Author

# Dietrich Stoyan

Other affiliations: Australian National University, UPRRP College of Natural Sciences

Bio: Dietrich Stoyan is an academic researcher from Freiberg University of Mining and Technology. The author has contributed to research in topics: Point process & Estimator. The author has an hindex of 42, co-authored 218 publications receiving 17235 citations. Previous affiliations of Dietrich Stoyan include Australian National University & UPRRP College of Natural Sciences.

##### Papers published on a yearly basis

##### Papers

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18 Jul 1996TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.

Abstract: Mathematical Foundation. Point Processes I--The Poisson Point Process. Random Closed Sets I--The Boolean Model. Point Processes II--General Theory. Point Processes III--Construction of Models. Random Closed Sets II--The General Case. Random Measures. Random Processes of Geometrical Objects. Fibre and Surface Processes. Random Tessellations. Stereology. References. Indexes.

4,079 citations

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12 Mar 2002

TL;DR: In this article, the authors present an univariate Stochastic model for queuing systems and compare its properties with those of other non-stochastic models and compare risks.

Abstract: Preface. Univariate Stochastic Orders Theory of Integral Stochastic Orders Multivariate Stochastic Orders Stochastic Models, Comparison and Monotonicity Monotonicity and Comparability of Stochastic Processes Monotonicity Properties and Bounds for Queueing Systems Applications to Various Stochastic Models Comparing Risks. List of Symbols. References. Index.

1,739 citations

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22 Jan 2008

TL;DR: In this article, the authors proposed a method to estimate the intensity function of a point process with respect to the number of points in the process and the distance to each point in a graph.

