Bayesian inference Books

Book SynopsisThe application of Bayesian Networks (BN) or Dynamic Bayesian Networks (DBN) in dependability and risk analysis is a recent development. A large number of scientific publications show the interest in the applications of BN in this field. Unfortunately, this modeling formalism is not fully accepted in the industry. The questions facing today's engineers are focused on the validity of BN models and the resulting estimates. Indeed, a BN model is not based on a specific semantic in dependability but offers a general formalism for modeling problems under uncertainty. This book explains the principles of knowledge structuration to ensure a valid BN and DBN model and illustrate the flexibility and efficiency of these representations in dependability, risk analysis and control of multi-state systems and dynamic systems. Across five chapters, the authors present several modeling methods and industrial applications are referenced for illustration in real industrial contexts.Table of ContentsForeword by J.-F. Aubry ix Foreword by L. Portinale xiii Acknowledgments xv Introduction xvii Part 1. Bayesian Networks 1 Chapter 1. Bayesian Networks: a Modeling Formalism for System Dependability 3 1.1. Probabilistic graphical models: BN 5 1.1.1. BN: a formalism to model dependability 5 1.1.2. Inference mechanism 7 1.2. Reliability and joint probability distributions 8 1.2.1. Multi-state system example 8 1.2.2. Joint distribution 9 1.2.3. Reliability computing 9 1.2.4. Factorization 10 1.3. Discussion and conclusion 14 Chapter 2. Bayesian Network: Modeling Formalism of the Stucture Function of Boolean Systems 17 2.1. Introduction 17 2.2. BN models in the Boolean case 19 2.2.1. BN model from cut-sets 20 2.2.2. BN model from tie-sets 23 2.2.3. BN model from a top-down approach 25 2.2.4. BN model of a bowtie 26 2.3. Standard Boolean gates CPT 29 2.4. Non-deterministic CPT 31 2.5. Industrial applications 38 2.6. Conclusion 41 Chapter 3. Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems 43 3.1. Introduction 43 3.2. BN models in the multi-state case 43 3.2.1. BN model of multi-state systems from tie-sets 44 3.2.2. BN model of multi-state systems from cut-sets 49 3.2.3. BN model of multi-state systems from functional and dysfunctional analysis 52 3.3. Non-deterministic CPT 58 3.4. Industrial applications 59 3.5. Conclusion 62 Part 2. Dynamic Bayesian Networks 65 Chapter 4. Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation 67 4.1. Introduction 67 4.2. Component modeled by a DBN 69 4.2.1. DBN model of a MC 70 4.2.2. DBN model of non-homogeneous MC 71 4.2.3. Stochastic process with exogenous constraint 72 4.3. Model of a dynamic multi-state system 75 4.4. Discussion on dependent processes 79 4.5. Conclusion 81 Chapter 5. Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System 83 5.1. Introduction 83 5.2. Integrating reliability information into the control 84 5.3. Control integrating reliability modeled by DBN 85 5.3.1. Modeling and controlling an over-actuated system 86 5.3.2. Integrating reliability 88 5.4. Application to a drinking water network 90 5.4.1. DBN modeling 91 5.4.2. Results and discussion 92 5.5. Conclusion 95 5.6. Acknowledgments 96 Conclusion 97 Bibliography 101 Index 113

