Download or read book Bayesian Methods in Engineering Design Problems written by Laura Painton Swiler and published by . This book was released on 2006 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Methods for Structural Dynamics and Civil Engineering written by Ka-Veng Yuen and published by John Wiley & Sons. This book was released on 2010-02-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods are a powerful tool in many areas of science and engineering, especially statistical physics, medical sciences, electrical engineering, and information sciences. They are also ideal for civil engineering applications, given the numerous types of modeling and parametric uncertainty in civil engineering problems. For example, earthquake ground motion cannot be predetermined at the structural design stage. Complete wind pressure profiles are difficult to measure under operating conditions. Material properties can be difficult to determine to a very precise level – especially concrete, rock, and soil. For air quality prediction, it is difficult to measure the hourly/daily pollutants generated by cars and factories within the area of concern. It is also difficult to obtain the updated air quality information of the surrounding cities. Furthermore, the meteorological conditions of the day for prediction are also uncertain. These are just some of the civil engineering examples to which Bayesian probabilistic methods are applicable. Familiarizes readers with the latest developments in the field Includes identification problems for both dynamic and static systems Addresses challenging civil engineering problems such as modal/model updating Presents methods applicable to mechanical and aerospace engineering Gives engineers and engineering students a concrete sense of implementation Covers real-world case studies in civil engineering and beyond, such as: structural health monitoring seismic attenuation finite-element model updating hydraulic jump artificial neural network for damage detection air quality prediction Includes other insightful daily-life examples Companion website with MATLAB code downloads for independent practice Written by a leading expert in the use of Bayesian methods for civil engineering problems This book is ideal for researchers and graduate students in civil and mechanical engineering or applied probability and statistics. Practicing engineers interested in the application of statistical methods to solve engineering problems will also find this to be a valuable text. MATLAB code and lecture materials for instructors available at http://www.wiley.com/go/yuen
Download or read book Bayesian Inverse Problems written by Juan Chiachio-Ruano and published by CRC Press. This book was released on 2021-11-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them. Through this book, the reader will learn how this class of methods can be useful to rigorously address a range of engineering problems where empirical data and fundamental knowledge come into play. The book is written for a non-expert audience and it is contributed to by many of the most renowned academic experts in this field.
Download or read book An Engineering Design Methodology with Bayesian Surrogates and Optimal Sampling written by Ignacio G. Osio and published by . This book was released on 1994 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper develops an adaptive engineering design methodology based on Bayesian surrogates for the efficient use of computer simulations of physical models. These surrogates are nonlinear regression models fitted with data obtained from deterministic numerical models using optimal sampling. Surrogates can be used for design, optimization, sensitivity and tradeoff studies. The statistical theory of Bayesian inference is used in the formulation of surrogates to support the evolutionary nature of engineering design within a multistage approach. Information from computer simulations of different levels of accuracy and detail is integrated, updating surrogates sequentially to improve their accuracy. Optimal sampling is conducted by minimizing the average variance of the unknowns. The proposed engineering design methodology is tested with a known analytical function to illustrate accuracy and cost tradeoffs. This methodology then is applied to a thermal design problem of embedded electronic packages with five control parameters. The temperature distributions of embedded electronic chip configurations are calculated using spectral element direct numerical simulations of the heat transfer process. Surrogates, built from 30 simulations in two stages, are used to predict new design combinations and to minimize the maximum chip temperature. Metrics to quantify prediction errors are proposed and tested to evaluate surrogate accuracy given cost and time constraints."
Download or read book Practice of Bayesian Probability Theory in Geotechnical Engineering written by Wan-Huan Zhou and published by Springer Nature. This book was released on 2020-11-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces systematically the application of Bayesian probabilistic approach in soil mechanics and geotechnical engineering. Four typical problems are analyzed by using Bayesian probabilistic approach, i.e., to model the effect of initial void ratio on the soil–water characteristic curve (SWCC) of unsaturated soil, to select the optimal model for the prediction of the creep behavior of soft soil under one-dimensional straining, to identify model parameters of soils and to select constitutive model of soils considering critical state concept. This book selects the simple and easy-to-understand Bayesian probabilistic algorithm, so that readers can master the Bayesian method to analyze and solve the problem in a short time. In addition, this book provides MATLAB codes for various algorithms and source codes for constitutive models so that readers can directly analyze and practice. This book is useful as a postgraduate textbook for civil engineering, hydraulic engineering, transportation, railway, engineering geology and other majors in colleges and universities, and as an elective course for senior undergraduates. It is also useful as a reference for relevant professional scientific researchers and engineers.
