Hierarchical integrated spatial process modeling of monotone West Antarctic snow density curves

White, Philip A.; Keeler, D. G.; Rupper, S.

doi:10.1214/21-aoas1443

Cited by 9 publications

(4 citation statements)

References 35 publications

(44 reference statements)

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“…Ferrier et al, 2007), the variable importance parameters add interpretability to the GDM framework. In sufficiently rich datasets, h and/or f k could be spatially varying and estimated by combining approaches in White et al (2021White et al ( , 2022.…”

Section: Model Specificationsmentioning

confidence: 99%

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Generative spatial generalized dissimilarity mixed modelling (spGDMM): An enhanced approach to modelling beta diversity

White,

Frye,

Slingsby

et al. 2023

Methods Ecol Evol

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Turnover, or change in the composition of species over space and time, is one of the primary ways to define beta diversity. Inferring what factors impact beta diversity is not only important for understanding biodiversity processes but also for conservation planning. At present, a popular approach to understanding the drivers of compositional turnover is through generalized dissimilarity modelling (GDM). We argue that the current GDM approach suffers several limitations and provide an alternative modelling approach that remedies these issues. We propose using generative spatial random effects models implemented in a Bayesian framework. We offer hierarchical specifications to yield full regression and spatial predictive inference, both with associated full uncertainties. The approach is illustrated by examining dissimilarity in three datasets: tree survey data from Panama's Barro Colorado Island (BCI), plant occurrence data from southwest Australia and plant abundance surveys from the Greater Cape Floristic Region (GCFR) of South Africa. We select a best model using out‐of‐sample predictive performance. We find that the form of the best model differs across the three datasets, but our models provide performance ranging from comparable to significant improvement over GDMs. Within the GCFR, the spatial random effects play a more important role in the modelling than all the environmental variables. We have proposed a model that provides several improvements to the current GDM framework. This includes advantages such as a flexible spatially varying mean function, spatial random effects that capture dependence unaccounted for by explanatory variables, and spatially heterogeneous variance structure. All these features are offered in a model that can adequately handle a large incidence of total dissimilarity through ‘one‐inflation’, as would be expected from highly biodiverse areas with steep turnover gradients.

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Section: Model Specificationsmentioning

confidence: 99%

“…In sufficiently rich datasets,

h

and/or

f_{k}

could be spatially varying and estimated by combining approaches in White et al. (2021, 2022).…”

Section: Our Modelling Approachmentioning

confidence: 99%

Generative spatial generalized dissimilarity mixed modelling (spGDMM): An enhanced approach to modelling beta diversity

White,

Frye,

Slingsby

et al. 2023

Methods Ecol Evol

Self Cite

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“…I‐splines are defined as the integral of M‐spline, or, equivalently, as the integral of a scaled B‐spline (see Meyer, 2008; Ramsay, 1988, for more details). White et al (2021) use M‐spline basis functions to construct integrated spatial processes for monotone function estimation.…”

Section: Spatially Varying Snow Density Modelsmentioning

confidence: 99%

Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing

et al. 2022

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Snow density estimates as a function of depth are used for understanding climate processes, evaluating water accumulation trends in polar regions, and estimating glacier mass balances. The common and interpretable physically derived differential equation models for snow density are piecewise linear as a function of depth (on a transformed scale); thus, they can fail to capture important data features. Moreover, the differential equation parameters show strong spatial autocorrelation. To address these issues, we allow the parameters of the physical model, including random change points over depth, to vary spatially.We also develop a framework for functionally smoothing the physically motivated model. To preserve inference on the interpretable physical model, we project the smoothing function into the physical model's spatially varying null space. The proposed spatially and functionally smoothed snow density model better fits the data while preserving inference on physical parameters. Using this model, we find significant spatial variation in the parameters that govern snow densification.

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“…For example, current methods to estimate ice sheet mass loss and associated sea level rise (Church et al(2013); Rignot et al(2019)) rely on accurate modelling of snow density estimates to effectively convert ice sheet surface elevation changes to mass changes (Lenaerts et al(2019)). Snow density estimates are also essential for direct measurements of water accumulation trends and glacier surface mass balance (see, e.g., Herron and Langway (1980); Hörhold et al(2011); Verjans et al(2020); White et al(2021) and citations therein).…”

Section: Introductionmentioning

confidence: 99%

Outlier accommodation with semiparametric density processes: A study of Antarctic snow density modelling

Sheanshang

White

Keeler

2021

Statistical Modelling

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In many settings, data acquisition generates outliers that can obscure inference. Therefore, practitioners often either identify and remove outliers or accommodate outliers using robust models. However, identifying and removing outliers is often an ad hoc process that affects inference, and robust methods are often too simple for some applications. In our motivating application, scientists drill snow cores and measure snow density to infer densification rates that aid in estimating snow water accumulation rates and glacier mass balances. Advanced measurement techniques can measure density at high resolution over depth but are sensitive to core imperfections, making them prone to outliers. Outlier accommodation is challenging in this setting because the distribution of outliers evolves over depth and the data demonstrate natural heteroscedasticity. To address these challenges, we present a two-component mixture model using a physically motivated snow density model and an outlier model, both of which evolve over depth. The physical component of the mixture model has a mean function with normally distributed depth-dependent heteroscedastic errors. The outlier component is specified using a semiparametric prior density process constructed through a normalized process convolution of log-normal random variables. We demonstrate that this model outperforms alternatives and can be used for various inferential tasks.

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Hierarchical integrated spatial process modeling of monotone West Antarctic snow density curves

Cited by 9 publications

References 35 publications

Generative spatial generalized dissimilarity mixed modelling (spGDMM): An enhanced approach to modelling beta diversity

Generative spatial generalized dissimilarity mixed modelling (spGDMM): An enhanced approach to modelling beta diversity

Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing

Outlier accommodation with semiparametric density processes: A study of Antarctic snow density modelling

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