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| 2. |
- Comas, Carles, et al.
(författare)
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A third order point process characteristic for multi-type point processes
- 2010
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Ingår i: Statistica Neerlandica. - : Wiley. - 0039-0402 .- 1467-9574. ; 64:1, s. 19-44
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Tidskriftsartikel (refereegranskat)abstract
- The description and analysis of spatial point patterns have mainly been based on first- and second-order characteristics. However, and especially when analyzing complex and multivariate point patterns, the use of higher-order characteristics would be more informative. In this paper, we introduce a third-order characteristic for multi-type point processes, which is based on the number of r-close triples of points, where the three points are of three different types (species). This characteristic is useful, when the second-order characteristics indicate that the three point patterns are pairwise uncorrelated but there is some relationship between triples of points. Furthermore, we conjecture that the new statistic can be used to test independence between the three point processes.
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| 3. |
- Cronie, Ottmar, et al.
(författare)
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Functional marked point processes : Unifying spatio-temporal frameworks and analysing spatially dependent functional data
- 2019
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Ingår i: Statistical Analysis for Space-Time Data. - : Eurpean Courses in Advanced Statistics (ECAS). ; , s. 7-7
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Konferensbidrag (refereegranskat)abstract
- This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent e.g. spatial paths or functions of time. To be able to consider e.g. multivariate FMPPs, we also attach an additionally, Euclidean, mark to each point. We indicate how the FMPP framework quite naturally connects the point process framework with both the functional data analysis framework and the geostatistical framework; in particular we define spatio-temporal geostatistical marking for point processes. We further show that various existing stochastic models fit well into the FMPP framework, in particular marked point processes with real valued marks. To be able to carry out non-parametric statistical analyses for functional marked point patterns, we study characteristics such as product densities and Palm distributions, which are the building blocks for summary statistics such as marked inhomogeneous J-functions and our so-called K-functionals. We finally apply these statistical tools to analyse a few different functional marked point patterns.
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| 4. |
- Cronie, Ottmar, 1979, et al.
(författare)
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Inhomogeneous higher-order summary statistics for point processes on linear networks
- 2020
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Ingår i: Statistics and computing. - : Springer Science and Business Media LLC. - 0960-3174 .- 1573-1375. ; 30, s. 1221-1239
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Tidskriftsartikel (refereegranskat)abstract
- As a workaround for the lack of transitive transformations on linear network structures, which are required to consider different notions of distributional invariance, including stationarity, we introduce the notions of pseudostationarity and intensity reweighted moment pseudostationarity for point processes on linear networks. Moreover, using arbitrary so-called regular linear network distances, e.g. the Euclidean and the shortest-path distance, we further propose geometrically corrected versions of different higher-order summary statistics, including the inhomogeneous empty space function, the inhomogeneous nearest neighbour distance distribution function and the inhomogeneous J-function. Such summary statistics detect interactions of order higher than two. We also discuss their nonparametric estimators and through a simulation study, considering models with different types of spatial interaction and different networks, we study the performance of our proposed summary statistics by means of envelopes. Our summary statistic estimators manage to capture clustering, regularity as well as Poisson process independence. Finally, we make use of our new summary statistics to analyse two different datasets: motor vehicle traffic accidents and spiderwebs.
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| 5. |
- Cronie, Ottmar, et al.
(författare)
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Spatio-temporal càdlàg functional marked point processes : Unifying spatio-temporal frameworks
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 6. |
- Ghorbani, Mohammad, et al.
(författare)
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A new class of spatial covariance functions generated by higher-order kernels
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier transform of some higher-order kernels. Further, we extend this class of the spatial covariance functions to the spatio-temporal setting by using the idea used in Ma (2003).
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| 7. |
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| 8. |
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| 9. |
- Ghorbani, Mohammad, et al.
(författare)
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Functional marked point processes : a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data
- 2021
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Ingår i: Test (Madrid). - : Sociedad de Estadística e Investigación Operativa (Spanish Society of Statistics and Operations Research). - 1133-0686 .- 1863-8260. ; 30:3, s. 529-568
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Tidskriftsartikel (refereegranskat)abstract
- This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent, for example, spatial paths or functions of time. To be able to consider, for example, multivariate FMPPs, we also attach an additional, Euclidean, mark to each point. We indicate how the FMPP framework quite naturally connects the point process framework with both the functional data analysis framework and the geostatistical framework. We further show that various existing stochastic models fit well into the FMPP framework. To be able to carry out nonparametric statistical analyses for FMPPs, we study characteristics such as product densities and Palm distributions, which are the building blocks for many summary statistics. We proceed to defining a new family of summary statistics, so-called weighted marked reduced moment measures, together with their nonparametric estimators, in order to study features of the functional marks. We further show how other summary statistics may be obtained as special cases of these summary statistics. We finally apply these tools to analyse population structures, such as demographic evolution and sex ratio over time, in Spanish provinces.