Abstract: Preface. List of Examples. 1. Introduction. 1.1 Point process statistics. 1.2 Examples of point process data. 1.2.1 A pattern of amacrine cells. 1.2.2 Gold particles. 1.2.3 A pattern of Western Australian plants. 1.2.4 Waterstriders. 1.2.5 A sample of concrete. 1.3 Historical notes. 1.3.1 Determination of number of trees in a forest. 1.3.2 Number of blood particles in a sample. 1.3.3 Patterns of points in plant communities. 1.3.4 Formulating the power law for the pair correlation function for galaxies. 1.4 Sampling and data collection. 1.4.1 General remarks. 1.4.2 Choosing an appropriate study area. 1.4.3 Data collection. 1.5 Fundamentals of the theory of point processes. 1.6 Stationarity and isotropy. 1.6.1 Model approach and design approach. 1.6.2 Finite and infinite point processes. 1.6.3 Stationarity and isotropy. 1.6.4 Ergodicity. 1.7 Summary characteristics for point processes. 1.7.1 Numerical summary characteristics. 1.7.2 Functional summary characteristics. 1.8 Secondary structures of point processes. 1.8.1 Introduction. 1.8.2 Random sets. 1.8.3 Random fields. 1.8.4 Tessellations. 1.8.5 Neighbour networks or graphs. 1.9 Simulation of point processes. 2. The Homogeneous Poisson point process. 2.1 Introduction. 2.2 The binomial point process. 2.2.1 Introduction. 2.2.2 Basic properties. 2.2.3 The periodic binomial process. 2.2.4 Simulation of the binomial process. 2.3 The homogeneous Poisson point process. 2.3.1 Introduction. 2.3.2 Basic properties. 2.3.3 Characterisations of the homogeneous Poisson process. 2.4 Simulation of a homogeneous Poisson process. 2.5 Model characteristics. 2.5.1 Moments and moment measures. 2.5.2 The Palm distribution of a homogeneous Poisson process. 2.5.3 Summary characteristics of the homogeneous Poisson process. 2.6 Estimating the intensity. 2.7 Testing complete spatial randomness. 2.7.1 Introduction. 2.7.2 Quadrat counts. 2.7.3 Distance methods. 2.7.4 The J-test. 2.7.5 Two index-based tests. 2.7.6 Discrepancy tests. 2.7.7 The L-test. 2.7.8 Other tests and recommendations. 3. Finite point processes. 3.1 Introduction. 3.2 Distributions of numbers of points. 3.2.1 The binomial distribution. 3.2.2 The Poisson distribution. 3.2.3 Compound distributions. 3.2.4 Generalised distributions. 3.3 Intensity functions and their estimation. 3.3.1 Parametric statistics for the intensity function. 3.3.2 Non-parametric estimation of the intensity function. 3.3.3 Estimating the point density distribution function. 3.4 Inhomogeneous Poisson process and finite Cox process. 3.4.1 The inhomogeneous Poisson process. 3.4.2 The finite Cox process. 3.5 Summary characteristics for finite point processes. 3.5.1 Nearest-neighbour distances. 3.5.2 Dilation function. 3.5.3 Graph-theoretic statistics. 3.5.4 Second-order characteristics. 3.6 Finite Gibbs processes. 3.6.1 Introduction. 3.6.2 Gibbs processes with fixed number of points. 3.6.3 Gibbs processes with a random number of points. 3.6.4 Second-order summary characteristics of finite Gibbs processes. 3.6.5 Further discussion. 3.6.6 Statistical inference for finite Gibbs processes. 4. Stationary point processes. 4.1 Basic definitions and notation. 4.2 Summary characteristics for stationary point processes. 4.2.1 Introduction. 4.2.2 Edge-correction methods. 4.2.3 The intensity lambda. 4.2.4 Indices as summary characteristics. 4.2.5 Empty-space statistics and other morphological summaries. 4.2.6 The nearest-neighbour distance distribution function. 4.2.7 The J-function. 4.3 Second-order characteristics. 4.3.1 The three functions: K, L and g. 4.3.2 Theoretical foundations of second-order characteristics. 4.3.3 Estimators of the second-order characteristics. 4.3.4 Interpretation of pair correlation functions. 4.4 Higher-order and topological characteristics. 4.4.1 Introduction. 4.4.2 Third-order characteristics. 4.4.3 Delaunay tessellation characteristics. 4.4.4 The connectivity function. 