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Most industrial and natural materials exhibit a macroscopic behaviour which results from the existence of microscale inhomogeneities. The influence of such inhomogeneities is commonly modelled using probabilistic methods. Most of the approaches to the evaluation of the safety of structures according to probabilistic criteria are somewhat scattered, however, and it is time to present such material in a coherent and up-to-date form. Probabilities and Materials undertakes this task, and also defines the great tasks that must be tackled in coming years. For engineers and researchers dealing with materials, geotechnics, solid mechanics, soil mechanics, statistics and stochastic processes. The expository nature of the book means that no prior knowledge of statistics or probability is required of the reader. The book can thus serve as an excellent introduction to the nature of applied statistics and stochastic modelling.
There are numerous technological materials - such as metals, polymers, ceramics, concrete, and many others - that vary in properties and serviceability. However, the almost universal common theme to most real materials is that their properties depend on the scale at which the analysis or observation takes place and at each scale "probabilities" play an important role. Here the word "probabilities" is used in a wider than the classical sense. In order to increase the efficiency and serviceability of these materials, researchers from NATO, CP and other countries were brought together to exchange knowledge and develop avenues for progress and applications in the st 21 century. The workshop began by reviewing progress in the subject area over the past few years and by identifying key questions that remain open. One point was how to observe/measure material properties at different scales and whether a probabilistic approach, at each scale, was always applicable and advantageous. The wide range of materials, from wood to advanced metals and from concrete to complex advanced composites, and the diversity of applications, e.g. fatigue, fracture, deformation, etc., were recognized as "obstacles" in identifying a "universal" approach.
Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus.
An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
This book illuminates the fundamental principle and applications of probability-based multi-objective optimization for material selection systematically, in which a brand new concept of preferable probability and its assessment as well as other treatments are introduced by authors for the first time. Hybrids of the new approach with experimental design methodologies, such as response surface methodology, orthogonal experimental design, and uniform experimental design, are all performed; the conditions of the material performance utility with desirable value and robust assessment are included; the discretization treatment of complicated integral in the evaluation is presented. The authors wish this work will cast a brick to attract jade and would make its contributions to relevant fields as a paving stone. This book can be used as a textbook for postgraduate and advanced undergraduate students in material relevant majors, and a reference book for scientists and engineers digging in the related fields.