Recent advances in stochastic modeling and data analysis: Chania, Greece, 29 May – 1 June 2007

Christos H. Skiadas, Christos H. Skiadas9789812709684, 981-270-968-1

This volume presents the most recent applied and methodological issues in stochastic modeling and data analysis. The contributions cover various fields such as stochastic processes and applications, data analysis methods and techniques, Bayesian methods, biostatistics, econometrics, sampling, linear and nonlinear models, networks and queues, survival analysis, and time series. The volume presents new results with potential for solving real-life problems and provides novel methods for solving these problems by analyzing the relevant data. The use of recent advances in different fields is emphasized, especially new optimization and statistical methods, data warehouse, data mining and knowledge systems, neural computing, and bioinformatics.

---

Table of contents :
Contents……Page 8
Preface……Page 6
1 Stochastic Processes and Models……Page 14
1 Introduction……Page 15
2 Distribution of a functional random variable……Page 16
3 The QAMM and QAMML distributions……Page 17
4 QAMML properties……Page 21
References……Page 22
1 Introduction……Page 23
2 Fractional quantum operator of momentum……Page 24
3 Wave function normalization……Page 26
4 Translation operator……Page 27
5 The shift operator in a superspace of fractional dimension……Page 28
References……Page 29
1 Introduction……Page 31
2 Model……Page 32
3.1 Mappings of State Variable……Page 33
3.2 Multiple State Variables……Page 34
3.3 Alternative Characterizations of State Variables Processes……Page 37
References……Page 38
1 Introduction……Page 39
2 Preliminary results……Page 40
3 Theoretical results……Page 41
4 Applications to the Stochastic Resonance……Page 43
References……Page 45
2 Distributions……Page 47
1 Introduction……Page 48
2 Negative binomial model……Page 50
3 Fit by a UGWD……Page 51
4 Fit by an Extended Waring distribution……Page 53
5 Conclusions……Page 54
References……Page 55
2 Johnson score……Page 56
3 Johnson mean and Johnson variance……Page 59
4 Estimates……Page 61
References……Page 63
1 Introduction……Page 64
2 Methods……Page 65
3 Results……Page 68
References……Page 70
1 Introduction……Page 72
2.1 Stationary ergodic arrivals of negative customers……Page 73
2.2 Stationary ergodic service times……Page 75
3.2 Stationary ergodic service times……Page 76
4 Work Removals……Page 78
References……Page 79
1 Introduction……Page 81
2.1 Unimodality on R……Page 82
3 Univariat e and multivariate partial convexification……Page 83
3.2 Partial convexification on R2……Page 84
4 om bivariate multimo~al probability measures……Page 87
References……Page 88
1 Introduction……Page 89
2 The model……Page 90
3.1 The generator……Page 91
3.2 Performance measures……Page 92
4 Numerical application……Page 93
5 Specifying references……Page 94
1 Introduction……Page 95
2 Models for a priori uncertainty of noise……Page 97
3 Statistical synthesis of asymptotically robust algorithms……Page 99
References……Page 103
1. Introduction……Page 104
2.1 Maximum likelihood estimator……Page 105
2.3. Improved analytical estimator……Page 108
3 Computer modeling……Page 111
5. References……Page 113
3 Insurance……Page 114
1 Introduction……Page 115
2.1 The Chain-Ladder technique……Page 117
2.2 Semi-stochastic methods……Page 118
3 The MCMC method……Page 120
4 The results……Page 122
5 Testing……Page 124
6 Conclusion……Page 125
References……Page 126
1 INTRODUCTION……Page 127
2 METHODOLOGY……Page 128
3 DISCUSSION AND RESULTS……Page 129
4 CONCLUSIONS……Page 133
REFERENCES……Page 134
1.1 Basic guidelines on solvency……Page 135
1.2 An overview on longevity risk: the dynamic aspect of mortality and the projected survival models……Page 137
2 The mathematical provision fair value in living benefit products……Page 138
3 Risk indexes in living benefit contract fair valuation……Page 139
4 Numerical applications……Page 140
References……Page 142
1 Introduction – Risk models with spatial components……Page 143
2 Model construction……Page 144
3 Implementation of the model……Page 146
4 Data and results……Page 147
5 Conclusion: Model performance and comparison……Page 148
References……Page 149
1 Introduction……Page 150
