Statistics for Spatial Data.

The plastic in microplastics: A review.

Plastic waste is currently generated at a rate approaching 400 Mt year–1. The amount of plastics accumulating in the environment is growing rapidly, yet our understanding of its persistence is very...

Degradation Rates of Plastics in the Environment

Current opinion: What is a nanoplastic?

A substantial fraction of marine plastic debris originates from land-based sources and rivers potentially act as a major transport pathway for all sizes of plastic debris. We analyzed a global compilation of data on plastic debris in the water column across a wide range of river sizes. Plastic debris loads, both microplastic (particles 5 mm) are positively related to the mismanaged plastic waste (MMPW) generated in the river catchments. This relationship is nonlinear where large rivers with  population-rich catchments delivering a disproportionately higher fraction of MMPW into the sea. The 10 top-ranked rivers transport 88–95% of the global load into the sea. Using MMPW as a predictor we calculate the global plastic debris inputs form rivers into the sea to range between 0.41 and 4 × 106 t/y. Due to the limited amount of data high uncertainties were expected and ultimately confirmed. The empirical analysis to quantify plastic loads in rivers can be extended easily by a...

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Export of Plastic Debris by Rivers into the Sea

The global estimation of microplastic afloat in the ocean is only approximately 1% of annual global plastic inputs. This reflects fundamental knowledge gaps in the transformation, fragmentation, and fates of microplastics in the ocean. In order to better understand microplastic fragmentation we proceeded to a thorough physicochemical characterization of samples collected from the North Artlantic subtropical gyre during the sea campaign Expedition seventh Continent in May 2014. The results were confronted with a mathematical approach. The introduction of mass distribution in opposition to the size distribution commonly proposed in this area clarify the fragmentation pattern. The mathematical analysis of the mass distribution points out a lack of debris with mass lighter than 1 mg. Characterization by means of microscopy, microtomography, and infrared microscopy gives a better understanding of the behavior of microplastic at sea. Flat pieces of debris (2 to 5 mm in length) typically have one face that is more photodegraded (due to exposure to the sun) and the other with more biofilm, suggesting that they float in a preferred orientation. Smaller debris, with a cubic shape (below 2 mm), seems to roll at sea. All faces are evenly photodegraded and they are less colonized. The breakpoint in the mathematical model and the experimental observation around 2 mm leads to the conclusion that there is a discontinuity in the rate of fragmentation: we hypothesized that the smaller microplastics, the cubic ones mostly, are fragmented much faster than the parallelepipeds.

https://hal.archives-ouvertes.fr/hal-01597071/document

Understanding the Fragmentation Pattern of Marine Plastic Debris

https://hal.archives-ouvertes.fr/hal-01167015/document

Combined effect of atmospheric nitrogen deposition and climate change on temperate forest soil biogeochemistry: A modeling approach

https://hal.archives-ouvertes.fr/hal-01597074/document

Impact of tree canopy on thermal and radiative microclimates in a mixed temperate forest: A new statistical method to analyse hourly temporal dynamics

Let Y be a Gaussian vector of ℝn of mean s and diagonal covariance matrix Γ. Our aim is to estimate both s and the entries σi=Γi,i, for i=1,…,n, on the basis of the observation of two independent copies of Y. Our approach is free of any prior assumption on s but requires that we know some upper bound γ on the ratio max iσi/min iσi. For example, the choice γ=1 corresponds to the homoscedastic case where the components of Y are assumed to have common (unknown) variance. In the opposite, the choice γ>1 corresponds to the heteroscedastic case where the variances of the components of Y are allowed to vary within some range. Our estimation strategy is based on model selection. We consider a family {Sm×Σm, m∈ℳ} of parameter sets where Sm and Σm are linear spaces. To each m∈ℳ, we associate a pair of estimators (ŝm,σm) of (s,σ) with values in Sm×Σm. Then we design a model selection procedure in view of selecting some m among ℳ in such a way that the Kullback risk of (ŝm,σm) is as close as possible to the minimum of the Kullback risks among the family of estimators {(ŝm,σm), m∈ℳ}. Then we derive uniform rates of convergence for the estimator (ŝm,σm) over Holderian balls. Finally, we carry out a simulation study in order to illustrate the performances of our estimators in practice.

/pdf/simultaneous-estimation-of-the-mean-and-the-variance-in-rnwzdqs6cn.pdf

Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regression

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of Frechet mean that is a generalization of the standard notion of averaging to non-Euclidean spaces. We derive a minimax rate for this estimation problem, and we show that our estimator achieves this optimal rate under the asymptotics where both the number of curves and the number of sampling points go to infinity.

Xavier Gendre

Papers

Understanding the Fragmentation Pattern of Marine Plastic Debris

Combined effect of atmospheric nitrogen deposition and climate change on temperate forest soil biogeochemistry: A modeling approach

Impact of tree canopy on thermal and radiative microclimates in a mixed temperate forest: A new statistical method to analyse hourly temporal dynamics

Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regression

Minimax properties of Fr\'echet means of discretely sampled curves