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Denis Allard

Directeur de Recherche (DR1) / Senior Researcher

Biostatistics and Spatial Processes (BioSP), INRAE, Avignon

Tel: +33 (0) 4 32 72 21 71
Fax: +33 (0) 4 32 72 21 82

Member of the Mathematics and digital technologies (MathNum) of the
French National Research Institute for Agriculture, Food & Environment

Denis Allard    


  • Chaire Geolearning I am the Principal Investigator of the Geolearning Chair, with a funding from 2023 to 2027 This Chair brings together two research groups: the Geostatistics team from the Centre de Géosciences (CG) at Mines Paris, and the Biostatistics and Spatial Processes Unit (BioSP), belonging to the MathNum division at INRAE. The general objective of the Geolearning Chair is to develop and apply methods originating from the recent revolution in data science to challenges induced by the climate and ecological transitions our world is facing. More specifically, we will design models and methods in geostatistics, extreme events theory and Machine Learning with applications to environmental, climate and risk sciences.


  • Sébastien Coube-Sisqueille, currently post-doc at the Basque Center for Applied Mathematics visited me to work on multivariate spatio-temporal models in Bayesian context, with an application to air pollution. 


  • Thomas Opitz is now the coordinator of the research network on risks, extreme events and spatio-temporal statitstics RESSTE (Risques, Extrêmes et StatistiquesSpatio-Temporelles). RESSTE is funded by the Mathematics and digital technologies division (MathNum) of INRAE. It gathers more than 60 researches from about 20 research teams in France and abroad. We organize seminars and workshops and we support all sorts of actions actions in view of developping models and methods for analyzing space-time data. Feel free to contact me or Thomas if you wish to be on the RESSTE mailing list.


  • A RESSTE team, with Denis Allard (BioSP, INRAE), Lucia Clarotto (Geostatistics, Mines ParisTech), Thomas Opitz (BioSP, INRAE) and Thomas Romary (Geostatistics, Mines ParisTech) won the "2021 KAUST Competition on Spatial Statistics for Large Datasets" organized by the Spatio-Temporel Statistics & Data Science group of KAUST. 22 teams from all over the world took part in this competition.
    The competition was organized in 4 challenges consisting in estimating the parameters of several Gaussian fields and in making spatial predictions (kriging) under different conditions. The size of the datasets ranged from 90,000 data to 900,000 data. The RESSTE team came out on top of 3 exercises and placed themselves on the podium in the fourth exercise.
    All details are available on the competition website at https://cemse.kaust.edu.sa/stsds/2021-kaust-competition-spatial-statistics-large-dataset


  • The Journal de la Société Française de Statistique recently published a Special Issue Statistics for spatial and spatio-temporal data and RESSTE Network, containing very interesting contributions by several RESSTE network members.


  • The paper Anisotropy Models for Spatial Data, Math. Geosc. Volume 48(3): 305–328, doi: 10.1007/s11004-015-9594-x., co-authered with Rachid Senoussi from BioSP and Emilio Porcu from University of Newcastle was awarded best 2016 paper by the Journal Mathematical Geoscience. The paper offers a full characterization of anisotropic variograms, in terms of both regularity and range. It is first shown that, if the regularity parameter is a continuous function of direction, it must necessarily be constant, whereas the scale parameter can vary in  a continuous or discontinuous fashion with direction. As a second result, it is then established that all valid anisotropies for the range parameter can be represented as a directional mixture of zonal anisotropies. This representation makes it possible to build a very large class of anisotropic variograms, far more flexible than the classical anisotropies. A turning band algorithm for the simulation of Gaussian anisotropic random fields, derived from the mixture representation, is then presented and illustrated.

Recent conferences I (co-) organized and/or I have been involved with:

  • METMA 2018 is the ninth of a series of workshops on the topic of Spatio-Temporal Modelling, which have been held every two years since 17 years. We are proud to organize the first "French" edition of this event in Montpellier. This workshop aims to promote the development and application of spatial, temporal, and mainly spatio-temporal statistical methods in different fields related to the environment. It seeks to bring together practitioners and researchers of different areas and countries all over the world.The scientific program features sessions covering topics on the latest advancements in theory, methods and applications.
  • L’Université d’Avignon (UAVP) accueillera les Journées de Statistique 2017 du 29 mai au 2 juin sur le campus Hannah Arendt (anciennement Sainte-Marthe) au centre-ville d’Avignon. L'événement est co-organisé par le laboratoire de mathématique d'Avignon, BioSP, le laboratoire d'Informatique d'Avignon et par l'UMR ESPACE.
  • The 2015 edition of the Spatial Statistics Conference took place in Avignon, 9 - 12 June, 2015. It was co-chaired by Denis Allard (BioSP, INRA) and Alfred Stein (ITC). It was sponsored by the Applied Mathematics and Computer Science division of INRA.     
  • BioSP hosted the Workshop on Stochastic Weather Generators from 17 - 19 september, 2014. This workshop brought together a wide range of researchers, practitioners, and graduate students whose work is related to the stochastic modelling of meteorological variables and stochastic weather generators. Presentations can be found here.
  • The 9th edition of the French-Danish Workshop took place in May 2012 in Avignon, France. It was jointly organized by the Biostatistics and Spatial Processes research unit (INRA) and the Dpt. of Mathematics, LANLG (University of Avignon). It was devoted to spatial statistics and image analysis and their applications in biology (agriculture, aquaculture, ecology, economy, environment, health, medicine, ...). Presentations can be found here.


