Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics. Each chapter is self-contained and focuses on a Bayesian methodology. It gives an overview of the area, presents theoretical insights, and emphasizes applications through motivating examples. This book reflects the diversity of Bayesian analysis, from novel Bayesian methodology, such as nonignorable response and factor analysis, to state-of-the-art applications in economics, astrophysics, biomedicine, oceanography, and other areas. It guides readers in using Bayesian techniques for a range of statistical analyses.

An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Provides an overview of the fundamentals of Bayesian inference and its applications within astrophysics, for graduate students and researchers.

This book covers computational statistics-based approaches for Artificial Intelligence. The aim of this book is to provide comprehensive coverage of the fundamentals through the applications of the different kinds of mathematical modelling and statistical techniques and describing their applications in different Artificial Intelligence systems. The primary users of this book will include researchers, academicians, postgraduate students, and specialists in the areas of data science, mathematical modelling, and Artificial Intelligence. It will also serve as a valuable resource for many others in the fields of electrical, computer, and optical engineering. The key features of this book are: Presents development of several real-world problem applications and experimental research in the field of computational statistics and mathematical modelling for Artificial Intelligence Examines the evolution of fundamental research into industrialized research and the transformation of applied investigation into real-time applications Examines the applications involving analytical and statistical solutions, and provides foundational and advanced concepts for beginners and industry professionals Provides a dynamic perspective to the concept of computational statistics for analysis of data and applications in intelligent systems with an objective of ensuring sustainability issues for ease of different stakeholders in various fields Integrates recent methodologies and challenges by employing mathematical modeling and statistical techniques for Artificial Intelligence

This book provides empirical applications of macroeconometric methods through discussions on key issues in the Indian economy. It deals with issues of topical relevance in the arena of macroeconomics. The aim is to apply time series and financial econometric methods to macroeconomic issues of an emerging economy such as India. The data sources are given in each chapter, and students and researchers may replicate the analyses.The book is divided into three parts—Part I: Macroeconomic Modelling and Policy; Part II: Forecasting the Indian Economy and Part III: Business Cycles and Global Crises. It provides a holistic understanding of the techniques with each chapter delving into a relevant issue analysed using appropriate methods—Chapter 1: Introduction; Chapter 2: Macroeconomic Modelling and Bayesian Methods; Chapter 3: Monetary Policy Framework in India; Chapter 4: Determinants of Yields on Government Securities in India; Chapter 5: Monetar y Transmission in the Indian Economy; Chapter 6: India’s Bilateral Export Growth and Exchange Rate Volatility: A Panel GMM Approach; Chapter 7: Aggregate and Sectoral Productivity Growth in the Indian Economy: Analysis and Determinants; Chapter 8: Forecasting the INR/USD Exchange Rate: A BVAR Framework; Chapter 9: Forecasting India’s Inflation in a Data-Rich Environment: A FAVAR Study; Chapter 10: A Structural Macroeconometric Model for India; Chapter 11: International Synchronization of Growth Rate Cycles: An Analysis in Frequency Domain; Chapter 12: Inter-Linkages Between Asian and U.S. Stock Market Returns: A Multivariate GARCH Analysis; Chapter 13: The Increasing Synchronization of International Recessions. Since the selection of issues is from macroeconomic aspects of the Indian economy, the book has wide applications and is useful for students and researchers of fields such as applied econometrics, time series econometrics, financial econometrics, forecasting methods and macroeconomics.

Data Driven Methods for Civil Structural Health Monitoring and Resilience: Latest Developments and Applications provides a comprehensive overview of data-driven methods for structural health monitoring (SHM) and resilience of civil engineering structures, mostly based on artificial intelligence or other advanced data science techniques. This allows existing structures to be turned into smart structures, thereby allowing them to provide intelligible information about their state of health and performance on a continuous, relatively real-time basis. Artificial-intelligence-based methodologies are becoming increasingly more attractive for civil engineering and SHM applications; machine learning and deep learning methods can be applied and further developed to transform the available data into valuable information for engineers and decision makers.

