Applied Modeling Techniques and Data Analysis 1

Yannis Dimotikalis is Assistant Professor within the Department of Management Science and Technology at the Hellenic Mediterranean University, Greece. Alex Karagrigoriou is Professor of Probability and Statistics, Deputy Director of Graduate Studies in Statistics and Actuarial-Financial Mathematics, and Director of the Laboratory of Statistics and Data Analysis within the Department of Statistics and Actuarial-Financial Mathematics at the University of the Aegean, Greece. Christina Parpoula is Assistant Professor of Applied Statistics and Research Methodology within the Department of Psychology at the Panteion University of Social and Political Sciences, Greece. Christos H. Skiadas is Former Vice-Rector at the Technical University of Crete, Greece, and founder of its Data Analysis and Forecasting Laboratory. He continues his research in ManLab, within the faculty�s Department of Production Engineering and Management.

• Preface xiYannis DIMOTIKALIS, Alex KARAGRIGORIOU, Christina PARPOULA and Christos H. SKIADASPart 1. Computational Data Analysis 1Chapter 1. A Variant of Updating PageRank in Evolving Tree Graphs 3Benard ABOLA, Pitos Seleka BIGANDA, Christopher ENGSTRÖM, John Magero MANGO, Godwin KAKUBA and Sergei SILVESTROV1.1. Introduction 31.2. Notations and definitions 51.3. Updating the transition matrix 51.4. Updating the PageRank of a tree graph 101.4.1. Updating the PageRank of tree graph when a batch of edges changes 121.4.2. An example of updating the PageRank of a tree 151.5. Maintaining the levels of vertices in a changing tree graph 171.6. Conclusion 211.7. Acknowledgments 211.8. References 21Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks 23Benard ABOLA, Pitos Seleka BIGANDA, Sergei SILVESTROV, Dmitrii SILVESTROV, Christopher ENGSTRÖM, John Magero MANGO and Godwin KAKUBA2.1. Introduction 232.2. Stationary distributions for Markov chains with damping component 262.2.1. Stationary distributions for Markov chains with damping component 262.2.2. The stationary distribution of the Markov chain X0,n 282.3. A perturbation analysis for stationary distributions of Markov chains with damping component 292.3.1. Continuity property for stationary probabilities 292.3.2. Rate of convergence for stationary distributions 292.3.3. Asymptotic expansions for stationary distributions 302.3.4. Results of numerical experiments 322.4. Coupling and ergodic theorems for perturbed Markov chains with damping component 392.4.1. Coupling for regularly perturbed Markov chains with damping component 392.4.2. Coupling for singularly perturbed Markov chains with damping component 412.4.3. Ergodic theorems for perturbed Markov chains with damping component in the triangular array mode 422.4.4. Numerical examples 432.5. Acknowledgments 512.6. References 51Chapter 3. PageRank and Perturbed Markov Chains 57Pitos Seleka BIGANDA, Benard ABOLA, Christopher ENGSTRÖM, Sergei SILVESTROV, Godwin KAKUBA and John Magero MANGO3.1. Introduction 573.2. PageRank of the first-order perturbed Markov chain 593.3. PageRank of the second-order perturbed Markov chain 603.4. Rates of convergence of Page Ranks of first- and second-order perturbed Markovchains 703.5. Conclusion 723.6. Acknowledgments 723.7. References 72Chapter 4. Doubly Robust Data-driven Distributionally Robust Optimization 75Jose BLANCHET, Yang KANG, Fan ZHANG, Fei HE and Zhangyi HU4.1. Introduction 754.2. DD-DRO, optimal transport and supervised machine learning 794.2.1. Optimal transport distances and discrepancies 804.3. Data-driven selection of optimal transport cost function 814.3.1. Data-driven cost functions via metric learning procedures 814.4. Robust optimization for metric learning 834.4.1. Robust optimization for relative metric learning 834.4.2. Robust optimization for absolute metric learning 864.5. Numerical experiments 884.6. Discussion and conclusion 894.7. References 89Chapter 5. A Comparison of Graph Centrality Measures Based on Lazy Random Walks 91Collins ANGUZU, Christopher ENGSTRÖM and Sergei SILVESTROV5.1. Introduction 915.1.1. Notations and abbreviations 935.1.2. Linear systems and the Neumann series 945.2. Review on some centrality measures 955.2.1. Degree centrality 955.2.2. Katz status and β-centralities 955.2.3. Eigenvector and cumulative nomination centralities 965.2.4. Alpha centrality 975.2.5. PageRank centrality 985.2.6. Summary of the centrality measures as steady