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The doubly stochastic mechanism generating the realizations of spatial log-Gaussian Cox processes is empirically assessed in terms of generalized entropy, divergence and complexity measures. The aim is to characterize the contribution to stochasticity from the two phases involved, in relation to the transfer of information from the intensity field to the resulting point pattern, as well as regarding their marginal random structure. A number of scenarios are explored regarding the Matérn model for the covariance of the underlying log-intensity random field. Sensitivity with respect to varying values of the model parameters, as well as of the deformation parameters involved in the generalized informational measures, is analyzed on the basis of regular lattice partitionings. Both a marginal global assessment based on entropy and complexity measures, and a joint local assessment based on divergence and relative complexity measures, are addressed. A Poisson process and a log-Gaussian Cox process with white noise intensity, the first providing an upper bound for entropy, are considered as reference cases. Differences regarding the transfer of structural information from the intensity field to the subsequently generated point patterns, reflected by entropy, divergence and complexity estimates, are discussed according to the specifications considered. In particular, the magnitude of the decrease in marginal entropy estimates between the intensity random fields and the corresponding point patterns quantitatively discriminates the global effect of the additional source of variability involved in the second phase of the double stochasticity.
Adriana Medialdea; José Miguel Angulo; Jorge Mateu. Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes. Entropy 2021, 23, 1135 .
AMA StyleAdriana Medialdea, José Miguel Angulo, Jorge Mateu. Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes. Entropy. 2021; 23 (9):1135.
Chicago/Turabian StyleAdriana Medialdea; José Miguel Angulo; Jorge Mateu. 2021. "Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes." Entropy 23, no. 9: 1135.
Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its omnipresence in scientific research, in almost every area of knowledge, particularly in Physics, Communications, Geosciences, Life Sciences, etc. Information-theoretic aspects underlie modern developments on complexity and risk. A proper use and exploitation of structural characteristics inherent to spatial data motivates, according to the purpose, special considerations in this context. In this paper, some relevant approaches introduced regarding the informational analysis of spatial data, related aspects concerning complexity analysis, and, in particular, implications in relation to the structural assessment of multifractal point patterns, are reviewed under a conceptually connective evolutionary perspective.
José M. Angulo; Francisco J. Esquivel; Ana E. Madrid; Francisco J. Alonso. Information and complexity analysis of spatial data. Spatial Statistics 2020, 42, 100462 .
AMA StyleJosé M. Angulo, Francisco J. Esquivel, Ana E. Madrid, Francisco J. Alonso. Information and complexity analysis of spatial data. Spatial Statistics. 2020; 42 ():100462.
Chicago/Turabian StyleJosé M. Angulo; Francisco J. Esquivel; Ana E. Madrid; Francisco J. Alonso. 2020. "Information and complexity analysis of spatial data." Spatial Statistics 42, no. : 100462.
This paper introduces a new family of the convex divergence-based risk measure by specifying ( h , ϕ ) -divergence, corresponding with the dual representation. First, the sensitivity characteristics of the modified divergence risk measure with respect to profit and loss (P&L) and the reference probability in the penalty term are discussed, in view of the certainty equivalent and robust statistics. Secondly, a similar sensitivity property of ( h , ϕ ) -divergence risk measure with respect to P&L is shown, and boundedness by the analytic risk measure is proved. Numerical studies designed for Rényi- and Tsallis-divergence risk measure are provided. This new family integrates a wide spectrum of divergence risk measures and relates to divergence preferences.
Meng Xu; José M. Angulo. Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions. Entropy 2019, 21, 634 .
AMA StyleMeng Xu, José M. Angulo. Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions. Entropy. 2019; 21 (7):634.
Chicago/Turabian StyleMeng Xu; José M. Angulo. 2019. "Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions." Entropy 21, no. 7: 634.
Structural characteristics of random field excursion sets defined by threshold exceedances provide meaningful indicators for the description of extremal behaviour in the spatiotemporal dynamics of environmental systems, and for risk assessment. In this paper a conditional approach for analysis at global and regional scales is introduced, performed by implementation of risk measures under proper model-based integration of available knowledge. Specifically, quantile-based measures, such as Value-at-Risk and Average Value-at-Risk, are applied based on the empirical distributions derived from conditional simulation for different threshold exceedance indicators, allowing the construction of meaningful dynamic risk maps. Significant aspects of the application of this methodology, regarding the nature and the properties (e.g. local variability, dependence range, marginal distributions) of the underlying random field, as well as in relation to the increasing value of the reference threshold, are discussed and illustrated based on simulation under a variety of scenarios.
