models for georeferenced data is challenging, since the conclusions can vary significantly depending on the locations of the validation set. This work proposes the use of cross-validation techniques to assess the goodness of fit of spatial models in different regions of the spatial domain to account for uncertainty in the choice of the validation sets. An obvious problem with the basic cross-validation scheme is that it is based on selecting only a few out of sample locations to validate the model, possibily making the conclusions sensitive to which partition of the data into training and validation cases is utilized. A possible solution to this issue would be to consider all possible configurations of data divided into training and validation observations. From a Bayesian point of view, this could be computationally demanding, as estimation of parameters usually requires Monte Carlo Markov Chain methods. To deal with this problem, we propose the use of estimated discrepancy functions considering all configurations of data partition in a computationally efficient manner based on sampling importance resampling. In particular, we consider uncertainty in the locations by assigning a prior distribution to them. Furthermore, we propose a stratified cross-validation scheme to take into account spatial heterogeneity, reducing the total variance of estimated predictive discrepancy measures considered for model assessment. We illustrate the advantages of our proposal with simulated examples of homogeneous and inhomogeneous spatial processes to investigate the effects of our proposal in scenarios of preferential sampling designs. The methods are illustrated with an application to a rainfall dataset.

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Dynamical non-Gaussian modelling of spatial processes

Fonseca

Schmidt

2023

Journal of the Royal Statistical Society Series C: Applied Statistics

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Environmental data are often assumed to follow a spatio-temporal Gaussian process, possibly after transformation. However, heterogeneity might have a pattern not accommodated by transformation and modelling the variance laws is an appealing alternative. This work extends the multivariate dynamic Gaussian model by defining the process as a scale mixture with the scale depending on covariates. State-space equations define the temporal dynamics, resulting in feasible inference and prediction. Various simulations studies show that the parameters are identifiable and our proposal recovers simpler structures. The analyses of temperature and ozone illustrate the improvement in quantifying the uncertainty of predictions.

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Bayesian residual analysis for spatially correlated data

Cited by 4 publications

References 33 publications

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Bayesian cross-validation of geostatistical models

Dynamical non-Gaussian modelling of spatial processes

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