state, shifted and power series 995.3. Generalizations of centrality measures 995.3.1. Priors to centrality measures 995.3.2. Lazy variants of centrality measures 1005.3.3. Lazy α-centrality 1005.3.4. Lazy Katz centrality 1025.3.5. Lazy cumulative nomination centrality 1035.4. Experimental results 1045.5. Discussion 1065.6. Conclusion 1095.7. Acknowledgments 1095.8. References 110Chapter 6. Error Detection in Sequential Laser Sensor Input 113Gwenael GATTO and Olympia HADJILIADIS6.1. Introduction 1136.2. Data description 1146.3. Algorithms 1166.3.1. Algorithm for consecutive changes in mean 1186.3.2. Algorithm for burst detection 1206.4. Results 1256.5. Acknowledgments 1276.6. References 127Chapter 7. Diagnostics and Visualization of Point Process Models for Event Times on a Social Network 129Jing WU, Anna L. SMITH and Tian ZHENG7.1. Introduction 1297.2. Background 1317.2.1. Univariate point processes 1317.2.2. Network point processes 1327.3. Model checking for time heterogeneity 1347.3.1. Time rescaling theorem 1347.3.2. Residual process 1367.4. Model checking for network heterogeneity and structure 1387.4.1. Kolmogorov–Smirnov test 1387.4.2. Structure score based on the Pearson residual matrix 1417.5. Summary 1437.6. Acknowledgments 1447.7. References 144Part 2. Data Analysis Methods and Tools 147Chapter 8. Exploring the Distribution of Conditional Quantile Estimates: An Application to Specific Costs of Pig Production in the European Union 149Dominique DESBOIS8.1. Introduction 1508.2. Conceptual framework and methodological aspects 1508.2.1. The empirical model for estimating the specific production costs 1518.2.2. The procedures for estimating and testing conditional quantiles 1528.2.3. Symbolic PCA of the specific cost distributions 1548.2.4. Symbolic clustering analysis of the specific cost distributions 1628.3. Results 1658.3.1. The SO-PCA of specific cost estimates 1678.3.2. The divisive hierarchy of specific cost estimates 1708.4. Conclusion 1718.5. References 172Chapter 9. Maximization Problem Subject to Constraint of Availability in Semi-Markov Model of Operation 175Franciszek GRABSKI9.1. Introduction 1759.2. Semi-Markov decision process 1769.3. Semi-Markov decision model of operation 1779.3.1. Description and assumptions 1779.3.2. Model construction 1779.4. Optimization problem 1789.4.1. Linear programming method 1799.5. Numerical example 1829.6. Conclusion 1849.7. References 185Chapter 10. The Impact of Multicollinearity on Big Data Multivariate Analysis Modeling 187Kimon NTOTSIS and Alex KARAGRIGORIOU10.1. Introduction 18710.2. Multicollinearity 18810.3. Dimension reduction techniques 19110.3.1. Beale et al 19210.3.2. Principal component analysis 19210.4. Application 19410.4.1. The modeling of PPE 19410.4.2. Concluding remarks 20010.5. Acknowledgments 20010.6. References 200Chapter 11. Weak Signals in High-Dimensional Poisson Regression Models 203Orawan REANGSEPHET, Supranee LISAWADI and Syed Ejaz AHMED11.1. Introduction 20311.2. Statistical background 20411.3. Methodologies 20511.3.1. Predictor screening methods 20511.3.2. Post-screening parameter estimation methods 20611.4. Numerical studies 20811.4.1. Simulation settings and performance criteria 20811.4.2. Results 20911.5. Conclusion 21711.6. Acknowledgments 21811.7. References 218Chapter 12. Groundwater Level Forecasting for Water Resource Management 221Andrea ZIRULIA, Alessio BARBAGLI and Enrico GUASTALDI12.1. Introduction 22112.2. Materials and methods 22212.2.1. Study area 22212.2.2. Forecast method 22212.3. Results 22412.4. Conclusion 23012.5. References 230Chapter 13. Phase I Non-parametric Control Charts for Individual Observations: A Selective Review and Some Results 233Christina PARPOULA13.1. Introduction 23413.1.1. Background 23413.1.2. Univariate non-parametric process monitoring 23513.2. Problem formulation 23713.3. A comparative study 23913.3.1. The existing methodologies 23913.3.2. Simulation settings 24013.3.3. Simulation-study results 24213.4. Concluding remarks 24713.5. References 247Chapter 14. On Divergence and Dissimilarity Measures for Multiple Time Series 249Konstantinos MAKRIS, Alex KARAGRIGORIOU and Ilia VONTA14.1. Introduction 24914.2. Classical measures 25014.3. Divergence measures 25214.4. Dissimilarity measures for ordered data 25414.4.1. Standard dissimilarity measures 25414.4.2. Advanced dissimilarity measures 25614.5. Conclusion 25914.6. References 259List of Authors 261Index 265