WACSgen is a single-site, stationary multivariate weather generator for daily climate variables based on weather-states that uses a Markov chain for modeling the succession of (an unlimited number of) weather states. Conditionally to the weather states, the multivariate variables are modeled using the family of Complete skew-normal distributions. It is described in Flecher et~al. (2010).

Version WACSgen 1.0 is now avaliable to download. Here is the zip file of the R pacakge WACS. Simply download in your owkring directory and install with the usual install command install.packages(,) or from the Rstudio tool. WACS is also available as a package on the R-CRAN repository. Follow this link.

A user guide with a full description of the model, methods and algorithms is accessible here. Feel free to use WCASgen and to contact me for complementary information. Do not forget to make proper reference to WACSgen and the original paper Flecher et~al. (2010).



Spatial statistics and stochastic partial differential equations: a mechanistic viewpoint (Spatial Statistics, in press) [with Lionel Roques and Samuel Soubeyrand]

The Stochastic Partial Differential Equation (SPDE) approach is revisited from a mechanistic perspective based on the movement of microscopic particles, thereby relating pseudo-differential operators to dispersal kernels. A connection  between L\'evy flights and PDEs involving the Fractional Laplacian (FL) operator is established. The corresponding Fokker-Planck PDEs will serve as a basis to propose new generalisations by considering a general form of SPDE with terms accounting for dispersal, drift and reaction.  The difference between the FL operator (with or without linear reaction term) associated with a fat-tailed dispersal kernel and therefore describing long-distance dependencies and the damped FL operator associated with a thin-tailed kernel, thus corresponding to short-distance dependencies, is detailed. Then, SPDE-based random fields with non-stationary external spatially and temporally varying force are illustrated and nonlinear bistable reaction term are introduced.  The physical meaning of the latter and possible applications are discussed. Returning to the particulate interpretation of the above-mentioned equations,  their links with point processes is described in a particular case. We unravel the nature of the point processes they generate and show how such mechanistic models, associated to a probabilistic observation model, can be used in a hierarchical setting to estimate the parameters of the particle dynamics.


A general framework for SPDE-based stationary random fields (Bernoulli) [with R. Carizo Vergara and N. Desassis]

The paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of SPDEs, with applications to spatio-temporal models having non-trivial properties. Within the framework of Generalized Random Fields, a criterion for existence and uniqueness of stationary solutions for a wide class of linear SPDEs is proposed and proven. Their covariance are then obtained through their associated spectral measure. We also present a result that relates the covariance in the case of a White Noise source term with that of a generic case through convolution. Using these results, we obtain a variety of SPDE-based stationary random fields. In particular, well-known results regarding the Matérn Model and models with Markovian behavior are recovered. A new relationship between the Stein model and a particular SPDE is obtained. New spatio-temporal models obtained from evolution SPDEs of arbitrary temporal derivative order are then obtained, for which properties of separability and symmetry can  easily be controlled. We also obtain results concerning stationary solutions for physically inspired models, such as solutions for the heat equation, the advection-diffusion equation, some Langevin's equations and the wave equation.   arXiv:1806.04999


Semi-parametric resampling with extremes (Spatial Statistics) [with Thomas Opitz and Grégoire Mariethoz]

Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed datasets while using only minimal assumptions. However, such methods cannot generate extreme events beyond the observed range of data values. We here propose using tools from extreme value theory for stochastic processes to extrapolate observed data towards yet unobserved high quantiles. Original data are first enriched with new values in the tail region, and then classical resampling algorithms are applied to enriched data. In a first approach to enrichment that we label “naive resampling”, we generate an independent sample of the marginal distribution while keeping the rank order of the observed data. We point out inaccuracies of this approach around the most extreme values, and therefore develop a second approach that works for datasets with many replicates. It is based on the asymptotic representation of extreme events through two stochastically independent components: a magnitude variable, and a profile field describing spatial variation. To generate enriched data, we fix a target range of return levels of the magnitude variable, and we resample magnitudes constrained to this range. We then use the second approach to generate heatwave scenarios of yet unobserved magnitude over France, based on daily temperature reanalysis training data for the years 2010 to 2016.


Simulating space-time random fields with nonseparable Gneiting-type covariance functions (Statistics and Computing) [with Xavier Emery, Céline Lacaux and Christian Lantuéjoul]

We propose two algorithms to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite function associated with the temporal structure. In both cases, the simulated random field is constructed as a weighted sum of cosine waves, with a Gaussian spatial frequency vector and a uniform phase. The difference lies in the way to handle the temporal component. The first algorithm relies on a spectral decomposition in order to simulate a temporal frequency conditional upon the spatial one, while in the second algorithm the temporal frequency is replaced by an intrinsic random field whose variogram is proportional to the conditionally negative definite function associated with the temporal structure. Both algorithms are scalable as their computational cost is proportional to the number of space-time locations, which may be unevenly spaced in space and/or in time. They are illustrated and validated through synthetic examples. arXiv: 1912.02026


A new class of α-transformations for the spatial analysis of Compositional Data (Spatial Statistics) [with Lucia Clarotto and Alessandra Menafoglio]

Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of -transformations, named the Isometric α-transformation (α-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. Similarly to other α-transformations existing in the literature, it is shown that the ILR is the limit case of the α-IT as tends to 0 and that corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when Maximum likelihood estimation of the parameter is established. Prediction using kriging on α-IT transformed data is validated on synthetic spatial compositional data, using prediction scores computed either in the geometry induced by the α-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the α-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplified as decreases, entailing poor kriging performances both within the α-IT geometry and for metrics in the simplex.