Download or read book Practical Applications of Bayesian Reliability written by Yan Liu and published by John Wiley & Sons. This book was released on 2019-03-18 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates how to solve reliability problems using practical applications of Bayesian models This self-contained reference provides fundamental knowledge of Bayesian reliability and utilizes numerous examples to show how Bayesian models can solve real life reliability problems. It teaches engineers and scientists exactly what Bayesian analysis is, what its benefits are, and how they can apply the methods to solve their own problems. To help readers get started quickly, the book presents many Bayesian models that use JAGS and which require fewer than 10 lines of command. It also offers a number of short R scripts consisting of simple functions to help them become familiar with R coding. Practical Applications of Bayesian Reliability starts by introducing basic concepts of reliability engineering, including random variables, discrete and continuous probability distributions, hazard function, and censored data. Basic concepts of Bayesian statistics, models, reasons, and theory are presented in the following chapter. Coverage of Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling comes next. The book then goes on to teach the concepts of design capability and design for reliability; introduce Bayesian models for estimating system reliability; discuss Bayesian Hierarchical Models and their applications; present linear and logistic regression models in Bayesian Perspective; and more. Provides a step-by-step approach for developing advanced reliability models to solve complex problems, and does not require in-depth understanding of statistical methodology Educates managers on the potential of Bayesian reliability models and associated impact Introduces commonly used predictive reliability models and advanced Bayesian models based on real life applications Includes practical guidelines to construct Bayesian reliability models along with computer codes for all of the case studies JAGS and R codes are provided on an accompanying website to enable practitioners to easily copy them and tailor them to their own applications Practical Applications of Bayesian Reliability is a helpful book for industry practitioners such as reliability engineers, mechanical engineers, electrical engineers, product engineers, system engineers, and materials scientists whose work includes predicting design or product performance.
Download or read book Bayesian Theory and Methods with Applications written by Vladimir Savchuk and published by Springer Science & Business Media. This book was released on 2011-09-01 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods are growing more and more popular, finding new practical applications in the fields of health sciences, engineering, environmental sciences, business and economics and social sciences, among others. This book explores the use of Bayesian analysis in the statistical estimation of the unknown phenomenon of interest. The contents demonstrate that where such methods are applicable, they offer the best possible estimate of the unknown. Beyond presenting Bayesian theory and methods of analysis, the text is illustrated with a variety of applications to real world problems.
Download or read book Bayesian Approach to Global Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: ·Et moi ... si j'avait su comment en revcnir. One service mathematics has rendered the je o'y semis point alle.' human race. It has put common sense back Jules Verne where it beloogs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense', able to do something with it. Eric T. BclI O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Download or read book Data Analysis written by Devinderjit Sivia and published by OUP Oxford. This book was released on 2006-06-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews.
Download or read book Maximum Entropy and Bayesian Methods in Science and Engineering written by G. Erickson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.
Download or read book Frontiers of Statistical Decision Making and Bayesian Analysis written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2010-07-24 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.
Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Download or read book Probability and Risk Analysis written by Igor Rychlik and published by Springer Science & Business Media. This book was released on 2006-10-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents notions and ideas at the foundations of a statistical treatment of risks. The focus is on statistical applications within the field of engineering risk and safety analysis. Coverage includes Bayesian methods. Such knowledge facilitates the understanding of the influence of random phenomena and gives a deeper understanding of the role of probability in risk analysis. The text is written for students who have studied elementary undergraduate courses in engineering mathematics, perhaps including a minor course in statistics. This book differs from typical textbooks in its verbal approach to many explanations and examples.
Download or read book Bayesian Methods in Reliability written by P. Sander and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: When data is collected on failure or survival a list of times is obtained. Some of the times are failure times and others are the times at which the subject left the experiment. These times both give information about the performance of the system. The two types will be referred to as failure and censoring times (cf. Smith section 5). * A censoring time, t, gives less information than a failure time, for it is * known only that the item survived past t and not when it failed. The data is tn and of censoring thus collected as a list of failure times t , . . . , l * * * times t , t , . . . , t • 1 z m 2. 2. Classical methods The failure times are assumed to follow a parametric distribution F(t;B) with and reliability R(t;B). There are several methods of estimating density f(t;B) the parameter B based only on the data in the sample without any prior assumptions about B. The availability of powerful computers and software packages has made the method of maximum likelihood the most popular. Descriptions of most methods can be found in the book by Mann, Schafer and Singpurwalla (1974). In general the method of maximum likelihood is the most useful of the classical approaches. The likelihood approach is based on constructing the joint probability distrilmtion or density for a sample.
