Regularized Radial Basis Function Networks: Theory and Applications

The author states in the Preface that “this book can be used in a variety of probability courses with a variety of teaching styles. ” After reviewing this text, I must agree. A Junior/Senior level probability course could be aptly taught from Chapters 1, 3, 4, 5, and 6. In addition, depending on the audience for this course (engineering undergraduate or nonengineering undergraduate), the instructor can tailor the examples and exercises. Within this context, the instructor can choose to use the Chapter 2 examples either piecemeal as the material is covered in detail in later chapters, or up front (which I do not recommend). Chapter 2 contains four very detailed excellent “case studies,” but Iwould recommend using Section 2.1 before Chapter 3, Section 2.2 before Chapter 4, and so forth. The chapter introduces so many concepts so quickly that, at least in an undergraduate course; they would cause more frustration than they would help. Of course, with all the  exibility that this text offers comes a price: An instructor using this text must spend extra time outlining the semester course. In addition, the text’s mathematical sophistication is at the paper level for a graduate-level MBA course. In fact, I would highly recommend it for an MBA curriculum, Chapters 9 and 10 in particular would be very useful at that level. I make some observations by chapter. Chapter 1: Presents good introduction with the right amount of history and de nitions. Chapter 2: Provides motivational examples, as discussed earlier. Chapter 3: Covers the usual introductory concepts, but uniquely puts the probability “rules” at the end of the chapter in an appendix. The combinatoric de nitions and examples are excellent. Chapter 4: Gives very good, solid introduction to random variables and probability distributions. Especially noteworthy are the examples of real world mixed distributions. The author introduces bivariate distributions and it then becomes a natural  t for introducing the concept of independent and dependent random variables. One side comment: The proof of characterization property in a special case should have probably been placed in Chapter 4’s Appendix. Chapter 5, Special Discrete Distributions: Introduces the Binomial, Poisson, (but omits the oft quoted np > 5 “rule”), Negative Binomial, and Geometric distributions. Included is the relationship among all these distributions, as well as their relationship to their continuous cousins. Chapter 6, Special Continuous Distributions: Covers the exponential, gamma, Pareto, normal, lognormal, and beta (useful for bounded data). It also covers the lifetime distributions Weibull and uniform (which the author calls DeMoivre). As an illustration of how the author uses examples to further expand the student’s knowledge, one of the examples in this chapter shows how Weibull distributed random numbers can be derived from the uniform. This is excellent example since the students will need to be familiar with Monte Carlo methods. Chapter 7, Transformations of Random Variables: This chapter should be used selectively. The demonstrations should probably be omitted except for very mathematically oriented engineers, as should Jensen’s inequality. In addition, Section 7.3 ( Insurance Contracts With Caps, Deductibles and Coinsurance) should be used for MBA classes, and Section 7.4 (Life Insurance and Annuity Contracts) and Section 7.5 (Reliability of Systems with Multiple Components or Processes) should be used in all classes. Section 7.6 on trigonometric transformations generally should be omitted. Chapter 8, Sums and Products of Random Variables: Covers the law of large numbers and the central limit theorem. In an engineering class, the premium determination in insurance should be omitted and a suitable engineering motivating example substituted. Also, the proof of the law of large numbers and the central limit theorem should be omitted. Chapter 9, Mixtures and Compound Distributions, and Chapter 10, Markowitz Investment Portfolio Selection Model: Should be considered only when the text is being used in an MBA program. In summary, I believe that this text would be extremely valuable for an MBA course and also could be used at several levels for an undergraduate course. It also would be a valuable addition to the library of any practitioner who uses statistical/probabilistic methods in his or her work.