2 Construction of the Hierarchical Bayesian model……Page 151
2.1 The MCMC based estimation for the parameters……Page 152
3.2 Confirming model fit……Page 154
3.3 Cross-validation and bootstrapping……Page 156
References……Page 157
4 Stochastic Modeling for Healthcare Management……Page 158
1 Introduction……Page 159
2 The Model……Page 160
3 The Non-homogenous Markov model……Page 162
4 Results……Page 165
References……Page 166
1 Introduction……Page 167
2 The DC-Ph model……Page 168
2.2 Na’ive Bayes classifier coniponent…….Page 169
4 Results……Page 170
4.1 A&E Bayesian network DC-Ph model……Page 171
5 Conclusion……Page 173
References……Page 174
Introduction……Page 175
Model……Page 177
The Data……Page 178
The Bayes Classifier……Page 179
Representing trollev waiting time……Page 181
Conclusion……Page 183
References……Page 184
1 Introduction……Page 185
2 The Coxian phase-type distribution……Page 186
3 Application……Page 188
4 Modelling costs in an A&E department……Page 190
5 Conclusion and further work……Page 192
References……Page 193
5 Markov and Semi Markov Models……Page 194
1 Introduction……Page 195
References……Page 202
1 Introduction……Page 203
2 Moments of the r.v.’s ni(t)……Page 204
3 The factorial moments of the overflow size……Page 206
References……Page 210
1 Introduction……Page 211
2 d-dimensional Archimedian copulas……Page 212
3.1 GOF statistics based on PIT……Page 213
4 Application for financial data sets……Page 214
5 Conclusions……Page 217
References……Page 218
1 Introduction……Page 219
2 The semi-Markov model……Page 220
3 The homogeneous semi-Markov model with fuzzy states……Page 221
References……Page 224
1 Introduction……Page 226
2 Main results……Page 227
3.1 The Metropolis-Hastings algorithm……Page 229
3.3 Dugongs dataset……Page 230
References……Page 233
1. Introduction……Page 234
2. Homogeneous case……Page 236
3. Non-homogeneous case……Page 238
4. On the algorithmic complexity……Page 240
References……Page 241
Abstract…….Page 242
References……Page 246
1. Introduction……Page 247
2. Triplet Markov chains and hidden semi-Markov chains……Page 248
3. Parameter estimation with ICE……Page 250
4. Experiments……Page 251
5. Conclusion……Page 253
References……Page 254
6 Parametricmon-Parametric……Page 255
1 Introduction……Page 256
2 Anderson’s non-parametric decomposition……Page 257
3 A transformation of a random vector……Page 258
4.1 A decomposition of Pearson’s sum for non-equiprobable cells……Page 260
4.2 A decomposition of the Rao-Robson-Nikulin statistic……Page 261
References……Page 262
1 Introduction……Page 264
2 Notations and description of the method……Page 265
3 Asymptotic results……Page 270
References……Page 271
1 Introduction……Page 272
2 Model and assumptions……Page 273
2.1 Estimating (non)linear regressions with censored data……Page 274
3 Nonparametric test procedures under censoring……Page 275
4 Asymptotic analysis……Page 276
4.2 Behavior of the tests under the null hypothesis……Page 277
References……Page 278
7 Dynamical Systems/Forecasting……Page 280
1 Introduction……Page 281
2 Description of the Models……Page 282
3 Creation the Models for the Inland Rail Passenger Conveyances Forecasting……Page 284
4 Cross-Validation Analysis……Page 286
Conclusions……Page 288
References……Page 289
Introduction……Page 290
1.1 Fisher-Pry Type of Models……Page 291
1.2 Lotka-Volterra Type of Models……Page 292
2 Empirical Analysis……Page 295
Conclusions……Page 298
References……Page 299
1. Introduction……Page 300
2.1. Central sink……Page 301
3. Eccentric Sink……Page 302
4.1. Aref’s blinking vortex system……Page 303
References……Page 307
8 Modeling and Stochastic Modeling……Page 308
1 Introduction……Page 309
2 Lognormal Diffusion Random Fields……Page 310
3.1 MLEs for the Drift and Diffusion Coefficients Using Exogenous Factors……Page 311
3.2 Distribution of the MLEs, +* and B*……Page 312
3.3 Fisher Information Matrix……Page 313
4 Parametric Hypothesis Testing……Page 314
References……Page 316
Cartographical Modeling as a Statistical Method for Monitoring of a Spatial Behaviour of Population Irina Pribytkova……Page 317
1 The common conception of a method……Page 318
3 The methodological premises……Page 319
4 Cartographical modeling of latent structures……Page 320