J. L. Romero; A. E. Madrid; J. M. Angulo. Quantile-based spatiotemporal risk assessment of exceedances. Stochastic Environmental Research and Risk Assessment 2018, 32, 2275 -2291.
AMA StyleJ. L. Romero, A. E. Madrid, J. M. Angulo. Quantile-based spatiotemporal risk assessment of exceedances. Stochastic Environmental Research and Risk Assessment. 2018; 32 (8):2275-2291.
Chicago/Turabian StyleJ. L. Romero; A. E. Madrid; J. M. Angulo. 2018. "Quantile-based spatiotemporal risk assessment of exceedances." Stochastic Environmental Research and Risk Assessment 32, no. 8: 2275-2291.
F.J. Esquivel; F.J. Alonso; José Miguel Angulo. Multifractal complexity analysis in space–time based on the generalized dimensions derivatives. Spatial Statistics 2017, 22, 469 -480.
AMA StyleF.J. Esquivel, F.J. Alonso, José Miguel Angulo. Multifractal complexity analysis in space–time based on the generalized dimensions derivatives. Spatial Statistics. 2017; 22 ():469-480.
Chicago/Turabian StyleF.J. Esquivel; F.J. Alonso; José Miguel Angulo. 2017. "Multifractal complexity analysis in space–time based on the generalized dimensions derivatives." Spatial Statistics 22, no. : 469-480.
G. Christakos; José Miguel Angulo; H. L. Yu; J. Wu. Space-Time Metric Determination in Environmental Modeling. Journal of Environmental Informatics 2017, 1 .
AMA StyleG. Christakos, José Miguel Angulo, H. L. Yu, J. Wu. Space-Time Metric Determination in Environmental Modeling. Journal of Environmental Informatics. 2017; ():1.
Chicago/Turabian StyleG. Christakos; José Miguel Angulo; H. L. Yu; J. Wu. 2017. "Space-Time Metric Determination in Environmental Modeling." Journal of Environmental Informatics , no. : 1.
Structural characteristics of random field threshold exceedance sets (e.g., size, connectivity, and boundary regularity) are used in practice for definition of different indicators in spatial and spatio-temporal risk analysis. In this work, point process techniques are applied to study the structural changes derived from random field deformations and blurring transformations, meaningful from both physical and methodological points of view in a variety of contexts. Specifically, based on simulations from a flexible random field model class, features such as aggregation/inhibition of patterns defined by centroids of connected components, as well as by boundary A-exit points, are investigated in relation to the local contraction/dilation effects of deformation and the smoothing properties of blurring. Supplementary materials accompanying this paper appear online.
Alfonso E. Madrid; J. M. Angulo; Jorge Mateu. Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances. Journal of Agricultural, Biological and Environmental Statistics 2016, 21, 512 -530.
AMA StyleAlfonso E. Madrid, J. M. Angulo, Jorge Mateu. Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances. Journal of Agricultural, Biological and Environmental Statistics. 2016; 21 (3):512-530.
Chicago/Turabian StyleAlfonso E. Madrid; J. M. Angulo; Jorge Mateu. 2016. "Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances." Journal of Agricultural, Biological and Environmental Statistics 21, no. 3: 512-530.
Generalized statistical complexity measures provide a means to jointly quantify inner information and relative structural richness of a system described in terms of a probability model. As a natural divergence-based extension in this context, generalized relative complexity measures have been proposed for the local comparison of two given probability distributions. In this paper, the behavior of generalized relative complexity measures is studied for assessment of structural dependence in a random vector leading to a concept of ‘generalized mutual complexity’. A related optimality criterion for sampling network design, which provides an alternative to mutual information based methods in the complexity context, is formulated. Aspects related to practical implementation, and conceptual issues regarding the meaning and potential use of this approach, are discussed. Numerical examples are used for illustration.
F. J. Alonso; M. C. Bueso; J. M. Angulo. Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design. Methodology and Computing in Applied Probability 2016, 18, 921 -933.
AMA StyleF. J. Alonso, M. C. Bueso, J. M. Angulo. Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design. Methodology and Computing in Applied Probability. 2016; 18 (3):921-933.
Chicago/Turabian StyleF. J. Alonso; M. C. Bueso; J. M. Angulo. 2016. "Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design." Methodology and Computing in Applied Probability 18, no. 3: 921-933.
