Dimensions of Uncertainty in Communication Engineering is a comprehensive and self-contained introduction to the problems of nonaleatory uncertainty and the mathematical tools needed to solve them. The book gathers together tools derived from statistics, information theory, moment theory, interval analysis and probability boxes, dependence bounds, nonadditive measures, and Dempster–Shafer theory. While the book is mainly devoted to communication engineering, the techniques described are also of interest to other application areas, and commonalities to these are often alluded to through a number of references to books and research papers. This is an ideal supplementary book for courses in wireless communications, providing techniques for addressing epistemic uncertainty, as well as an important resource for researchers and industry engineers. Students and researchers in other fields such as statistics, financial mathematics, and transport theory will gain an overview and understanding on these methods relevant to their field.
1. Dimensions of Uncertainty in Communication Engineering - p. i 2. Cover - p. i 3. Title Page - p. iii 4. Copyright Page - p. iv 5. Table of Contents - p. iv 6. Dedication - p. v 7. Preface - p. xi 8. 1 Model selection - p. 1 9. 2 Performance bounds from epistemic uncertainty - p. 27 10. 3 Moment bounds - p. 49 11. 3.1: Some classical results - p. 49 12. 3.2: The general moment-bound problem - p. 52 13. 3.3: Calculation of moments - p. 54 14. 3.4: Moments of unimodal pdfs - p. 57 15. 3.5: When is a sequence a valid moment sequence? - p. 59 16. 3.6: Moments in a parallelepiped - p. 63 17. 3.7: Geometric bounds - p. 64 18. 3.8: Quadrature-rule approximations and bounds - p. 73 19. 3.9: Čebyšev systems and principal representations - p. 81 20. 3.9.1: Principal and canonical representations as quadrature rules - p. 86 21. 3.9.2: Moment bounds and quadrature rules - p. 90 22. 3.9.3: Bounds on CDFs and quadrature rules - p. 91 23. 3.9.4: Bounds on Laplace–Stieltjes transform - p. 93 24. 3.9.5: Extension to nondifferentiable functions: the method of contact polynomials - p. 95 25. 3.10: Moment problems as semidefinite programs - p. 98 26. 3.11: Multidimensional moment bounds and approximations - p. 101 27. Sources and parerga - p. 109 28. 4 Interval analysis - p. 113 29. 5 Probability boxes - p. 131 30. 6 Dependence bounds - p. 145 31. 6.1: Copulas - p. 145 32. 6.2: Dependence p-boxes from copula bounds - p. 158 33. 6.3: Some examples of application - p. 163 34. 6.4: Bivariate dependence bounds on expectations - p. 175 35. 6.5: Bounds with monotone marginal densities - p. 177 36. 6.6: Deriving tighter dependence bounds - p. 183 37. 6.6.1: Degree of dependence - p. 184 38. 6.6.2: Linear correlation - p. 189 39. 6.6.3: Rank correlation: Kendall tau, Spearman rho, and Blomqvist beta - p. 189 40. 6.6.4: Tail dependence - p. 198 41. 6.6.5: Quadrant/orthant dependence - p. 199 42. Sources and parerga - p. 200 43. 7 Beyond probability - p. 203 44. 7.1: Decisions under uncertainty - p. 203 45. 7.2: Epistemic vs. aleatory uncertainty - p. 207 46. 7.3: Lotteries, prospects, and utility functions - p. 209 47. 7.4: Other paradoxes arising from EUT - p. 216 48. 7.5: Upper and lower probabilities - p. 219 49. 7.6: Expected utility with interval probabilities - p. 224 50. 7.7: Some applications to digital communication - p. 225 51. 7.8: Going beyond probability - p. 232 52. 7.9: Set functions and their properties - p. 233 53. 7.10: Infinite sets - p. 236 54. 7.11: Capacities and Choquet integral - p. 237 55. 7.12: Expected values and Choquet integral - p. 238 56. 7.13: Dempster–Shafer theory - p. 240 57. Sources and parerga - p. 250 58. Bibliography - p. 253 59. Index - p. 269
Dimensions of Uncertainty in Communication Engineering is a comprehensive and self-contained introduction to the problems of nonaleatory uncertainty and the mathematical tools needed to solve them. The book gathers together tools derived from statistics, information theory, moment theory, interval analysis and probability boxes, dependence bounds, nonadditive measures, and Dempster–Shafer theory. While the book is mainly devoted to communication engineering, the techniques described are also of interest to other application areas, and commonalities to these are often alluded to through a number of references to books and research papers. This is an ideal supplementary book for courses in wireless communications, providing techniques for addressing epistemic uncertainty, as well as an important resource for researchers and industry engineers. Students and researchers in other fields such as statistics, financial mathematics, and transport theory will gain an overview and understanding on these methods relevant to their field.