5 Monitoring of a spatial behaviour of population……Page 321
References……Page 322
1 Introduction……Page 325
2.1 Dynamic Factor Structure……Page 326
3 Learning……Page 327
3.1 The Variational Fixed Point Equations……Page 329
3.2 The EM Training……Page 330
4 Monte Carlo Experiments……Page 331
5 Financial Data……Page 333
References……Page 334
1 Introduction……Page 335
2 NARMAX modelling based data smoothing……Page 336
3 Validation Algorithm for NARMAX smoother……Page 337
4 Simulation study……Page 340
References……Page 342
1 Introduction……Page 343
2 Estimation……Page 344
3 Results……Page 347
A Proofs of theorems 1 and 2……Page 349
References……Page 350
Chaotic Data Analysis and Hybrid Modeling for Biomedical Applications Wlodzimierz Klonowski, Robert Stepien, Marek Darowski and Maciej Kozarski……Page 351
References……Page 354
2 Fractal interpolation function……Page 355
3 Random fractal interpolation function……Page 357
4 Applications……Page 360
References……Page 362
1 Introduction……Page 363
3 The Proposed Model……Page 364
4 Applications to Life Table Data and Comparisons……Page 367
5 Conclusions……Page 370
Bibliography……Page 372
1. Introduction……Page 373
3. The stochastic model and the related parameters……Page 374
4. The hitting time density function……Page 375
5. A Quadratic Health State Function……Page 376
6. The Extended Quadratic Health State function……Page 378
7. Conclusion……Page 381
References……Page 382
9 Statistical Applications in Socioeconomic Problems……Page 383
1 Introduction……Page 384
2 Non-iterative dynamics and dumping……Page 385
3.1 The final frequency of standard A……Page 386
3.2 Spatial correlations……Page 387
3.3 Spatial clustering measurements……Page 388
4 Distribution of the number of occupied neighbour sites……Page 391
References……Page 393
1 Introduction……Page 395
2 Data, measurement procedure and labor productivity……Page 397
3 Productivity growth analysis through transition matrices……Page 398
4 Decomposing productivity growth……Page 399
5 Conclusion……Page 401
References……Page 402
1. Introduction……Page 403
2. The economic model of CSP-1 under linear acceptance cost……Page 404
4.4. The effect of the replacement cost c,……Page 407
5 . Conclusions……Page 408
References……Page 410
2 Deterministic tool wear……Page 411
3 Stochastic tool wear……Page 414
4 Machine with tool magazine……Page 416
5 Numerical illustration……Page 417
References……Page 418
1 Introduction……Page 419
2.1 Traffic model in brief……Page 420
3.1 Data and Network Site……Page 422
3.3 State vector estimation and Travel time prediction……Page 423
Acknowledgements……Page 425
References……Page 426
1 Introduction……Page 427
2 Theoretical approach of ANFIS……Page 428
3 Model description……Page 431
4 Results……Page 433
References……Page 434
The team- working in libraries……Page 436
The goal of the survey is the comparative study on:……Page 437
The attitude of the staff to the changes…….Page 441
The organization of the work……Page 443
Bibliography……Page 445
10 Sampling and Optimization Problems……Page 446
1 Introduction……Page 447
2 Stochastic Modeling of Coupled Molecular Reactions……Page 448
2.1 Equivalence of CME and Kolmogorov Differential Equations……Page 449
3 Importance Sampling……Page 450
3.1 Application to Coupled Molecular Reactions……Page 451
4 Conclusions……Page 453
References……Page 454
1 Introduction……Page 455
2 Preliminaries……Page 456
3 Bispectrum estimation and its asymptotic properties……Page 457
4 Proofs……Page 460
References……Page 466
1 Introduction……Page 467
3.1 Probabilities of changes……Page 468
5 The Random Search via Probability Algorithm……Page 470
6.1. Minimization of the Weight of a Speed Reducer……Page 471
6.2. The problem of Himmelblau and two approximate problems……Page 473
7. CONCLUSIONS……Page 474
References……Page 475
1 Problem formulation……Page 477
2 Proposed GA……Page 479
3 Computational results……Page 481
References……Page 484
11 Data Mining and Applications……Page 485
1 Introduction……Page 486
2 Robust clustering method……Page 487
3 Initialization of clustering algorithms……Page 489
4 Numerical experiments……Page 490
4.1 Experiments on synthetic data……Page 491
4.2 Speed-up and classification error on real data……Page 493
5 Conclusions……Page 494
References……Page 495
