Compositional splines for representation of density functions

Machalová, Jitka; Talská, Renáta; Hron, Karel; Gába, Aleš

doi:10.1007/s00180-020-01042-7

Cited by 15 publications

(22 citation statements)

References 22 publications

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“…The estimation of the continuous densities

from their discretization

cannot be tackled with classical smoothing techniques, since the constrained nature of density data must be taken into account during the smoothing phase ( Machalová et al, 2015 ). Several splines expansions have been proposed for the

case, like the constrained

splines described in Machalová et al (2015) , or the compositional spline basis introduced in Machalová et al (2020) . Here we consider the procedure described in Machalová et al (2015) , and implemented in the R package robCompositions ( Templ et al, 2011 ), which is chosen for its simplicity and solid implementation.…”

Section: Modeling Death Data As Functional Compositionsmentioning

confidence: 99%

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

et al. 2022

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With the tools and perspective of Object Oriented Spatial Statistics, we analyze official daily data on mortality from all causes in the provinces and municipalities of Italy for the year 2020, the first of the COVID-19 pandemic. By comparison with mortality data from 2011 to 2019, we assess the local impact of the pandemic as perturbation factor of the natural spatio-temporal death process. For each Italian province and year, mortality data are represented by the densities of time of death during the calendar year. Densities are regarded as functional data belonging to the Bayes space In this space, we use functional-on-functional linear models to predict the expected mortality in 2020, based on mortality in previous years, and we compare predictions with actual observations, to assess the impact of the pandemic. Through spatial downscaling of the provincial data down to the municipality level, we identify spatial clusters characterized by mortality densities anomalous with respect to the surroundings. The proposed analysis pipeline could be extended to indexes different from death counts, measured at a granular spatio-temporal scale, and used as proxies for quantifying the local disruption generated by the pandemic.

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“…The estimation of the continuous densities

from their discretization

case, like the constrained

Section: Modeling Death Data As Functional Compositionsmentioning

confidence: 99%

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

et al. 2022

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“…, where ݊ is the number of corals observed at that site (Martín-Fernández et al, 2003;Machalová et al, 2021Machalová et al, , p. 1053. Then, the size-frequency distributions were centred log-ratio (clr) transformed to give standard addition and scalar multiplication operations, which allows for easier computation (van den Boogaart et al, 2014).…”

Section: Data Analysesmentioning

confidence: 99%

High-latitude marginal reefs support fewer but bigger corals than their tropical counterparts

Chong

Sommer

Stant

et al. 2022

Preprint

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AimDespite the awareness that climate change impacts are typically detrimental to tropical coral reefs, the effect of increasing environmental stress and variability on the population size structure of coral species remains poorly understood. This gap in knowledge limits our ability to effectively conserve coral reef ecosystems because size specific dynamics are rarely incorporated. Our aim is to quantify variation in the size structure of coral populations along a tropical-to-subtropical environmental gradient.Location20 coral populations along a latitudinal gradient on the east coast of Australia (∼23°S to 30°S).Time PeriodBetween 2010 and 2018.Major taxa studiedScleractinian corals.MethodsWe apply two methods to quantify the relationship between environmental covariates and coral population size structure along a latitudinal environmental gradient. First, we use linear regression with summary statistics, such as median size as response variables; a method frequently favoured by ecologists. The second method is compositional functional regression, a novel method using entire size-frequency distributions as response variables. We then predict coral population size structure with increasing environmental stress and variability.ResultsCompared to tropical reefs, we find fewer but larger coral colonies in marginal reefs, where environmental conditions are more variable and stressful for corals in the former. Our model predicts that coral populations may become gradually dominated by larger colonies (> 148 cm2) with increasing environmental stress.Main conclusionsWith increasing environmental stress and variability, we can expect shifts in coral population size structure towards more larger colonies. Fewer but bigger corals suggest low survival, slow growth, and poor recruitment. This finding is concerning for the future of coral reefs as it implies populations may have low recovery potential from disturbances. We highlight the importance and usefulness of continuously monitoring changes to population structure over large spatial scales.Data availabilityData is supplied in the supplementary information, or upon request. Once accepted for publication it will be made openly available on Dryad.

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“…Clearly, the choice of the parameter α and of the derivative orders (u, v) affects the smoothness of the resulting spline. For the optimal choice of α, the generalized cross-validation (GCV) criterion is used here, similarly as in [18]. Given that we aim to reconstruct clr-transformed PDFs, the zero-integral constraint needs to be incorporated into the tensor product splines.…”

Section: A Spline Representation For Bivariate Densities and Their De...mentioning

confidence: 99%

“…., [30,31). Note that the same age range was used also in [18]. The support of the marginal distribution of weights (X) and heights (Y ) was set to the respective interval of observation, namely to I 1 = [40, 100] for X and I 2 = [155,195] for Y ; the Sturge's rule was used to select the number of classes K,L along the variable X,Y , respectively, in each of the histograms.…”

Section: An Application To Anthropometric Densitiesmentioning

confidence: 99%

Bivariate Densities in Bayes Spaces: Orthogonal Decomposition and Spline Representation

Hron¹,

Machalová²,

Menafoglio³

2020

Preprint

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A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (which is commonly performed through copulas), and allows for the analysis of dataset of bivariate densities, in a Functional Data Analysis perspective. A spline representation for bivariate densities is also proposed, providing a computational cornerstone for the developed theory.

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Compositional splines for representation of density functions

Cited by 15 publications

References 22 publications

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

High-latitude marginal reefs support fewer but bigger corals than their tropical counterparts

Bivariate Densities in Bayes Spaces: Orthogonal Decomposition and Spline Representation

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