Means and covariance functions for spatial compositional data: an axiomatic approach (Mathematical Geosciences) [with T. Marchant]

Our work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented.As a first result, it is shown that the weighted  arithmetic mean is the only central tendency characteristic verifying a small set of axioms, namely reflexivity and marginal stability. Moreover, the weights must be identical for all components of the compositional vector.This result has deep consequences on the spatial multivariate covariance modeling of compositional data.  In a geostatistical setting,it is shown as a second result that the proportional model of covariance functions (i.e. the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability. A preprint can be found herePublication in Mathematical Geosciences is here.


Half-tapering strategy for conditional simulation with large datasets [with D. Marcotte]

Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (Half-Taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T. A preprint is avalaible here. Publication in SERRA is here.


Multivariate space-time models [with M. Bourotte and E. Porcu]

Multivariate space-time data are increasingly recorded in various scientific disciplines. When analyzing these data, one of the key issue is to describe the multivariate space-time dependencies. In a Gaussian framework, this necessitates to propose relevant models for multivariate space-time covariance functions, mathematically described as matrix-valued covariance functions for which non-negative definiteness must be ensured.  A new flexible parametric class of cross-covariance functions for multivariate space-time Gaussian random fields has been proposed where space-time components belong to the (univariate) Gneiting class of space-time covariance functions, with Matern or Cauchy covariance functions in the spatial dimensions. In this class, the smoothness and the scale parameters can be different for each variable. Sufficient conditions are provided, ensuring that this model is a valid matrix-valued covariance functionfor multivariate space-time random fields. Through a simulation study, it is shown that the parameters of this model can be efficiently estimated using weighted pairwise likelihood, which belongs to class of composite likelihood methods. A preprint is available here. Publication in Spatial Statistics is here.


Variograms for anisotropic random fields [with R. Senoussi and E. Porcu]

The question of building useful and valid models of anisotropic variograms for spatial data that go beyond classical anisotropy models (geometric and zonal models of anisotropy) is rarely addressed. In Allard, Senoussi and Porcu (Math. Geosciences) it is shown that if the regularity parameter is a continuous function of the direction, it must necessarily be constant. Instead, the scale parameter can vary in a continuous or discontinuous fashion with the direction according to a directional mixture representation, which allows to build a very large class of anisotropy models. A turning band algorithm for the simulation of Gaussian anisotropic processes, obtained from the mixture representation, is also presented.


Stochastic Weather Generators [with P. Naveau, P. Ailliot, V. Monbet, M. Bourotte]

A recurrent issue encountered in impact studies is to provide fast and realistic (in a distributional sense) simulations of atmospheric variables like temperatures, precipitation and winds at a few specific locations and at daily or hourly temporal scales. This stochastic inquiry leads to a large variety of so-called Stochastic Weather Generators (SWG) in the hydrological and weather literature. A concise and up-to-date review paper on Weather-states stochastic Weather Generators is available in Ailliot, Allard, Monbet and Naveau (2015).

To simulate multivariate daily time series (minimum and maximum temperatures, global radiation, wind speed and precipitation intensity) at a single site, WACS-Gen, a Weather-state Approach with conditionally multivariate Closed Skew-normal distribution is proposed in Flecher, Naveau, Allard, Brisson (WRR, 2010). WACS-Gen is able to accurately reproduce the statistical properties of these five variables, including time dependence. It takes advantage of two elements. First, the classical wet and dry days dichotomy used in most past weather generators is generalized to multiple weather states using clustering techniques. The transitions among weather states are modeled by a first order Markov chain. Secondly, the vector of our five daily variables of interest is sampled, conditionally on these weather states, from a closed skew-normal distribution, thus allowing to handle non-symmetric behaviors. WACS-Gen is coded in R, and is available upon request by emailing me.

Allard and Bourotte (2014) considers the problem disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Current researches aim at proposing relevant models for multisite, multivariate Stochastic Weather Generators.


Combining indicator probabilities [with D. D'Or, R. Froidevaux, A. Communian, P. Renard]

The need of combining in a probabilistic framework different sources of information is a frequent task in geoscience. For example, the probability of occurrence of a certain lithofacies at a given location can easily be computed conditionally on the values observed at other sources of information (sample observations, geophysics, remote sensing, training images). The problem of aggregating these different conditional probability distributions into a single conditional distribution arises as an approximation to the inaccessible genuine conditional probability given all information. Allard, Communian and Renard (2012) makes a formal review of most aggregation methods with a particular focus on their mathematical properties. Exact relationships relating the different methods is emphasized. The case of events with more than 2 possible outcomes is treated in details. It is shown that in this case, equivalence between different aggregation formulas is lost. It is proved that the log-linear pooling formulas with parameters estimated from maximum likelihood are calibrated. These results are illustrated on simulations from two common stochastic models for earth science: the truncated Gaussian model and the Boolean model.

When considering the problem of the spatial prediction of a categorical variable given a set of observations at surrounding locations, a useful approximation of the conditional probability of observing a category at a location is obtained with a particular maximum entropy principle. It leads to a simple combination of sums and products of univariate and bivariate probabilities. This prediction equation can be used for categorical estimation or categorical simulation. In Allard, D'Or and Froideveaux (2011), connections are made to earlier work on prediction of categorical variables. In particular, it is a parameter free, suboptimal, special case of log-linear pooling.