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Book SynopsisThis book describes how Bayesian methods work. Its primary aim is to demystify them, and to show readers: Bayesian thinking isn’t difficult and can be used in virtually every kind of research. In addition to revealing the underlying simplicity of statistical methods, the book explains how to parameterise and compare models while accounting for uncertainties in data, model parameters and model structures. How exactly should data be used in modelling? The literature offers a bewildering variety of techniques and approaches (Bayesian calibration, data assimilation, Kalman filtering, model-data fusion, etc). This book provides a short and easy guide to all of these and more. It was written from a unifying Bayesian perspective, which reveals how the multitude of techniques and approaches are in fact all related to one another. Basic notions from probability theory are introduced. Executable code examples are included to enhance the book’s practical use for scientific modellers, and all code is available online as well.Trade Review“The writing is succinct and easy to understand. … The book does cover a wide range of topics in Bayesian science, and that is indeed one of its best features. I do see it serving as a starting point for most non statistically minded researchers, who can get a basic idea about their topic of interest from consulting the book, and then consult references provided to get a more in-depth knowledge. Overall, I do congratulate the author on writing this book.” (Sayan Dasgupta, Biometrics, Vol. 78 (2), July, 2022)Table of ContentsPreface.- 1 Introduction to Bayesian thinking.- 2 Introduction to Bayesian science.- 3 Assigning a prior distribution.- 4 Assigning a likelihood function.- 5 Deriving the posterior distribution.- 6 Sampling from any distribution by MCMC.- 7 Sampling from the posterior distribution by MCMC.- 8 Twelve ways to fit a straight line.- 9 MCMC and complex models.- 10 Bayesian calibration and MCMC: Frequently asked questions.- 11 After the calibration: Interpretation, reporting, visualization.- 2 Model ensembles: BMC and BMA.- 13 Discrepancy.- 14 Gaussian Processes and model emulation.- 15 Graphical Modelling (GM).- 16 Bayesian Hierarchical Modelling (BHM).- 17 Probabilistic risk analysis and Bayesian decision theory.- 18 Approximations to Bayes.- 19 Linear modelling: LM, GLM, GAM and mixed models.- 20 Machine learning.- 21 Time series and data assimilation.- 22 Spatial modelling and scaling error.- 23 Spatio-temporal modelling and adaptive sampling.- 24 What next?.- Appendix 1: Notation and abbreviations.- Appendix 2: Mathematics for modellers.- Appendix 3: Probability theory for modellers.- Appendix 4: R.- Appendix 5: Bayesian software.

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Book SynopsisBayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability—keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information—scientific evidence—ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.This book is Open Access.Table of ContentsPart I - Introduction to the Bayes Factor (Likelihood Ratio)Presents the principal statistic discussed throughout this book: the Bayes factor, in the context of forensic science, more often known as the likelihood ratio. Subsections of this part: clarify the different roles (known as, respectively, the ‘investigative’ and ‘evaluative’ role) that forensic scientists may assume in their daily work articulate the reasons why forensic scientists should adhere to a Bayesian framework of inference in order to ensure coherence in their inferential and decision-making tasks formally describe what the Bayes factor is and how it relates to coherent decision analysis describe the advantages that Bayes factors offer in assessing, articulating and communicating the value of scientific evidence in general, and in legal proceedings in particular Part II - Bayes Factor for Investigative PurposesDeals with a peculiar task of the forensic scientist, known as the ‘investigative mode’ (i.e., one of the two main modes of functioning introduced in Part I). That is, in forensic settings, it may well be the case that a potential source (i.e., a suspect) is not available for comparative purposes, in particular in early stages of the legal process. Notwithstanding, data and measurements on recovered material (e.g., seized on a crime scene) can be used for an investigative purpose. In this mode of working, scientists can offer to investigative authorities (or, in a more general perspective, mandating parties) information to help discriminate between general propositions concerning, for instance, the characterizing features of the source that left the recovered material (e.g., gender, externally visible traits such as hair and eye color, handedness, etc.). At this stage in the process, the scientist tries to help answer questions such as ‘what happened?’ in the case under investigation, or ‘what can we infer about the offender?’. In this context, the Bayes factor can be used as a statistic to measure and help decide how to classify, for example, objects and substances on which measurements have been made. This use of the Bayes factor will be explained through practical examples involving topics such as handwriting characteristics, toner from printers in questioned document examination, drugs of abuse, toxicology, forensic anthropology and forensic DNA profiling (listing is not exhaustive and may evolve during the writing of the book). Both univariate and multivariate data will be considered, with or without replicates, and involving different statistical distributions (i.e. Binomial, Poisson, Normal, etc.). The examples refer to realistic forensic applications as they may be encountered in judicial contexts and the forensic practitioner’s own field of activity. Data will be selected from published literature or from the author’s own records. R sample code will be specified and explanations will be included on how to interpret results in context and convey their meaning appropriately.Part III - Bayes Factor for Evaluative PurposesFocuses on the scientist’s role in a more advanced stage of the legal process. That is, situations in which the evaluation of scientific findings will take into account a potential source of the recovered material (e.g., a suspect or an object/tool). This kind of reporting is typically required when scientists need to communicate their results for use at trial. It is of utmost importance at this juncture that scientists express the value of the observed data and findings under competing hypotheses, focusing on a potential (i.e., known) source versus an alternative source (e.g., propositions such as ‘the recovered item comes from the same source as the control material’, and ‘the recovered item is from a source that is different from that of the control material’). The Bayes factor is the central inferential concept for such expressions of weight of evidence. In this part of the book, too, examples will be chosen with the intention to reflect realistic scenarios as they may arise in current judicial practice. In particular, the outline will consider uni- and multi­-variate data from scenarios related to microtraces (e.g., glass and paint fragments), handwriting and drugs of abuse. Besides computational R code, this chapter will also include (i) sensitivity analyses to provide readers with a means to further investigate the properties of the proposed evaluative procedures based on the Bayes factor, and (ii) decision theoretic extensions to outline how to interface expressions of weight of evidence with the broader perspective of coherent decision-making. Part IV - ConclusionSummarizes the key messages developed throughout this book, emphasizing (i) the contribution of an extended use of the Bayes factor in a normative decision framework, and (ii) the role of the Bayes factor as the relevant statistic for both investigative and evaluative tasks that characterize current forensic science.