Download or read book Bayesian Methods for Data Analysis Third Edition written by Bradley P. Carlin and published by CRC Press. This book was released on 2008-06-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (MCMC) methods and related data analytic techniques. New to the Third Edition New data examples, corresponding R and WinBUGS code, and homework problems Explicit descriptions and illustrations of hierarchical modeling—now commonplace in Bayesian data analysis A new chapter on Bayesian design that emphasizes Bayesian clinical trials A completely revised and expanded section on ranking and histogram estimation A new case study on infectious disease modeling and the 1918 flu epidemic A solutions manual for qualifying instructors that contains solutions, computer code, and associated output for every homework problem—available both electronically and in print Ideal for Anyone Performing Statistical Analyses Focusing on applications from biostatistics, epidemiology, and medicine, this text builds on the popularity of its predecessors by making it suitable for even more practitioners and students.
Download or read book Bayesian Methods for Hackers written by Cameron Davidson-Pilon and published by Addison-Wesley Professional. This book was released on 2015-09-30 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.
Download or read book Using Bayesian Inference in Design Applications written by Chung Yong Chan and published by . This book was released on 2010 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents a new approach for solving scientific and engineering design problems such as the design of antenna arrays and finite impulse response (FIR) filters. In this approach, a design problem is cast as an inverse problem. Bayesian inference has been used extensively to solve inverse problems in various fields, and thus, the tools and methods previously developed for Bayesian inference are adapted and utilized to solve design problems in the present approach. Given a desired design output specified by upper and lower envelopes, the Bayesian inference framework for design is applied to achieve designs that meet the prescribed design specifications and practical design requirements. To obtain a design, Bayesian parameter estimation and model comparison are employed to determine the values of all design parameters. In the design of antenna arrays, the objective is to produce antenna arrays that realize the desired far-field radiation pattern while satisfying all prescribed practical design requirements. In the context of computation, the task is to determine the required number of antenna array elements and the values for the element parameters which include the position, current amplitude and phase. As for digital filter design, the aim is to design linear phase FIR filters that realize the desired frequency magnitude response and satisfy all prescribed practical design requirements. The computational task in this case is to determine the number of filter taps required, the tap positions and the filter coefficients. In the Bayesian inference framework for design, the solution to a design problem is the posterior probability distribution which is a function of the design parameters. The posterior--which comes from Bayes' theorem--is proportional to the product of the likelihood and priors. The likelihood is obtained via the assignment of a probability distribution function to the error between the desired and achieved design output. The assignment of an error distribution incorporates the desired design output into a design process. The priors are assigned probability distribution functions which express the constraints on the design parameters. In addition to the constraints on the design parameters, a design problem may have other practical design requirements which are implemented through the modifications of the likelihood. With the likelihood and priors obtained, the posterior--which cannot be determined analytically--is approximated by a Monte Carlo method. In the approximation, a reasonable number of samples are drawn from the posterior using an appropriate sampling technique such as a Markov chain Monte Carlo method. The sampling of the posterior produces an approximate solution to a design problem and concludes the inference portion of the Bayesian inference framework for design. In the context of design, each posterior sample drawn in the Monte Carlo approximation represents a design candidate. As a result, the solution to a design problem consists of a number of potential designs rather than a single final design. To obtain the final design, an additional decision step is required. This final step requires a designer to select a single design candidate as the final design based on additional design criteria. The Bayesian inference framework for design has been applied to the design of both antenna arrays and linear phase FIR filters. The antenna array design examples presented in this dissertation use different types of antenna array such as symmetric linear array with real-valued currents, asymmetric linear array with complex currents, reconfigurable linear array and planar array to realize various desired radiation patterns while satisfying certain prescribed practical design requirements. The radiation patterns that are desired include two broadside patterns, an end-fire pattern, a shaped beam pattern which is the sector beam pattern, and a three-dimensional radiation pattern. Various practical design requirements have been incorporated into the design examples presented in this dissertation. These practical design requirements include a minimum spacing between two adjacent array elements, limitations in the dynamic range and accuracy of the current amplitudes and phases, the ability to maintain a desired radiation pattern over a frequency band, and the ability to maintain a desired radiation pattern when one or more array elements are defective or failing. For the digital filter design application, four design examples are presented. All four examples employ a linear phase FIR filter that has symmetric impulse response and odd filter length to produce various desired frequency responses. In practice, the filter coefficients of a linear phase FIR filter are limited in dynamic range and accuracy. This practical design requirement has been incorporated into two of the design examples where the filter coefficient values are represented by a sum of signed power-of-two terms.