Skew normal random fields [with P. Naveau]

Skewness is often present in a wide range of environmental problems, and modelling it in the spatial context remains a challenging problem. In Allard and Naveau (2007), a new family of skewed random fields based on the multivariate closed skew-normal distribution is proposed. Such fields can be written as the sum of two independent fields; one Gaussian and the other truncated Gaussian. This model contains very few parameters while still incorporating the classical spatial structures used in geostatistics.  Crucially, a high degree of skewness can be induced through the use of a single skewness parameter. It is thus possible to compute the first- and second-order moments of our skewed fields, as well as deriving the properties of the sample variogram and covariance. This leads to a method of moments algorithm to estimate the parameters.


Zones of Abrupt Changes [with Edith Gabriel and J.N. Bacro]

Estimating the zones where a variable under study changes abruptly is a problem encountered in many biological, ecological, agricultural or environmental applications. In Gabriel, Allard and Bacro (2011), a method is proposed for detecting the zones where a spatially correlated variable irregularly sampled in the plane changes abruptly. The general model is that under the null hypothesis the variable is the realization of a stationary Gaussian process with constant expectation. The alternative is that the mean function is discontinuous on some curves in the plane. The general approach is a global aggregation of local tests of the hypothesis of a local constant mean vs. the alternative of the existence of a discontinuity. The theory that links the local and global levels is based on asymptotic distributions of excursion sets of non-stationary khi2 fields. It is thus possible to control the global type I error and to simultaneously estimate the covariance function and the ZACs in the case of an unknown mean. This method is easy to use, to visualise and to interpret. An R set of functions, detecZAC, can be downloaded from Edith Gabriel's homepage.


CART algorithm for spatial data [with Liliane Bel and Avner Bar-Hen]

Classification And Regression Trees (CART) assume independent samples to compute classification rules. This assumption is very practical for estimating  quantities involved in the algorithm and for assessing asymptotic properties of estimators. Unfortunately, in most environmental or ecological applications, the data under study present some amount of spatial correlation. When the sampling scheme is very irregular, a direct application of supervised classification algorithms leads to biased discriminant rules due, for example, to the possible oversampling of some areas. In Bel, Allard, Laurent, Cheddadi  and Bar-Hen (2009), two approaches for taking this spatial dependence into account are considered. The first one  takes into account the irregularity of the sampling by weighting the data according to their spatial pattern using two existing methods based on Voronoï tessellation and regular grid, and one original method based on kriging. The second one uses spatial estimates of the quantities involved in the construction of the discriminant rule at each step of the algorithm.

HDR Thesis can be found here  

Book edition  
Monestiez, P., Allard, D., Froidevaux, R. (2001) geoENV III Geostatistics for Environmental Applications. Kluwer Academic Publishers, Dordrecht, 540p.

Book reviews (avalaible upon request)

J.-P. Chilès, P. Delfiner: Geostatistics: Modeling Spatial Uncertainty 2nd Edition. Wiley, 2012. Mathematical Geosciences, 2012.  doi:10.1007/s11004-012-9429-y

A.E. Gelfand, P.J. Diggle, M. Fuentes, P. Guttorp (eds.): Handbook of spatial statistics, Chapman & Hall/CRC, Statistics and Computing, 2010. doi:10.1007/s11222-010-9211-2


Selection of publications (for a more complete list see my Google Scholar profile)

Allard D., François, B.,  García de Cortázar-Atauri, I. and Vrac, M. Assessing multivariate bias corrections of climate simulations on various impact models under climate change. https://hal.inrae.fr/hal-04227826

Vrac, M., Allard, D., Mariethoz G., Thao, S. and Schmutz, L. (2024) Distribution-based pooling for combination and multi-model bias correction of climate simulations. Earth System Dynamics: https://doi.org/10.5194/esd-15-735-2024 

Bonneu, F., Makowksi, D., Joly J. and Allard D. (2022) Machine learning based on functional principal component analysis to identify major influential factors of wheat yield. Preprint available here

Clarotto, L. Allard, D., Romary, T., Desassis N. The SPDE approach for spatio-temporal datasets with advection and diffusion. Spatial Statistics (accepted)  arXiv preprint 2208.14015

Pereira, M., Desassis, N., Allard D., Geostatistics for Large Datasets on Riemannian Manifolds: A Matrix-Free Approach, J. data sci. 20(2022), no. 4, 512-532, DOI 10.6339/22-JDS1075. Preprint available at arXiv 2208.14015

Allard, D., Clarotto, L. & Emery, X. (2022) Fully nonseparable Gneiting covariance functions for multivariate space-time data. Spatial Statistics, 52, 100706.https://doi.org/10.1016/j.spasta.2022.100706. Preprint available at https://hal.archives-ouvertes.fr/hal-03564931/

Roques, L., Allard, D., & Soubeyrand, S. (2021) Spatial statistics and stochastic partial differential equations: a mechanistic viewpoint. Spatial Statistics, 50, 100591. https://doi.org/10.1016/j.spasta.2022.100591. Preprint available at arXiv:2111.05724.
Clarotto, L., Allard, D. and Menafoglio, A. (2021) A new class of α-transformations for the spatial analysis of Compositional Data. Spatial Statistics, 47: 100570 https://doi.org/10.1016/j.spasta.2021.100570.   arXiv:2110.07967
Allard, D. Hristopulos, D.T., Opitz T. (2021) Linking physics and spatial statistics: A new family of Boltzmann-Gibbs random fields. Electron. J. Statist. 15(2): 4085-4116 DOI: 10.1214/21-EJS1879
Allard D., Fabbri, P. Gaetan, C. (2021) Modeling and simulating depositional sequences using latent Gaussian random fields.Mathematical Geosciences, 53: 469-497. doi:10.1007/s11004-020-09875-0   arxiv.org:2003.11383