Space deformation modelling and estimation techniques based on Multidimensional Scaling (MDS) methods play an important role in nonparametric approaches to the covariance structure analysis of the spatiotemporal processes underlying environmental studies. Since any related procedure depends on the planar MDS representation, the stability of the estimated dispersion, together with the determination of the most influential stations in the estimation of the dispersion space, are important issues that must be analysed before performing the final mapping. In this paper, stability analysis, both in terms of the MDS model and of the variogram function, as well as concerning the derivation of kriging interpolation estimates, is addressed using a special analytical jackknife procedure. Furthermore, the influence of each station in the solution given is assessed, thus providing relevant information regarding not only the MDS procedure but also the interpolation process and the variogram estimation of the spatial dispersion.
J. Fernando Vera; José M. Angulo; Juan A. Roldán. Stability analysis in nonstationary spatial covariance estimation. Stochastic Environmental Research and Risk Assessment 2016, 31, 815 -828.
AMA StyleJ. Fernando Vera, José M. Angulo, Juan A. Roldán. Stability analysis in nonstationary spatial covariance estimation. Stochastic Environmental Research and Risk Assessment. 2016; 31 (3):815-828.
Chicago/Turabian StyleJ. Fernando Vera; José M. Angulo; Juan A. Roldán. 2016. "Stability analysis in nonstationary spatial covariance estimation." Stochastic Environmental Research and Risk Assessment 31, no. 3: 815-828.
F.J. Esquivel; José Miguel Angulo. Non-extensive analysis of the seismic activity involving the 2011 volcanic eruption in El Hierro. Spatial Statistics 2015, 14, 208 -221.
AMA StyleF.J. Esquivel, José Miguel Angulo. Non-extensive analysis of the seismic activity involving the 2011 volcanic eruption in El Hierro. Spatial Statistics. 2015; 14 ():208-221.
Chicago/Turabian StyleF.J. Esquivel; José Miguel Angulo. 2015. "Non-extensive analysis of the seismic activity involving the 2011 volcanic eruption in El Hierro." Spatial Statistics 14, no. : 208-221.
M. Camacho-Collados; Federico Liberatore; José Miguel Angulo. A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector. European Journal of Operational Research 2015, 246, 674 -684.
AMA StyleM. Camacho-Collados, Federico Liberatore, José Miguel Angulo. A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector. European Journal of Operational Research. 2015; 246 (2):674-684.
Chicago/Turabian StyleM. Camacho-Collados; Federico Liberatore; José Miguel Angulo. 2015. "A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector." European Journal of Operational Research 246, no. 2: 674-684.
Potential theory and Dirichlet’s priciple constitute the basic elements of the well-known classical theory of Markov processes and Dirichlet forms. This paper presents new classes of fractional spatiotemporal covariance models, based on the theory of non-local Dirichlet forms, characterizing the fundamental solution, Green kernel, of Dirichlet boundary value problems for fractional pseudodifferential operators. The elements of the associated Gaussian random field family have compactly supported non-separable spatiotemporal covariance kernels admitting a parametric representation. Indeed, such covariance kernels are not self-similar but can display local self-similarity, interpolating regular and fractal local behavior in space and time. The associated local fractional exponents are estimated from the empirical log-wavelet variogram. Numerical examples are simulated for illustrating the properties of the space–time covariance model class introduced.
M. D. Ruiz-Medina; J. M. Angulo; G. Christakos; R. Fernández-Pascual. New compactly supported spatiotemporal covariance functions from SPDEs. Statistical Methods & Applications 2015, 25, 125 -141.
AMA StyleM. D. Ruiz-Medina, J. M. Angulo, G. Christakos, R. Fernández-Pascual. New compactly supported spatiotemporal covariance functions from SPDEs. Statistical Methods & Applications. 2015; 25 (1):125-141.
Chicago/Turabian StyleM. D. Ruiz-Medina; J. M. Angulo; G. Christakos; R. Fernández-Pascual. 2015. "New compactly supported spatiotemporal covariance functions from SPDEs." Statistical Methods & Applications 25, no. 1: 125-141.
Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced.
José M. Angulo; Francisco J. Esquivel. Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information. Entropy 2015, 17, 5382 -5401.
AMA StyleJosé M. Angulo, Francisco J. Esquivel. Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information. Entropy. 2015; 17 (12):5382-5401.
Chicago/Turabian StyleJosé M. Angulo; Francisco J. Esquivel. 2015. "Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information." Entropy 17, no. 12: 5382-5401.
The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.