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Book SynopsisThe book shows how risk, defined as the statistical expectation of loss, can be formally decomposed as the product of two terms: hazard probability and system vulnerability. This requires a specific definition of vulnerability that replaces the many fuzzy definitions abounding in the literature. The approach is expanded to more complex risk analysis with three components rather than two, and with various definitions of hazard. Equations are derived to quantify the uncertainty of each risk component and show how the approach relates to Bayesian decision theory. Intended for statisticians, environmental scientists and risk analysts interested in the theory and application of risk analysis, this book provides precise definitions, new theory, and many examples with full computer code. The approach is based on straightforward use of probability theory which brings rigour and clarity. Only a moderate knowledge and understanding of probability theory is expected from the reader.Table of Contents- 1. Introduction to Probabilistic Risk Analysis (PRA). - 2. Distribution-Based Single-Threshold PRA. - 3. Sampling-Based Single-Threshold PRA. - 4. Sampling-Based Single-Threshold PRA: Uncertainty Quantification (UQ). - 5. Density Estimation to Move from Sampling- to Distribution-Based PRA. - 6. Copulas for Distribution-Based PRA. - 7. Bayesian Model-Based PRA. - 8. Sampling-Based Multi-Threshold PRA: Gaussian Linear Example. - 9. Distribution-Based Continuous PRA: Gaussian Linear Example. - 10. Categorical PRA with Other Splits than for Threshold-Levels: Spatio-Temporal Example. - 11. Three-Component PRA. - 12. Introduction to Bayesian Decision Theory (BDT). - 13. Implementation of BDT Using Bayesian Networks. - 14. A Spatial Example: Forestry in Scotland. - 15. Spatial BDT Using Model and Emulator. - 16. Linkages Between PRA and BDT. - 17. PRA vs. BDT in the Spatial Example. - 18. Three-Component PRA in the Spatial Example. - 19. Discussion.

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Book Synopsis- Introduction.- Bayesian Spatial Modelling.- Conjugate Inversion Models.- Random Fields.- Part I Traditional Conjugate Spatial Models.- Likelihood Models.- Prior Models.- Posterior Models.- Model Parameter Inference.- Computational Challenges.

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Book SynopsisFault diagnosis is useful for technicians to detect, isolate, identify faults, and troubleshoot. Bayesian network (BN) is a probabilistic graphical model that effectively deals with various uncertainty problems. This model is increasingly utilized in fault diagnosis.This unique compendium presents bibliographical review on the use of BNs in fault diagnosis in the last decades with focus on engineering systems. Subsequently, eleven important issues in BN-based fault diagnosis methodology, such as BN structure modeling, BN parameter modeling, BN inference, fault identification, validation, and verification are discussed in various cases.Researchers, professionals, academics and graduate students will better understand the theory and application, and benefit those who are keen to develop real BN-based fault diagnosis system.

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