Carrizo Vergara R., Allard, D., Desassis, N.  (2021) A general framework for SPDE-based stationary random field. Bernoulli, 28(1): 1-32. DOI: 10.3150/20-BEJ131. Preprint: arXiv:1806.04999

Opitz T., Allard D., Mariethoz G. (2021)  Semi-parametric resampling with extremes. Spatial Statistics, 42: 100445, doi.org/10.1016/j.spasta.2020.100445

Soubeyrand S., Ribaud M., Baudrot V., Allard D., Pommeret D., Roques L.  (2020) COVID-19 mortality dynamics: The future modelled as a (mixture of) past(s) PLOS-One  15(9) doi.org/10.1371/journal.pone.0238410

Allard, D. Emery X., Lacaux, C., Lantuéjoul, C. (2020) Simulating space-time random fields with nonseparable Gneiting-type covariance functions. Statistics and Computing, 30(5): 1479-1495, doi:10.1007/s11222-020-09956-4. Preprint: arXiv: 1912.02026

François B., Vrac M., Cannon A.J., Robin Y., Allard D. (2020) Multivariate bias corrections of climate simulations: Which benefits for which losses? Earths System Dynamics, 11, 537–562.

Tallieu, C. Badeau, V., Allard, D., Nageleisen, L.M., Bréda, N. (2020) Year-to-year crown condition poorly contributes to ring width variations of beech trees in French ICP level I network, Forest Ecology and Management, doi.org/10.1016/j.foreco.2020.118071

Soma M., Pimont F., Allard D., Fournier R., Dupuy, J.-L. (2020) Mitigating occlusion effects in LAD estimates from Terrestrial LiDAR through a specific kriging method. Remote Sensing of Environment 245-111836doi.org/10.1016/j.rse.2020.111836

Cuevas, F., Porcu, E., Allard, D. (2020)  Fast and exact simulation of isotropic Gaussian random fields defined on the sphere cross time. Statistics an Computing, 30(1), 187-194. doi.org/10.1007/s11222-019-09873-1     arXiv:1807.04145

Pimont, F., Allard, D., Soma M. Dupuy, J-L (2018) Estimators and confidence intervals for plant area density at voxel scale with T-LiDAR. Remote Sensing of Environment, 215, 343-370. doi.org/10.1016/j.rse.2018.06.024

Benoit L., Allard D., Mariethoz, G. (2018)  Stochastic Rainfall Modelling at Sub‐Kilometer Scale.  Water Resources Research, 54, 6, 4108-4130 doi.org/10.1029/2018WR022817

Marcotte, D. and Allard, D. (2018) Gibbs sampling on large lattice with GMRF. Computers and Geosciences, 111, 190-199. doi:10.1016/j.cageo.2017.11.012.

Allard, D. and Marchant, T.   (2018) Means and covariance functions for spatial compositional data: an axiomatic approach, Mathematical Geosciences, 50(3), 299-315; doi: 10.1007/s11004-017-9713-y.    Manuscript accessible here.

with RESSTE network (2017). Analyzing spatio-temporal data with R: Everything you always wanted to know - but were afraid to ask.     Journal de la Société Française de Statistique, 158(3), 124-158.    Supplementary material is here

Csilléry, K., Kunstler G., Courbaud, B., Allard, D., Lassegues, P., Haslinger, K., Gardiner, G.  Coupled effects of wind-storms and drought on tree mortality across 115 forest stands from the Western Alps and the Jura mountains, Global Change Biology 23(12) 5092-5107.  DOI : 10.1111/gcb.13773

Marcotte, D. and Allard, D. (2017) Half-tapering strategy for conditional simulation with large datasets, Stochastic Environmental Research and Risk Assessment, 32(1), 279-294. doi: 10.1007/s00477-017-1386-z.    Manuscript accessible here.

Bourotte M., Allard, D. and Porcu, E.   (2016) A Flexible Class of Non-separable Cross-Covariance Functions for Multivariate Space-Time Data, Spatial Statistics, 18(A), 125-146.    doi: 10.1016/j.spasta.2016.02.004.  (manusript: ArXiv 1510.07840)

Zaytsev, V. BIver, P., Wackernagel, H. and Allard, D. (2016) Change-of-Support Models on Irregular Grids for Geostatistical Simulation, Mathematical Geosciences, 48(4): 353-369.    doi: 10.1007/s11004-015-9614-x.

Allard, D. Senoussi, R., Porcu, E. (2016) Anisotropy models for spatial data. Mathematical Geosciences, 48(3): 305-328.    doi: 10.1007/s11004-015-9594-xPreprint accessible here.

Ailliot P., Allard, D., Monbet V. and Naveau, P. (2015)  Stochastic weather generators: an overview of weather type models. Journal de la Société Française de Statistiques, 156(1), 101-103.    Paper accessible here.

Allard, D., Bourotte, M. (2015) Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process. Stochastic Environmental Research and Risk Assesment, 29(2), 453-462   doi: 10.1007/s00477-014-0913-4. Preprint accessible here.