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| 10. |
- González, Jonatan A., et al.
(författare)
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Spatio-temporal point process statistics : a review
- 2016
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Ingår i: Spatial Statistics. - : Elsevier. - 2211-6753. ; 18:Part B, s. 505-544
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Forskningsöversikt (refereegranskat)abstract
- 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.
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| 11. |
- Jung, Christian, et al.
(författare)
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A comparison of very old patients admitted to intensive care unit after acute versus elective surgery or intervention
- 2019
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Ingår i: Journal of critical care. - : W B SAUNDERS CO-ELSEVIER INC. - 0883-9441 .- 1557-8615. ; 52, s. 141-148
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Tidskriftsartikel (refereegranskat)abstract
- Background: We aimed to evaluate differences in outcome between patients admitted to intensive care unit (ICU) after elective versus acute surgery in a multinational cohort of very old patients (80 years; VIP). Predictors of mortality, with special emphasis on frailty, were assessed.Methods: In total, 5063 VIPs were induded in this analysis, 922 were admitted after elective surgery or intervention, 4141 acutely, with 402 after acute surgery. Differences were calculated using Mann-Whitney-U test and Wilcoxon test. Univariate and multivariable logistic regression were used to assess associations with mortality.Results: Compared patients admitted after acute surgery, patients admitted after elective surgery suffered less often from frailty as defined as CFS (28% vs 46%; p < 0.001), evidenced lower SOFA scores (4 +/- 5 vs 7 +/- 7; p < 0.001). Presence of frailty (CFS >4) was associated with significantly increased mortality both in elective surgery patients (7% vs 12%; p = 0.01), in acute surgery (7% vs 12%; p = 0.02).Conclusions: VIPs admitted to ICU after elective surgery evidenced favorable outcome over patients after acute surgery even after correction for relevant confounders. Frailty might be used to guide clinicians in risk stratification in both patients admitted after elective and acute surgery.
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| 12. |
- Mateu, Jorge, et al.
(författare)
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Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation
- 2020
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Ingår i: Spatial Statistics. - : Elsevier. - 2211-6753. ; 37
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Tidskriftsartikel (refereegranskat)abstract
- Aside from reviewing different intensity estimation schemes for point processes on linear networks, this paper introduces two Voronoi-based intensity estimation approaches for spatio-temporal linear network point processes. The first is a separable estimator, which is obtained as a scaled product of a resample-smoothed Voronoi intensity estimator on the linear network in question and another one on the time domain. The second one, which we refer to as a pseudo-separable resample-smoothed Voronoi intensity estimator, uses a slightly different thinning strategy. Through a simulation study we show that the latter performs slightly better than the former. We finally apply the latter estimator to a spatio-temporal traffic accident point pattern.
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| 13. |
- Moradi, M. Mehdi, et al.
(författare)
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Resample-smoothing of Voronoi intensity estimators
- 2019
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Ingår i: Statistics and computing. - : Springer. - 0960-3174 .- 1573-1375. ; 29:5, s. 995-1010
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Tidskriftsartikel (refereegranskat)abstract
- 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).
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| 14. |
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| 15. |
- Strandberg, Johan, et al.
(författare)
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A comparison of spatiotemporal and functional kriging approaches
- 2021
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Ingår i: Geostatistical functional data analysis. - : John Wiley & Sons. - 9781119387916 - 9781119387848 ; , s. 375-402
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Bokkapitel (refereegranskat)abstract
- Here we present and compare functional and spatiotemporal (Sp.T.) kriging approaches to predict spatial functional random processes, which can also be viewed as Sp.T. random processes. Comparisons are focused on Sp.T. kriging versus ordinary kriging for functional data (OKFD), since more flexible functional kriging approaches like pointwise functional kriging and functional kriging total model coincide with OKFD in several situations. Prediction performance is evaluated via functional cross-validation on simulated data as well as on a Canadian weather data set. The two kriging approaches perform in many cases rather equal for stationary Sp.T. processes. For nonstationary Sp.T. processes, OKFD performs better than Sp.T. kriging. The computational time for OKFD is considerably lower compared to those for the Sp.T. kriging methods.
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| 16. |
- Strandberg, Johan, et al.
(författare)
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Prediction of spatial functional random processes : comparing functional and spatio-temporal kriging approaches
- 2019
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Ingår i: Stochastic environmental research and risk assessment (Print). - : Springer. - 1436-3240 .- 1436-3259. ; 33:10, s. 1699-1719
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Tidskriftsartikel (refereegranskat)abstract
- We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.
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| 17. |
- Wijayatunga, Priyantha, 1967-, et al.
(författare)
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Discussion on the meeting on 'Data visualization'
- 2019
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Ingår i: Journal of the Royal Statistical Society. - UK : Royal Statistical Society. - 0964-1998 .- 1467-985X. ; 182:2, s. 433-441
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Visualizing both conditional and marginal associations in contingency tables by using simple diagrams is discussed
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