1. Dimensions of Uncertainty in Communication Engineering - p. i 2. Cover - p. i 3. Title Page - p. iii 4. Copyright Page - p. iv 5. Table of Contents - p. iv 6. Dedication - p. v 7. Preface - p. xi 8. 1 Model selection - p. 1 9. 2 Performance bounds from epistemic uncertainty - p. 27 10. 3 Moment bounds - p. 49 11. 3.1: Some classical results - p. 49 12. 3.2: The general moment-bound problem - p. 52 13. 3.3: Calculation of moments - p. 54 14. 3.4: Moments of unimodal pdfs - p. 57 15. 3.5: When is a sequence a valid moment sequence? - p. 59 16. 3.6: Moments in a parallelepiped - p. 63 17. 3.7: Geometric bounds - p. 64 18. 3.8: Quadrature-rule approximations and bounds - p. 73 19. 3.9: Čebyšev systems and principal representations - p. 81 20. 3.9.1: Principal and canonical representations as quadrature rules - p. 86 21. 3.9.2: Moment bounds and quadrature rules - p. 90 22. 3.9.3: Bounds on CDFs and quadrature rules - p. 91 23. 3.9.4: Bounds on Laplace–Stieltjes transform - p. 93 24. 3.9.5: Extension to nondifferentiable functions: the method of contact polynomials - p. 95 25. 3.10: Moment problems as semidefinite programs - p. 98 26. 3.11: Multidimensional moment bounds and approximations - p. 101 27. Sources and parerga - p. 109 28. 4 Interval analysis - p. 113 29. 5 Probability boxes - p. 131 30. 6 Dependence bounds - p. 145 31. 6.1: Copulas - p. 145 32. 6.2: Dependence p-boxes from copula bounds - p. 158 33. 6.3: Some examples of application - p. 163 34. 6.4: Bivariate dependence bounds on expectations - p. 175 35. 6.5: Bounds with monotone marginal densities - p. 177 36. 6.6: Deriving tighter dependence bounds - p. 183 37. 6.6.1: Degree of dependence - p. 184 38. 6.6.2: Linear correlation - p. 189 39. 6.6.3: Rank correlation: Kendall tau, Spearman rho, and Blomqvist beta - p. 189 40. 6.6.4: Tail dependence - p. 198 41. 6.6.5: Quadrant/orthant dependence - p. 199 42. Sources and parerga - p. 200 43. 7 Beyond probability - p. 203 44. 7.1: Decisions under uncertainty - p. 203 45. 7.2: Epistemic vs. aleatory uncertainty - p. 207 46. 7.3: Lotteries, prospects, and utility functions - p. 209 47. 7.4: Other paradoxes arising from EUT - p. 216 48. 7.5: Upper and lower probabilities - p. 219 49. 7.6: Expected utility with interval probabilities - p. 224 50. 7.7: Some applications to digital communication - p. 225 51. 7.8: Going beyond probability - p. 232 52. 7.9: Set functions and their properties - p. 233 53. 7.10: Infinite sets - p. 236 54. 7.11: Capacities and Choquet integral - p. 237 55. 7.12: Expected values and Choquet integral - p. 238 56. 7.13: Dempster–Shafer theory - p. 240 57. Sources and parerga - p. 250 58. Bibliography - p. 253 59. Index - p. 269