Allard, D., Lopez-Lozano, R. and Baret, F. (2013) Modeling forest canopies with a hierarchical multi-ring Boolean model for estimating Leaf Area Index. Spatial Statistics, 5, 42-56.    doi:10.1016/j.spasta.2013.04.007.    Preprint accessible here.

Renard, P. and Allard, D. (2013)  Connectivity metrics for subsurface flow and transport.  Advances in Water Resources, 51, 168-196.    doi:10.1016/j.advwatres.2011.12.001    Preprint accesstible here.

Girard, R. and Allard, D. (2013) Spatio-temporal propagation of wind power prediction errors. Wind Energy,16, 999-1012.    doi:10.1002/we.1527

Allard, D. Soubeyrand, S.  (2012) Skew-normality for climatic data and dispersal models for plant epidemiology: when application fields drive spatial statistics. Spatial Statistics, 1, 50-64.    doi: 10.1016/j.spasta.2012.03.001.    Preprint accessible here.

Allard, D., Communian, A. and Renard, P. (2012)  Probability aggregation methods in geoscience. Mathematical Geosciences, 44: 545-581.    doi: 10.1007/s11004-012-9396-3.    Preprint accessible here.

Allard, D. (2012)  Modeling spatial and spatio-temporal non Gaussian processes. In  Space-Time Processes and Challenges Related to Environmental Problem,  
Eds. Porcu, E., Montero, J.-M. and Schlather M., Lecture Notes in Statistics, Vol. 207, Springer. pp. 141-164.    doi: 10.1007/978-3-642-17086-7_7

Allard, D., D'Or, D. and Froidevaux, R. (2011)  Letter to the Editor: Response to W. Li and C. Zhang,  
European Journal of Soil Science, 63, 125-128.  doi: 10.1111/j.1365-2389.2011.01414.x.    Preprint accessible here.

Allard, D., D'Or, D. and Froidevaux, R. (2011) An efficient maximum entropy approach for categorical variable prediction, European Journal of Soil Science, 61, 381-293.    doi:10.1111/j.1365-2389.2011.01362.x. preprint accessible here.

Flecher, C. Allard, D. and Naveau P. (2010) Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data.Metron - International Journal of Statistics -- Special Issue on Skew-symmetric and flexible distributions, LXVIII, 331-345.    Prepint is accessible here.

Flecher, C., Naveau P.,  Allard D. and Brisson, N. (2010) A Stochastic Daily Weather Generator for Skewed Data, Water Resource Research, 46, W07519.    doi:10.1029/2009WR008098.     Preprint accessible here.

Gabriel, E., Allard, D. and Bacro, J.-N. (2010) Estimating and testing zones of abrupt change for spatial data, Statistics and Computing21, 107-120.    doi:10.1007/s11222-009-9151-x.    Preprint accessible here.  

Flecher, C., Naveau, Ph. and Allard, D. (2009) Estimating the Closed Skew-Normal distributions parameters using weighted moments",  Statistics and Probability Letters, 79, 1977-1984.    doi:10.1016/j.spl.2009.06.004.    Preprint accessible here.  

Bel, L., Allard, D., Laurent, J.M., Cheddadi, R. and Bar-Hen, A.  (2009) CART algorithm for spatial data: Application to environmental and ecological data, Computational Statistics and Data Analysis, 53, 3082-3093.    doi:10.1016/j.csda.2008.09.012.     Preprint accessible here.  

Garrigues, S., Allard, D., Baret, F. Modeling Temporal Changes in Surface Spatial Heterogeneity over an Agricultural site (2008) Remote Sensing of Environment, 112, 588-602.   doi:10.1016/j.rse.2007.05.014.  

Gabriel, E. and Allard, D. Evaluating the Sampling Pattern When Detecting Zones of Abrupt Change (2008)  Environmental and Ecological Statistics, 15, 469-489.    doi:10.1007/s10651-007-0067-3.    Manuscrit accessible ici.  

Gabriel, E., Allard, D., Mary, B. & Guérif, M.  (2007) Detecting zones of abrupt change in soil data, with an application to an agricultural field. European Journal of Soil Science, 58, 1273-1284.    doi:10.1111/j.1365-2389.2007.00920.x.  

Garrigues, S., Allard, D., Baret, F. & Morisette, J. (2007) Multivariate Quantification of Landscape Spatial Heterogeneity using Variogram Models. Remote Sensing of Environment, 112, 216-230.    doi:10.1016/j.rse.2007.04.017  

Garrigues, S., Allard, D., & Baret, F. (2007) Using first and second order variograms for characterizing landscape spatial structures from remote sensing imagery, IEEE TGARS, 45, 1823 - 1834.    doi:10.1109/TGRS.2007.894572  

Allard D. & Naveau, P. (2007) A new spatial skew-normal random field model, Communications in Statistics, 36, 1821 - 1834.    doi:10.1080/03610920601126290.    Manuscrit accessible ici.  
Allard D., Froidevaux R. & Biver, P. (2006) Conditional Simulation of Multi-Type Non Stationary Markov Object Models Respecting Specified Proportions, Mathematical Geology, 38, 959-986.    doi:10.1007/s11004-006-9057-5.    Manuscit accessible ici.  
Allard, D. & Gabriel, E. (2007), Détection de zones de changement abrupts pour des variables non permanentes du sol: vers la définition de zones homogènes ?, in Agriculture de Précision, Guérif, M. and King, D., Coords., Editions Quae, Paris, pp. 165--76.  