1 Introduction……Page 496
2.1 Basic elements……Page 497
2.2 Malingering scenarios……Page 498
3 Empirical data example……Page 499
3.2 Modeling malingering scenarios……Page 500
3.3 Results……Page 501
4 Concluding remarks……Page 502
References……Page 503
1. Introduction……Page 504
2. Method……Page 505
3. Data……Page 506
4. Results……Page 507
5. Discussion……Page 509
References……Page 510
Qualitative Indicators of Libraries’ Services and Management of Resources: Methodologies of Analysis and Strategic Planning Aristeidis Meletiou……Page 512
2. General description of process of knowledge’s exploration……Page 513
3.1.2. Circulation data for users and data about material’s (printed or electronic) usage……Page 516
3.1.5. Interlibrary loan……Page 517
3.1.7. Parameters that are receivedfiom Institution……Page 518
3.4. Data Coding……Page 519
3.5. Knowledge minina – Application of models / techniclues……Page 520
References……Page 522
12 Clustering and Classification……Page 524
1 Introduction……Page 525
2 On the similarity of languages……Page 527
3 Measuring and testing……Page 528
4 Conclusions……Page 532
References……Page 533
1 Introduction……Page 534
2 Syllables and the similarity……Page 536
3 Clustering Romance languages……Page 537
Acknowledgements……Page 540
References……Page 541
1 Introduction……Page 542
2.1 Pseudoclosure……Page 543
2.3 Minimal closed subsets……Page 544
3.1 Structuring process……Page 545
3.2 Determining the initial centres……Page 547
References……Page 548
1 Introduction……Page 550
2 The functional multinomial model……Page 551
4 Acknowledgements……Page 553
References……Page 554
1 Introduction……Page 555
2 GARCH-feature based distance……Page 556
3 Data description……Page 557
4 Cluster analysis……Page 558
5 Conclusions……Page 560
References……Page 563
13 Applications of Data Analysis……Page 565
Introduction……Page 566
1. Reliability and longevity……Page 567
2. Heterogeneity……Page 568
3. Stress experiments……Page 570
4. Changing environment and resource allocation……Page 572
References……Page 573
1 Introduction……Page 575
3.1 Applications on mobiles: descriptions……Page 576
3.2 Inferential analysis……Page 581
4 Conclusions……Page 582
References……Page 583
1 Introduction……Page 584
2 PCA and Factor Analysis……Page 585
4 Application to air pollution sources detection……Page 587
References……Page 590
1 Introduction……Page 591
2 Some fundamentals of Rhyi’s and THC statistics……Page 592
3 Path-integral representation with Tsallis distribution……Page 594
4 Option pricing formula and generalized statistics……Page 595
5 Conclusions and outlooks……Page 598
References……Page 599
14 Miscellaneous……Page 601
1 Introduction……Page 602
2 Characterization of efficient estimators……Page 603
3 Construction of efficient estimators……Page 606
4 Equal innovation densities……Page 608
References……Page 609
1 Introduction……Page 610
2.1 Riesz and Nagy method……Page 612
3 Estimation of l……Page 613
3.2 Estimation of p……Page 614
3.3 Main Results……Page 615
References……Page 616
1 Introduction……Page 618
2 Stochastic model……Page 620
3 Monte-Carlo approximation……Page 621
4 Numerical results……Page 622
5 Conclusion……Page 623
References……Page 625
1 Introduction……Page 626
2 The model……Page 627
3 Examples of optimal stopping domains……Page 628
4 The Monte Carlo algorithm……Page 629
5 Classification errors……Page 630
6 Conclusions……Page 632
References……Page 633
1 Introduction……Page 634
2 The proposed denoising method……Page 637
4 Conclusion……Page 640
References……Page 641
1 Themodel……Page 643
3 Approximations……Page 644
4 The QNA Method……Page 645
Conclusion……Page 646
References……Page 647
1. Introduction……Page 649
2. Groundwater monitoring network……Page 650
3. Applied Methodology……Page 653
4. Assessment of groundwater quality monitoring network……Page 654
Acknowledgments……Page 656
References……Page 657
1 Introduction……Page 658
2 Simultaneous test of a large number of hypotheses……Page 659
2.3 Impact of a high correlation on the type I1 error rate……Page 660
3 Testing in the presence of an auxiliary covariate……Page 661
3.2 Small-sample distribution……Page 662
4 Double-sampling Benjamini-Hochberg procedure……Page 663
5 Illustration……Page 664
References……Page 665
Author Index……Page 666