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  • 1.
    Bayisa, Fekadu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhou, Zhiyong
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Adaptive algorithm for sparse signal recovery2019In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 87, p. 16p. 10-18Article in journal (Refereed)
    Abstract [en]

    The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.

  • 2.
    Cronie, Ottmar
    Anton de Kom University of Suriname, Paramaribo, Suriname; Chalmers University of Technology, Göteborg.
    Likelihood Inference for a Functional Marked Point Process with Cox-Ingersoll-Ross Process MarksManuscript (preprint) (Other academic)
    Abstract [en]

    This paper considers maximum likelihood inference for a functional marked point process - the stochastic growth-interaction process - which is an extension of the spatio-temporal growth-interaction process to the stochastic mark setting. As a pilot study we here consider a particular version of this extended process, which has a homogenous Poisson process as unmarked point process and shifted independent Cox-Ingersoll-Ross processes as functional marks. These marks have supports determined by the lifetimes generated by an immigration-death process. By considering a (temporally) discrete sample scheme for the marks and by considering the process' alternative evolutionary representation as a multivariate diffusion (Markovian) with jumps, the likelihood function is expressed as a product of the process' closed form transition densities. Additionally, under the assumption that the mark processes are started in their common stationary distribution, and under some restrictions on the underlying parameters, consistency and asymptotic normality of the maximum likelihood (ML) estimators are proved. The ML-estimators derived from the stationarity assumption are then compared numerically to the ML-estimators derived under non-stationarity, in order to investigate the robustness of the stationarity assumption. To illustrate the model's use in forestry, it is fitted to a data set of Scots pines.

  • 3.
    Cronie, Ottmar
    et al.
    Stochastics research group, CWIy, Amsterdam, The Netherlands.
    Mateu, Jorge
    Department of Mathematics, Universitat Jaume I, Campus Riu Sec, Castellón, Spain.
    Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworksManuscript (preprint) (Other academic)
    Abstract [en]

    This paper defines the class of càdlàg functional marked point processes (CFMPPs). These are (spatio-temporal) point processes marked by random elements which take values in a càdlàg function space, i.e. the marks are given by càdlàg stochastic processes. We generalise notions of marked (spatio-temporal) point processes and indicate how this class, in a sensible way, connects the point process framework with the random fields framework. We also show how they can be used to construct a class of spatio-temporal Boolean models, how to construct different classes of these models by choosing specific mark functions, and how càdlàg functional marked Cox processes have a double connection to random fields. We also discuss finite CFMPPs, purely temporally well-defined CFMPPs and Markov CFMPPs. Furthermore, we define characteristics such as product densities, Palm distributions and conditional intensities, in order to develop statistical inference tools such as likelihood estimation schemes.

  • 4.
    Cronie, Ottmar
    et al.
    Mathematical Sciences, Chalmers University of Technology and University of Gothenburg.
    Nyström, Kenneth
    SLU, Department of Forest Resource Management.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spatiotemporal Modeling of Swedish Scots Pine Stands2013In: Forest Science, ISSN 0015-749X, E-ISSN 1938-3738, Vol. 59, no 5, p. 505-516Article in journal (Refereed)
    Abstract [en]

    The growth-interaction (GI) process is employed for the spatiotemporal modelling of measurements of locations and radii at breast height made at three different time points of the individual trees in ten Scots pine (Pinus sylvestris) plots from the Swedish NFI. The GI-process places trees at random locations in the study region and assigns sizes to the trees, which interact and grow with time. It has been used to model plots in previous studies and to improve the fit we suggest some modifications: a different location assignment strategy and a different open-growth (growth under negligible competition) function. We believe that the calibration data contain trees that are too small to reflect the open-growth properly, which primarily affects the carrying capacity parameter. To better represent the open-growth of Scots pines, we evaluate the open-growth from a separate set of data (size and age measurements of older and larger single Scots pines). A linear relationship is found between the plot's estimated site indices and the sizes, and this is exploited in the estimation of the carrying capacity. We finally estimate the remaining GI-process parameters and test the goodness-of-fit on simulated predictions from the fitted model.

  • 5.
    Cronie, Ottmar
    et al.
    Mathematical Sciences, Chalmers University of Technology and University of Gothenburg.
    Särkkä, Aila
    Mathematical Sciences, Chalmers University of Technology and University of Gothenburg.
    Some edge correction methods for marked spatio-temporal point process models2011In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 55, no 7, p. 2209-2220Article in journal (Refereed)
    Abstract [en]

    Three edge correction methods for (marked) spatio-temporal point processes are proposed. They are all based on the idea of placing an approximated expected behaviour of the process at hand (simulated realisations) outside the study region which interacts with the data during the estimation. These methods are applied to the so-called growth-interaction model. The specific choices of growth function and interaction function made are purely motivated by the forestry applications considered. The parameters of the growth and interaction functions, i.e. the parameters related to the development of the marks, are estimated using the least-squares approach together with the proposed edge corrections. Finally, the edge corrected estimation methods are applied to a data set of Swedish Scots pine.