Garrigues, S., Allard, D., Baret, F. & Weiss, M. (2006) Influence of the spatial heterogeneity on the non linear Estimation of Leaf Area Index from moderate resolution remote sensing data, Remote Sensing of Environment, 105, 286-298.    doi:10.1016/jrse.2006.07.013  

Magnussen S., Allard D., & Wulder M. (2006) Poisson Voronoï tiling for finding clusters in spatial point patterns, Scan. J. For. Res., 21, 239-248.    doi:10.1080/02827580600688178  

Allard, D. (2006), Validation d'un modèle géostatistique pour l'interpolation : application à un événement pluvieux, in Statistiques Spatiales, Eds. Droesbeke, J.-J. et Lejeune, M., Technip, Paris, pp. 403--414.  
Chilès, J.-P. & Allard, D. (2005), Stochastic Simulation of Soil Variation, in Geographic Information Technologies for Environmental Soil-Landscape Modelling, Ed. Grunwald, S., CRC Press, Boca Raton, pp. 289-321.

PhD Students

Antoine Doizé (2023-2026) Modèles statistiques pour simuler les périodes de fortes pluies et de longues sécheresses. Co-supervised with Philippe Naveau (LSCE) and Olivier Wintenberger (Sorbonne Université)

Grégoire Jacquemin (2022-2025) Co-supervised with Mathieu Vrac (LSCE) and Xavier Freulon (Mines Paris)

Lucia Clarotto (2020-2023) Prédiction spatio-temporelle par équations différentielles partielles stochastiques. Co-supervised with Thomas Romary and Nicolas Desassis, Mines Paris.

Rocardo Carrizo (2015-2018) Spatio-temporal statistical models from stochastic partial derivative equations. Co-supervised with Nicolas Desassis, MinesParisTech.

Marc Bourotte (2012-2016)  Modèles et algorithmes pour un générateur de temps spatialisé (SWgen) prenant en compte les valeurs extrêmes. Université d'Avignon. Co-supervised with Liliane Bel, AgroParisTech.

Cédric Flécher (2006-2009 ) Développement de méthodes statistiques pour la mise au point d'un générateur de climat adapté à l'utilisation des scénarii de changement climatique, University Montpellier II, ED SIBAGHE, co-supervised with Ph. Naveau, LSCE, CNRS and N. Brisson AgroClim, INRA Avignon. Today with Isatis, Montréal.

Sébastien Garrigues (2001-2004) Hétérogénéité spatiale des surfaces terrestres en télédétection ; caractérisation et influence sur l'estimation des variables biophysiques, ENSA-R. co-supervised with F. Baret, EMMAH INRA Avignon. Today at EMMAH, INRA Avignon.

Edith Gabriel (2001-2004) Détection de zones de changement abrupt dans des données spatiales et application à l'agriculture de précision, Univsersity Montpellier II, ED ISS. Co-supervised with M. Guérif, EMMAH, INRA Avignon. Has been Maître de Conférence (Assitant Professor) at Laboratoire d'Analyse Non Linéaire et géométrie d'Avignon, Université d'Avignon. Now Directrice de Recherhe (Senior Research) at BioSP, INRAE.  





Teaching (mostly in french)

Géostatistique spatio-temporelle: Mines Paris, 3A, option Géostatistique et Probabilités Appliquées.

    Première partie : les modèles 

    Seconde partie : estimation, prédiction et simulation

Environmental data analysis, for the Doctoral Program in Environmental Sciences, Universita Ca'Foscari, Venezia, Italy.

Part I: Introduction; Exploratory data analysis; estimation and hypothsis testing; linear model

Part II: Time series; spatial statistics; geostatistics

R scripts

Atelier Statistique de la SFdS: Introduction aux méthodes spatiales et spatio-temporelles, 23 et 24 juin 2016. Présentations "Géostatistique multivariée", "Géostatistique Spatio-temporelle" et script R.

Cargèse Fall School on "statistical and mathematical tools for climate extremes", November 2015.  Slides on Stochastic Weather Generators are here.  Compressed directory for exercises is here

Journées R pour la fédération ECCOREV   Scripts R pour le TD

Pratiques des statistiques paramétriques. Séquence I: statistique inférentielle   Transparents d'introduction; Transparents Inférence et TestsJeu de données du Jura Suisse  Script R pour le TD

Toledo Spring School on Advances And Challenges In Space-time Modelling Of Natural Events. Introduction to Non-Gaussian Random Fields: a Journey Beyond Gaussianity. Slides

Statistiques Spatiales : introduction à la géostatistique (20 h), M2 Biostatistique, Université Montpellier II.     

Polycopié du cours.

Transparents d'introduction

Transparents variogrammes

Transparents krigeage

Transparents simulation

Probabilité et Statistiques (27 h), Centre de Recherche et d'Enseignement en Informatique, Université d'Avignon. Polycopié du cours.  

Processus Stochastiques (40 h),Centre de Recherche et d'Enseignement en Informatique. Université d'Avignon


Denis Allard obtained his MSc and PhD in Geostatistics from the Ecole des Mines de Paris, in Fontainebleau, France. He has been Assistant Professor at the Statistics Department, University of Washington (Seattle, U.S.A.) and Senior Geostatisticians for BP. In 1996 he joined the French National Institute for Agricultural Research (INRA) in Avignon, France, which he found to be an excellent place for doing research and which he never left. From 2005 to 2011 he has been the head of the BioSP (Biostatistics and Spatial Processes) group.