4.5 Orientation analysis for stationary point processes. 4.5.1 Introduction. 4.5.2 Nearest-neighbour orientation distribution. 4.5.3 Second-order orientation analysis. 4.6 Outliers, gaps and residuals. 4.6.1 Introduction. 4.6.2 Simple outlier detection. 4.6.3 Simple gap detection. 4.6.4 Model-based outliers. 4.6.5 Residuals. 4.7 Replicated patterns. 4.7.1 Introduction. 4.7.2 Aggregation recipes. 4.8 Choosing appropriate observation windows. 4.8.1 General ideas. 4.8.2 Representative windows. 4.9 Multivariate analysis of series of point patterns. 4.10 Summary characteristics for the non-stationary case. 4.10.1 Formal application of stationary characteristics and estimators. 4.10.2 Intensity reweighting. 4.10.3 Local rescaling. 5. Stationary marked point processes. 5.1 Basic definitions and notation. 5.1.1 Introduction. 5.1.2 Marks and their properties. 5.1.3 Marking models. 5.1.4 Stationarity. 5.1.5 First-order characteristics. 5.1.6 Mark-sum measure. 5.1.7 Palm distribution. 5.2 Summary characteristics. 5.2.1 Introduction. 5.2.2 Intensity and mark-sum intensity. 5.2.3 Mean mark, mark d.f. and mark probabilities. 5.2.4 Indices for stationary marked point processes. 5.2.5 Nearest-neighbour distributions. 5.3 Second-order characteristics for marked point processes. 5.3.1 Introduction. 5.3.2 Definitions for qualitative marks. 5.3.3 Definitions for quantitative marks. 5.3.4 Estimation of second-order characteristics. 5.4 Orientation analysis for marked point processes. 5.4.1 Introduction. 5.4.2 Orientation analysis for non-isotropic processes with angular marks. 5.4.3 Orientation analysis for isotropic processes with angular marks. 5.4.4 Orientation analysis with constructed marks. 6. Modelling and simulation of stationary point processes. 6.1 Introduction. 6.2 Operations with point processes. 6.2.1 Thinning. 6.2.2 Clustering. 6.2.3 Superposition. 6.3 Cluster processes. 6.3.1 General cluster processes. 6.3.2 Neyman-Scott processes. 6.4 Stationary Cox processes. 6.4.1 Introduction. 6.4.2 Properties of stationary Cox processes. 6.5 Hard-core point processes. 6.5.1 Introduction. 6.5.2 Matern hard-core processes. 6.5.3 The dead leaves model. 6.5.4 The RSA model. 6.5.5 Random dense packings of hard spheres. 6.6 Stationary Gibbs processes. 6.6.1 Basic ideas and equations. 6.6.2 Simulation of stationary Gibbs processes. 6.6.3 Statistics for stationary Gibbs processes. 6.7 Reconstruction of point patterns. 6.7.1 Reconstructing point patterns without a specified model. 6.7.2 An example: reconstruction of Neyman-Scott processes. 6.7.3 Practical application of the reconstruction algorithm. 6.8 Formulas for marked point process models. 6.8.1 Introduction. 6.8.2 Independent marks. 6.8.3 Random field model. 6.8.4 Intensity-weighted marks. 6.9 Moment formulas for stationary shot-noise fields. 6.10 Space-time point processes. 6.10.1 Introduction. 6.10.2 Space-time Poisson processes. 6.10.3 Second-order statistics for completely stationary event processes. 6.10.4 Two examples of space-time processes. 6.11 Correlations between point processes and other random structures. 6.11.1 Introduction. 6.11.2 Correlations between point processes and random fields. 6.11.3 Correlations between point processes and fibre processes. 7. Fitting and testing point process models. 7.1 Choice of model. 7.2 Parameter estimation. 7.2.1 Maximum likelihood method. 7.2.2 Method of moments. 7.2.3 Trial-and-error estimation. 7.3 Variance estimation by bootstrap. 7.4 Goodness-of-fit tests. 7.4.1 Envelope test. 7.4.2 Deviation test. 7.5 Testing mark hypotheses. 7.5.1 Introduction. 7.5.2 Testing independent marking, test of association. 7.5.3 Testing geostatistical marking. 7.6 Bayesian methods for point pattern analysis. Appendix A Fundamentals of statistics. Appendix B Geometrical characteristics of sets. Appendix C Fundamentals of geostatistics. References. Notation index. Author index. Subject index.