  • 6.
    Cronie, Ottmar
    et al.
    CWI, Amsterdam, The Netherlands.
    van Lieshout, M N M
    CWI, Amsterdam, The Netherlands.
    J-function for Inhomogeneous Spatio-temporal Point Processes2015In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 42, no 2, p. 562-579Article in journal (Refereed)
    Abstract [en]

    We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.

  • 7.
    Cronie, Ottmar
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    van Lieshout, M. N. M.
    Summary statistics for inhomogeneous marked point processes2016In: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 68, no 4, p. 905-928Article in journal (Refereed)
    Abstract [en]

    We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the -point correlation functions and reduce to cross - and -functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

  • 8.
    Cronie, Ottmar
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Van Lieshout, Marie-Colette N.M.
    CWI/University of Twente.
    A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions2018In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 105, no 2, p. 455-462Article in journal (Refereed)
    Abstract [en]

    We propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.

  • 9.
    Cronie, Ottmar
    et al.
    Stochastics, CWI, Amsterdam, The Netherlands.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The discretely observed immigration-death process: Likelihood inference and spatiotemporal applications2016In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 18, p. 5279-5298Article in journal (Refereed)
    Abstract [en]

    We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.

  • 10. González, Jonatan A.
    et al.
    Rodríguez-Cortés, Francisco J.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Mateu, Jorge
    Spatio-temporal point process statistics: a review2016In: Spatial Statistics, E-ISSN 2211-6753, Vol. 18, no Part B, p. 505-544Article, review/survey (Refereed)
    Abstract [en]

    Spatio-temporal point process data have been analysed quite a bit in specialised fields, with the aim of better understanding the inherent mechanisms that govern the temporal evolution of events placed in a planar region. In particular, in the last decade there has been an acceleration of methodological developments, accompanied by a broad collection of applications as spatiotemporally indexed data have become more widely available in many scientific fields. We present a self-contained review describing statistical models and methods that can be used to analyse patterns of points in space and time when the questions of scientific interest concern both their spatial and their temporal behaviour. We revisit moment characteristics that define summary statistics, as well as conditional intensities which uniquely characterise certain spatiotemporal point processes. We make use of these concepts to describe models and associated methods of inference for spatiotemporal point process data. Three new motivating real-data examples are described and analysed throughout the paper to illustrate the most relevant techniques, discussing the pros and cons of the different considered approaches.

  • 11.
    Iftimi, Adina
    et al.
    Department of Biosciences and Nutrition, Karolinska Institutet, Stockholm, Sweden.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Montes, Francisco
    Department of Statistics and Operations Research, University of Valencia, Valencia, Spain.
    Second-order analysis of marked inhomogeneous spatio-temporal point processes: applications to earthquake data2019In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 46, no 3, p. 661-685Article in journal (Refereed)
    Abstract [en]

    To analyse interactions in marked spatio-temporal point processes (MSTPPs), we introduce marked second-order reduced moment measures and K-functions for inhomogeneous second-order intensity reweighted stationary MSTPPs. These summary statistics, which allow us to quantify dependence between different mark-based classifications of the points, are depending on the specific mark space and mark reference measure chosen. Unbiased and consistent minus-sampling estimators are derived for all statistics considered and a test for random labelling is indicated. In addition, we treat Voronoi intensity estimators for MSTPPs. These new statistics are finally employed to analyse an Andaman sea earthquake data set.

  • 12.
    Iftimi, Adina
    et al.
    University of Valencia, Spain.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Montes, Francisco
    University of Valencia, Spain.
    The second-order statistical analysis of marked inhomogeneous spatio-temporal point processes2016In: METMA VIII: Proceedings of the 8th International Workshop on Spatio-Temporal Modelling / [ed] A. Iftimi, J. Mateu, F. Montes, 2016, p. 89-93Conference paper (Other academic)
    Abstract [en]

    An earthquake is characterised by the shaking of the surface of the Earth, and can range from being imperceptible to causing huge damage and killing thousands of people. Magnitude is a measure of the size of an earthquake source, and does not depend on the spatio-temporal location of the event. The data in this study includes all earthquakes with magnitude larger than or equal to 5, with a total of 1248 earthquakes registered from 2004 to 2008, in the area of Sumatra (Indonesia). We analyse the interaction between different types of earthquakes, classified according to their magnitude, at different space-time scales. We want to identify spatio-temporal interaction between high magnitude earthquakes (magnitude larger than 5:5) and smaller magnitude earthquakes ( 5:5). The analysis shows a strong relation between big earthquakes and aftershocks. We observe that aftershocks could span their power as far as 3,000 km and 400 days. Random labelling testing shows, as expected, that we do not have random labelling.