Hwa-Lung Yu; José Miguel Angulo; Ming-Hung Cheng; Jiaping Wu; George Christakos. An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan). Biometrical Journal 2014, 56, 428 -440.
AMA StyleHwa-Lung Yu, José Miguel Angulo, Ming-Hung Cheng, Jiaping Wu, George Christakos. An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan). Biometrical Journal. 2014; 56 (3):428-440.
Chicago/Turabian StyleHwa-Lung Yu; José Miguel Angulo; Ming-Hung Cheng; Jiaping Wu; George Christakos. 2014. "An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan)." Biometrical Journal 56, no. 3: 428-440.
Knowledge about structural aspects of spatiotemporal dynamics can be obtained, among other approaches, in terms of a variety of information-theoretic related measures. In this context, multifractal analysis tools such as generalized dimensions and multifractal spectrum are useful to study different aspects of scaling behaviour. Recent research has been focused on statistical complexity measures. Conceptual connections between multifractality and complexity, generally understood from intuitive interpretation, can be established based on limiting behaviour according to scale, in terms of variational properties of generalized dimension curves. Complexity and multifractality analysis, in combination with suitable transformations of the data space-time coordinates, allows to identify and assess dimensional interaction and evolutionary changes, two important issues in structural analysis of dependence and heterogeneity. These aspects are investigated and illustrated with application to seismic data.
José M. Angulo; Francisco J. Esquivel. Statistical Complexity Analysis of Spatiotemporal Dynamics. Lecture Notes in Earth System Sciences 2013, 185 -188.
AMA StyleJosé M. Angulo, Francisco J. Esquivel. Statistical Complexity Analysis of Spatiotemporal Dynamics. Lecture Notes in Earth System Sciences. 2013; ():185-188.
Chicago/Turabian StyleJosé M. Angulo; Francisco J. Esquivel. 2013. "Statistical Complexity Analysis of Spatiotemporal Dynamics." Lecture Notes in Earth System Sciences , no. : 185-188.
Different approaches and tools have been adopted for the analysis and characterization of regional seismicity based on spatio–temporal series of event occurrences. Two main aspects of interest in this context concern scaling properties and dimensional interaction. This paper is focused on the statistical use of information-theoretic concepts and measures in the analysis of structural complexity of seismic distributional patterns. First, contextual significance is motivated, and preliminary elements related to informational entropy, complexity and multifractal analysis are introduced. Next, several technical and methodological extensions are proposed. Specifically, limiting behaviour of some complexity measures in connection with generalized dimensions is established, justifying a concept of multifractal complexity. Under scaling behaviour, a mutual-information-related dependence coefficient for assessing spatio–temporal interaction is defined in terms of generalized dimensions. Also, an alternative form of generalized dimensions based on Tsallis entropy convergence rates is formulated. Further, possible incorporation of effects, such as earthquake magnitude, is achieved in terms of weighted box-counting distributions. Different aspects in relation to the above elements are analyzed and illustrated using two well-known series of seismic event data of an underlying different nature, occurred in the areas of Agrón (Granada, Spain) and El Hierro (Canary Islands, Spain). Finally, various related directions for continuing research are indicated.
José M. Angulo; Francisco J. Esquivel. Structural complexity in space–time seismic event data. Stochastic Environmental Research and Risk Assessment 2013, 28, 1187 -1206.
AMA StyleJosé M. Angulo, Francisco J. Esquivel. Structural complexity in space–time seismic event data. Stochastic Environmental Research and Risk Assessment. 2013; 28 (5):1187-1206.
Chicago/Turabian StyleJosé M. Angulo; Francisco J. Esquivel. 2013. "Structural complexity in space–time seismic event data." Stochastic Environmental Research and Risk Assessment 28, no. 5: 1187-1206.
This paper is concerned with the modeling of infectious disease spread in a composite space-time domain under conditions of uncertainty. We focus on stochastic modeling that accounts for basic mechanisms of disease distribution and multi-sourced in situ uncertainties. Starting from the general formulation of population migration dynamics and the specification of transmission and recovery rates, the model studies the functional formulation of the evolution of the fractions of susceptible-infected-recovered individuals. The suggested approach is capable of: a) modeling population dynamics within and across localities, b) integrating the disease representation (i.e. susceptible-infected-recovered individuals) with observation time series at different geographical locations and other sources of information (e.g. hard and soft data, empirical relationships, secondary information), and c) generating predictions of disease spread and associated parameters in real time, while considering model and observation uncertainties. Key aspects of the proposed approach are illustrated by means of simulations (i.e. synthetic studies), and a real-world application using hand-foot-mouth disease (HFMD) data from China.