1,510 citations

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26 Feb 2008

TL;DR: In this article, the power law for the pair correlation function for point processes is defined and a set of properties of point process data are presented, including stationarity and isotropy.

Abstract: Preface List of Examples 1 Introduction 11 Point process statistics 12 Examples of point process data 121 A pattern of amacrine cells 122 Gold particles 123 A pattern of Western Australian plants 124 Waterstriders 125 A sample of concrete 13 Historical notes 131 Determination of number of trees in a forest 132 Number of blood particles in a sample 133 Patterns of points in plant communities 134 Formulating the power law for the pair correlation function for galaxies 14 Sampling and data collection 141 General remarks 142 Choosing an appropriate study area 143 Data collection 15 Fundamentals of the theory of point processes 16 Stationarity and isotropy 161 Model approach and design approach 162 Finite and infinite point processes 163 Stationarity and isotropy 164 Ergodicity 17 Summary characteristics for point processes 171 Numerical summary characteristics 172 Functional summary characteristics 18 Secondary structures of point processes 181 Introduction 182 Random sets 183 Random fields 184 Tessellations 185 Neighbour networks or graphs 19 Simulation of point processes 2 The Homogeneous Poisson point process 21 Introduction 22 The binomial point process 221 Introduction 222 Basic properties 223 The periodic binomial process 224 Simulation of the binomial process 23 The homogeneous Poisson point process 231 Introduction 232 Basic properties 233 Characterisations of the homogeneous Poisson process 24 Simulation of a homogeneous Poisson process 25 Model characteristics 251 Moments and moment measures 252 The Palm distribution of a homogeneous Poisson process 253 Summary characteristics of the homogeneous Poisson process 26 Estimating the intensity 27 Testing complete spatial randomness 271 Introduction 272 Quadrat counts 273 Distance methods 274 The J-test 275 Two index-based tests 276 Discrepancy tests 277 The L-test 278 Other tests and recommendations 3 Finite point processes 31 Introduction 32 Distributions of numbers of points 321 The binomial distribution 322 The Poisson distribution 323 Compound distributions 324 Generalised distributions 33 Intensity functions and their estimation 331 Parametric statistics for the intensity function 332 Non-parametric estimation of the intensity function 333 Estimating the point density distribution function 34 Inhomogeneous Poisson process and finite Cox process 341 The inhomogeneous Poisson process 342 The finite Cox process 35 Summary characteristics for finite point processes 351 Nearest-neighbour distances 352 Dilation function 353 Graph-theoretic statistics 354 Second-order characteristics 36 Finite Gibbs processes 361 Introduction 362 Gibbs processes with fixed number of points 363 Gibbs processes with a random number of points 364 Second-order summary characteristics of finite Gibbs processes 365 Further discussion 366 Statistical inference for finite Gibbs processes 4 Stationary point processes 41 Basic definitions and notation 42 Summary characteristics for stationary point processes 421 Introduction 422 Edge-correction methods 423 The intensity lambda 424 Indices as summary characteristics 425 Empty-space statistics and other morphological summaries 426 The nearest-neighbour distance distribution function 427 The J-function 43 Second-order characteristics 431 The three functions: K, L and g 432 Theoretical foundations of second-order characteristics 433 Estimators of the second-order characteristics 434 Interpretation of pair correlation functions 44 Higher-order and topological characteristics 441 Introduction 442 Third-order characteristics 443 Delaunay tessellation characteristics 444 The connectivity function 45 Orientation analysis for stationary point processes 451 Introduction 452 Nearest-neighbour orientation distribution 453 Second-order orientation analysis 46 Outliers, gaps and residuals 461 Introduction 462 Simple outlier detection 463 Simple gap detection 464 Model-based outliers 465 Residuals 47 Replicated patterns 471 Introduction 472 Aggregation recipes 48 Choosing appropriate observation windows 481 General ideas 482 Representative windows 49 Multivariate analysis of series of point patterns 410 Summary characteristics for the non-stationary case 4101 Formal application of stationary characteristics and estimators 4102 Intensity reweighting 4103 Local rescaling 5 Stationary marked point processes 51 Basic definitions and notation 511 Introduction 512 Marks and their properties 513 Marking models 514 Stationarity 515 First-order characteristics 516 Mark-sum measure 517 Palm distribution 52 Summary characteristics 521 Introduction 522 Intensity and mark-sum intensity 523 Mean mark, mark df and mark probabilities 524 Indices for stationary marked point processes 525 Nearest-neighbour distributions 53 Second-order characteristics for marked point processes 531 Introduction 532 Definitions for qualitative marks 533 Definitions for quantitative marks 534 Estimation of second-order characteristics 54 Orientation analysis for marked point processes 541 Introduction 542 Orientation analysis for non-isotropic processes with angular marks 543 Orientation analysis for isotropic processes with angular marks 544 Orientation analysis with constructed marks 6 Modelling and simulation of stationary point processes 61 Introduction 62 Operations with point processes 621 Thinning 622 Clustering 623 Superposition 63 Cluster processes 631 General cluster processes 632 Neyman-Scott processes 64 Stationary Cox processes 641 Introduction 642 Properties of stationary Cox processes 65 Hard-core point processes 651 Introduction 652 Matern hard-core processes 653 The dead leaves model 654 The RSA model 655 Random dense packings of hard spheres 66 Stationary Gibbs processes 661 Basic ideas and equations 662 Simulation of stationary Gibbs processes 663 Statistics for stationary Gibbs processes 67 Reconstruction of point patterns 671 Reconstructing point patterns without a specified model 672 An example: reconstruction of Neyman-Scott processes 673 Practical application of the reconstruction algorithm 68 Formulas for marked point process models 681 Introduction 682 Independent marks 683 Random field model 684 Intensity-weighted marks 69 Moment formulas for stationary shot-noise fields 610 Space-time point processes 6101 Introduction 6102 Space-time Poisson processes 6103 Second-order statistics for completely stationary event processes 6104 Two examples of space-time processes 611 Correlations between point processes and other random structures 6111 Introduction 6112 Correlations between point processes and random fields 6113 Correlations between point processes and fibre processes 7 Fitting and testing point process models 71 Choice of model 72 Parameter estimation 721 Maximum likelihood method 722 Method of moments 723 Trial-and-error estimation 73 Variance estimation by bootstrap 74 Goodness-of-fit tests 741 Envelope test 742 Deviation test 75 Testing mark hypotheses 751 Introduction 752 Testing independent marking, test of association 753 Testing geostatistical marking 76 Bayesian methods for point pattern analysis Appendix A Fundamentals of statistics Appendix B Geometrical characteristics of sets Appendix C Fundamentals of geostatistics References Notation index Author index Subject index

1,131 citations

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6,278 citations

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30 Jun 2002

TL;DR: This paper presents a meta-anatomy of the multi-Criteria Decision Making process, which aims to provide a scaffolding for the future development of multi-criteria decision-making systems.

Abstract: List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

5,994 citations

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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

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ENSAE ParisTech

^{1}TL;DR: This work considers approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non‐Gaussian response variables and can directly compute very accurate approximations to the posterior marginals.

Abstract: Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

4,164 citations

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TL;DR: A Bayesian calibration technique which improves on this traditional approach in two respects and attempts to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best‐fitting parameter values is presented.

Abstract: We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of specific applications. However, in any specific application the values of necessary parameters may be unknown. In this case, physical observations of the system in the specific context are used to learn about the unknown parameters. The process of fitting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc fitting, and after calibration the model is used, with the fitted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the fitted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-fitting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.

3,745 citations