  • 13.
    Moradi, M. Mehdi
    et al.
    Institute of New Imaging Technologies (INIT), University Jaume I, Castellon, Spain.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Rubak, Ege
    Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
    Lachieze-Rey, Raphael
    Université Paris Descartes, Sorbonne Paris Cité, Paris, France.
    Mateu, Jorge
    Department of Mathematics, University Jaume I, Castellon, Spain.
    Baddeley, Adrian
    Department of Mathematics and Statistics, Curtin University, Perth, Australia.
    Resample-smoothing of Voronoi intensity estimators2019In: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 29, no 5, p. 995-1010Article in journal (Refereed)
    Abstract [en]

    Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern).

  • 14.
    Toreti, Andrea
    et al.
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Belward, Alan
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Perez-Dominguez, Ignacio
    European Commission, Joint Research Centre (JRC), Seville, Spain.
    Naumann, Gustavo
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Luterbacher, Jürg
    Dept. of Geography, Climatology, Climate Dynamics and Climate Change, and Centre for International Development and Environmental Research, Justus-Liebig University of Giessen, Germany.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seguini, Lorenzo
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Manfron, Giacinto
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Lopez Lozano, Raul
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Baruth, Bettina
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    van den Berg, Maurits
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Dentener, Frank
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Ceglar, Andrej
    Joint Research Centre (JRC), European Commission, Ispra (VA), Italy.
    Chatzopoulos, Thomas
    Joint Research Centre (JRC), European Commission, Seville, Spain.
    Zampieri, Matteo
    Joint Research Centre, European Commission, Ispra (VA), Italy.
    The exceptional 2018 European water seesaw calls for action on adaptation2019In: Earth's Future, ISSN 1384-5160, E-ISSN 2328-4277, Vol. 7, no 6, p. 652-663Article in journal (Refereed)
    Abstract [en]

    Temperature and precipitation are the most important factors responsible for agricultural productivity variations. In 2018 spring/summer growing season, Europe experienced concurrent anomalies of both. Drought conditions in central and northern Europe caused yield reductions up to 50% for the main crops, yet wet conditions in southern Europe saw yield gains up to 34%, both with respect to the previous 5‐years' mean. Based on the analysis of documentary and natural proxy based seasonal paleoclimate reconstructions for the past half millennium, we show that the 2018 combination of climatic anomalies in Europe was unique. The water seesaw, a marked dipole of negative water anomalies in central Europe and positive ones in southern Europe, distinguished 2018 from the five previous similar droughts since 1976. Model simulations reproduce the 2018 European water seesaw in only four years out of 875 years in historical runs and projections. Future projections under the RCP8.5 scenario show that 2018‐like temperature and rainfall conditions, favourable to crop growth, will occur less frequent in southern Europe. In contrast, in central Europe high‐end emission scenario climate projections show that droughts as intense as 2018 could become a common occurrence as early as 2043. Whilst integrated European and global agricultural markets limited agro‐economic shocks caused by 2018's extremes, there is an urgent need for adaptation strategies for European agriculture to consider futures without the benefits of any water seesaw.

  • 15.
    Toreti, Andrea
    et al.
    European Commission, Ispra (VA), Italy.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zampieri, Matteo
    European Commission, Ispra (VA), Italy.
    Concurrent climate extremes in the key wheat producing regions of the world2019In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 9, article id 5493Article in journal (Refereed)
    Abstract [en]

    Climate extremes have profound impacts on key socio-economic sectors such as agriculture. In a changing climate context, characterised by an intensification of these extremes and where the population is expected to grow, exposure and vulnerability must be accurately assessed. However, most risk assessments analyse extremes independently, thus potentially being overconfident in the resilience of the socio-economic sectors. Here, we propose a novel approach to defining and characterising concurrent climate extremes (i.e. extremes occurring within a specific temporal lag), which is able toidentify spatio-temporal dependences without making any strict assumptions. the method is applied to large-scale heat stress and drought events in the key wheat producing regions of the world, as these extremes can cause serious yield losses and thus trigger market shocks. Wheat regions likely to haveconcurrent extremes (heat stress and drought events) are identified, as well as regions independent ofeach other or inhibiting each other in terms of these extreme events. this tool may be integrated in all risk assessments but could also be used to explore global climate teleconnections.

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