His research covers a wide range of topics in geostatistics and spatial statistics for modeling and analyzing spatio-temporal data, with applications in geosciences, environment and climate sciences. Recent theoretical contributions include the aggregation of probabilities in geoscience, efficient geostatistical simulation techniques, new classes of multivariate space-time cross-covariance functions, full characterization of anisotopy for random fields, skew-normal distributions for spatial data and SPDEs for spatio-temporal data.

Recent areas of applications include

  • rainfall modelling, stochastic weather generators, and the use of climate variables in impact models in context of Climate Change;
  • estimation of vegetation indices using remote sensors such as satellite images, photographies and LIDAR measurements;
  • geostatistical modeling of indicators, probabilities and connectivity in geoscience.

From 2023 to 2027, he is the Principal Investigator of the Geolearning Chair, a collaborative project between BioSP and the Geostatistics team at Ecole des Mines de Paris.

He is member of the steering committee of the "Multiple Risks" metaprogram at INRAE.

He serves on the editorial board of Spatial Statistics since 2012. He is member of the Scientific Advisory Board of MeilleursAgents and Genesis.

He is currently associate editor for Spatial Statistics. He has been Associate Editor for Computing and Statistics (2006-2018) and Mathematical Geosciences (2015-2017). He has been a member of the editorial board of Spatial Statistics since 2012.

He has been member of the steering committee of the "Adaptation of Agriculture and Forest to Climate Change" INRA metaprogram (2016 - 2021). From September 2017 to February 2020, he has been in charge of Innovation, Partnership and Transfer on Digital Agriculture for INRAE.


1993 PhD in geostatistics, Paris School of Mines  / Centre de Géostatistique de l'Ecole des Mines de Paris, maintenant Equipe de Géostatistique du Centre de Géoscience de Mines ParisTech 
1994 - 1995 Visting Assistant Professor, Department of Statistics, University of Washington, Seattle (WA, USA) 

1995 - 1996 Geostatistician, BP Exploration - Subsurface Technology, Londres 
since 1996 Researcher, Biostatistics and Spatial Processes (BioSP),  INRA, Avignon 
2007 Habilitation à Diriger les Recherches (Université Montpellier II)

2008 Senior Researcher, BioSP, INRA / Directeur de Recherche INRA 

2005 - 2011  Head of BioSP / Directeur de l'Unité Biostatistique et Processus Spatiaux

2016  and 2019 Visiting Professor at Dipartimento di Scienze Ambietali, Informatica e Statistica (DAIS), University Ca'Foscari, Venezia.

From 2016 to 2021:  Member of the steering committee of the INRAE metaprogramme "Adaptation of Agriculture and Forest to Climate Change"

From 09/2017 to 02/2020: In charge of Innovation, Partnership and Transfer for "Digital Agriculture" at INRAE

Since 2022 : Member of the steering committee of the INRAE metaprogramme on Multiple Risks, XRISQUES.

Since 2023: Principal Investigator of the Geolearning Chair

Full vita in English here

Professional Services

  • Principal Investigator of the Geolearning chair, a collaborative project between BioSP and the Geostatistics team at Ecole des Mines de Paris
  • 2022 -  now  Member of the steering committee of the "Multiple Risks" INRAE meta-program
  • 2017 - 2019   In charge of Innovation, Partnership and Transfer for INRA on Digital Agriculture
  • 2017             49emes Journées de Statistiques, Avignon, Co-chair
  • 2016 - 2021   Member of the steering committee of the "Adaptation of Agriculture and Forest to Climate Change" INRA meta-program
  • 2015             Spatial Statistics 2015 conference in Avignon, June 9-12, Co-chair
  • 2010             Scientific committee, 42emes Journées de Statistique
  • 2008 - 2010  Scientfic committee,  Université d'Avignon
  • 2005 - 2016   Member of the Board, Environment Group, French Statitsical Society / Membre du bureau et trésorier du groupe environnement de la SFdS
  • 2000              Co-chair, Geostatistics for Environment, geoENV III, Avignon
  • 1999 - 2006  Scientfic Committee, Applied Mathematics and Computer Science division /  département Mathématiques et Informatique Appliquées, INRA
  • 2003 - 2006  Commission Scientifique Spécialisée Mathématique, Bio-informatique, Intelligence Artificielle, INRA
  • 2000 - 2003  Conseil scientifique du Centre d'Avignon, INRA
  • 2001 - Ongoing   External Scientific Adviser,  Ephesia-Consult
  • 2017 - Ongoing   Member of the Scientific Committee,  MeilleursAgents
  • 2022 - Ongoing   Member of the Scientific Committte, Genesis Live

Editorial Services

Reviewer for Acta Mechanica, Annals of Statistics, Annals of Applied Statistics, Biometrics, Biometrika, Chilean Journal of Statistics, Climate Dynamics, Climate Research, Communications in Statistics - Theory and Methods, Computational Statistics and Data Analysis, Computer and Geoscience, Environmental Modelling & Software, Environmental Pollution, European Journal of Soil Science, IEEE Transactions in Geosciences and Remote Sensing, IEEE Transactions on Power Systems, International Journal of Climatology, Journal of African Earth Sciences, Journal of Agricultural, Biological, and Environmental Statistics, Journal of Computational and Applied Mathematics, Journal of Multivariate Analysis, Journal of the Royal Society Interface, Journal of the Royal Statistical Society, Journal for Stochastic Environmental Research and Risk Assessment, Operations Research, Physics Letters A, Probabilistic Engineering Mechanics, Statistics and Probability Letters, Water Resources Research, etc.