tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

Survival Analysis: Techniques for Censored and Truncated Data (2nd ed.) (Book)

: Scientific learning is an iterative process employing Criticism and Estimation. Correspondingly the formulated model factors into two complimentary parts - a predictive part allowing model criticism, and a Bayes posterior part allowing estimation. Implications for significance tests, the theory of precise measurement, and for ridge estimates are considered. Predictive checking functions for transformation, serial correlation, bad values, and their relation with Bayesian options are considered. Robustness is seen from a Bayesian viewpoint and examples are given. For the bad value problem a comparison with M estimators is made. (Author)

Sampling and Bayes' inference in scientific modelling and robustness

(1966). Mathematical Theory of Reliability. Journal of the Operational Research Society: Vol. 17, No. 2, pp. 213-215.

https://link.springer.com/content/pdf/10.1057%2Fjors.1966.43.pdf

Mathematical Theory of Reliability

However, despite its claims, this book is an excellent introduction to mathematical modelling, with a wealth of interesting case studies and lovely mathematics that will appeal to many of its target audience final year undergraduates, Masters and PhD students working in 'practical' mathematical modelling. The source of most of the case studies comes from the Study Groups with Industry and Mathematics that originated in 1968 at Oxford, organized by Alan Taylor and Leslie Fox, but is now a global activity. The book describes the type of problem, how they are approached and funded (typically a surprisingly cheap £10 000 to £15 000). The first chapter covers the mathematical preliminaries for the case studies which are all based on continuous media, and so all that is needed is diffusion and flow and deformation of solids and fluids. The next four chapters are based on elliptic partial differential equations and relate to simulation of a type of compressor, determination of the viscosity of a carbon paste used in smelting, simulation of an instrument for determining density, and modelling a form of nondestructive testing of pressure vessels. There follow six chapters devoted to a range of applications of the diffusion equation and various non-linear effects. These cover the cooking of a single cereal grain, waves of epidemics in animal populations, catalytic converters, problems with blast furnaces, the cooling of hot glass, and crystal growth. Chapter 11 looks at the load responses of filled viscoelastic materials. The last two chapters, based on hyperbolic equations, model the noise produced by a bird scare gun and the paper tension variations in a printing press.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FB9EBD3320909B8F7F968615CD8463B2/S0025557200173425a.pdf/div-class-title-span-class-italic-statistical-inference-span-2nd-edn-by-paul-h-garthwaite-ian-t-jolliffe-and-byron-jones-pp-328-40-hbk-2002-isbn-0-19-857226-3-oxford-university-press-div.pdf

Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press).

Perusal of quality- and reliability-engineering literature indicates some confusion over the meaning of accelerated life testing (ALT), highly accelerated life testing (HALT), highly accelerated stress screening (HASS), and highly accelerated stress auditing (HASA). In addition, there is a significant conflict between testing as part of an iterative process of finding and removing defects and testing as a means of estimating or predicting product reliability. We review the basics of these testing methods and describe how they relate to statistical methods for estimation and prediction of reliability and reliability growth. We also outline potential synergies to help reconcile statistical and engineering approaches to accelerated testing, resulting in better product quality at lower cost.

Accelerated Test Methods for Reliability Prediction

Accelerated test methods for reliability prediction

Semi-Markov processes (SMPs) provide a rich framework for many real-world problems. However, due to diculty implementing practical solutions they are rarely used with their full capability. The theory of SMPs is quite mature but was mainly developed at a time when computational resources were not widely available. With the exception of some of the simplest cases, solutions to SMPs are inherently numerical, and SMPs have been underutilized by practitioners because of diculty implementing the theory in applications. This paper demonstrates the theory and computational methods needed to implement SMP models in practical settings. Methods are illustrated with an application modeling the movement of coronary patients in a hospital. Our aim is to allow practitioners to use richer SMP models without being burdened with the rigorous mathematical theory.

An Introduction to Solving for Quantities of Interest in Finite-State Semi-Markov Processes

First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. Finding or computing first passage distributions is, in general, quite challenging. We take the approach of using characteristic functions (or Fourier transforms) and inverting them to numerically calculate the first passage distribution. Numerical inversion of characteristic functions can be unstable for a general probability measure. However, we show they can be quickly and accurately calculated using the inverse discrete Fourier transform for lattice distributions. Using the fast Fourier transform algorithm these computations can be extremely fast. In addition to the speed of this approach, we are able to prove a few useful bounds for the numerical inversion error of the characteristic functions. These error bounds rely on the existence of a first or second moment of the distribution, or on an eventual monotonicity condition. We demonstrate these techniques with two examples.

Richard L. Warr

Papers

Accelerated Test Methods for Reliability Prediction

Accelerated test methods for reliability prediction

An Introduction to Solving for Quantities of Interest in Finite-State Semi-Markov Processes

Numerical Approximation of Probability Mass Functions via the Inverse Discrete Fourier Transform

Failure time distributions for complex equipment