José Miguel Angulo; Hwa-Lung Yu; Andrea Langousis; Alexander Kolovos; Jinfeng Wang; Ana Esther Madrid; George Christakos. Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach. PLOS ONE 2013, 8, e72168 .
AMA StyleJosé Miguel Angulo, Hwa-Lung Yu, Andrea Langousis, Alexander Kolovos, Jinfeng Wang, Ana Esther Madrid, George Christakos. Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach. PLOS ONE. 2013; 8 (9):e72168.
Chicago/Turabian StyleJosé Miguel Angulo; Hwa-Lung Yu; Andrea Langousis; Alexander Kolovos; Jinfeng Wang; Ana Esther Madrid; George Christakos. 2013. "Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach." PLOS ONE 8, no. 9: e72168.
This paper derives conditions under which a stable solution to the least-squares linear estimation problem for multifractional random fields can be obtained. The observation model is defined in terms of a multifractional pseudodifferential equation. The weak-sense and strong-sense formulations of this problem are studied through the theory of fractional Sobolev spaces of variable order, and the spectral theory of multifractional pseudodifferential operators and their parametrix. The Theory of Reproducing Kernel Hilbert Spaces is also applied to define a stable solution to the direct and inverse estimation problems. Numerical projection methods are proposed based on the construction of orthogonal bases of these spaces. Indeed, projection into such bases leads to a regularization, removing the ill-posed nature of the estimation problem. A simulation study is developed to illustrate the estimation results derived. Some open research lines in relation to the extension of the derived results to the multifractal process context are also discussed.
M. D. Ruiz-Medina; V. V. Anh; R. M. Espejo; José Miguel Angulo; M. P. Frías. Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context. Journal of Optimization Theory and Applications 2013, 167, 888 -911.
AMA StyleM. D. Ruiz-Medina, V. V. Anh, R. M. Espejo, José Miguel Angulo, M. P. Frías. Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context. Journal of Optimization Theory and Applications. 2013; 167 (3):888-911.
Chicago/Turabian StyleM. D. Ruiz-Medina; V. V. Anh; R. M. Espejo; José Miguel Angulo; M. P. Frías. 2013. "Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context." Journal of Optimization Theory and Applications 167, no. 3: 888-911.
A key objective in spatio-temporal modeling consists of providing an appropriate representation of complexity in interactive spatio-temporal dynamics inherent to real phenomena. Propagated effect of dynamical spatial deformation provides a meaningful way to describe certain forms of heterogeneous behaviour; in particular, in relation to processes evolving in unstable media, or to account for the possible effect of covariates, to mention some significant interpretations. In this paper, the formulation of a discrete time and continuous space spatio-temporal interaction model with autoregressive dynamics, incorporating the effect of continuous deformation of the spatial support over time, is studied. Among other fields, this approach provides a suitable representation for a variety of geophysical and environmental applications. In particular, a vast family of heterogeneous models is generated from models which display homogeneity in the absence of deformation. Structural characteristics and variability properties, as well as self-consistency conditions for a limiting continuous-time approximation, are analyzed.
José Miguel Angulo; A. E. Madrid. A deformation/blurring-based spatio-temporal model. Stochastic Environmental Research and Risk Assessment 2013, 28, 1061 -1073.
AMA StyleJosé Miguel Angulo, A. E. Madrid. A deformation/blurring-based spatio-temporal model. Stochastic Environmental Research and Risk Assessment. 2013; 28 (4):1061-1073.
Chicago/Turabian StyleJosé Miguel Angulo; A. E. Madrid. 2013. "A deformation/blurring-based spatio-temporal model." Stochastic Environmental Research and Risk Assessment 28, no. 4: 1061-1073.
This chapter contains sections titled: Introduction Adaptive sampling network design Predictive information based on data transformations Application to Upper Austria temperature data Acknowledgments References
José Miguel Angulo; María C. Bueso; Francisco J. Alonso. Space-Time Adaptive Sampling and Data Transformations. Spatio-Temporal Design 2012, 231 -248.
AMA StyleJosé Miguel Angulo, María C. Bueso, Francisco J. Alonso. Space-Time Adaptive Sampling and Data Transformations. Spatio-Temporal Design. 2012; ():231-248.
Chicago/Turabian StyleJosé Miguel Angulo; María C. Bueso; Francisco J. Alonso. 2012. "Space-Time Adaptive Sampling and Data Transformations." Spatio-Temporal Design , no. : 231-248.