Researchers often have difficulties collecting enough data to test their hypotheses, either because target groups are small or hard to access, or because data collection entails prohibitive costs. Such obstacles may result in data sets that are too small for the complexity of the statistical model needed to answer the research question. This unique book provides guidelines and tools for implementing solutions to issues that arise in small sample research. Each chapter illustrates statistical methods that allow researchers to apply the optimal statistical model for their research question when the sample is too small. This essential book will enable social and behavioral science researchers to test their hypotheses even when the statistical model required for answering their research question is too complex for the sample sizes they can collect. The statistical models in the book range from the estimation of a population mean to models with latent variables and nested observations, and solutions include both classical and Bayesian methods. All proposed solutions are described in steps researchers can implement with their own data and are accompanied with annotated syntax in R. The methods described in this book will be useful for researchers across the social and behavioral sciences, ranging from medical sciences and epidemiology to psychology, marketing, and economics.

In an era marked by exponential growth in data generation and an unprecedented convergence of technology and healthcare, the intersection of biostatistics and data science has become a pivotal domain. This book is the ideal companion in navigating the convergence of statistical methodologies and data science techniques with diverse applications implemented in the open-source environment of R. It is designed to be a comprehensive guide, marrying the principles of biostatistics with the practical implementation of statistics and data science in R, thereby empowering learners, researchers, and practitioners with the tools necessary to extract meaningful knowledge from biological, health, and medical datasets. This book is intended for students, researchers, and professionals eager to harness the combined power of biostatistics, data science, and the R programming language while gathering vital statistical knowledge needed for cutting-edge scientists in all fields. It is useful for those seeking to understand the basics of data science and statistical analysis, or looking to enhance their skills in handling any simple or complex data including biological, health, medical, and industry data. Key Features: Presents contemporary concepts of data science and biostatistics with real-life data analysis examples Promotes the evolution of fundamental and advanced methods applying to real-life problem-solving cases Explores computational statistical data science techniques from initial conception to recent developments of biostatistics Provides all R codes and real-world datasets to practice and competently apply into reader’s own domains Written in an exclusive state-of-the-art deductive approach without any theoretical hitches to support all contemporary readers

The perfect learning exists. We mean a learning model that can be generalized, and moreover, that can always fit perfectly the test data, as well as the training data. We have performed in this thesis many experiments that validate this concept in many ways. The tools are given through the chapters that contain our developments. The classical Multilayer Feedforward model has been re-considered and a novel $N_k$-architecture is proposed to fit any multivariate regression task. This model can easily be augmented to thousands of possible layers without loss of predictive power, and has the potential to overcome our difficulties simultaneously in building a model that has a good fit on the test data, and don't overfit. His hyper-parameters, the learning rate, the batch size, the number of training times (epochs), the size of each layer, the number of hidden layers, all can be chosen experimentally with cross-validation methods. There is a great advantage to build a more powerful model using mixture models properties. They can self-classify many high dimensional data in a few numbers of mixture components. This is also the case of the Shallow Gibbs Network model that we built as a Random Gibbs Network Forest to reach the performance of the Multilayer feedforward Neural Network in a few numbers of parameters, and fewer backpropagation iterations. To make it happens, we propose a novel optimization framework for our Bayesian Shallow Network, called the {Double Backpropagation Scheme} (DBS) that can also fit perfectly the data with appropriate learning rate, and which is convergent and universally applicable to any Bayesian neural network problem. The contribution of this model is broad. First, it integrates all the advantages of the Potts Model, which is a very rich random partitions model, that we have also modified to propose its Complete Shrinkage version using agglomerative clustering techniques. The model takes also an advantage of Gibbs Fields for its weights precision matrix structure, mainly through Markov Random Fields, and even has five (5) variants structures at the end: the Full-Gibbs, the Sparse-Gibbs, the Between layer Sparse Gibbs which is the B-Sparse Gibbs in a short, the Compound Symmetry Gibbs (CS-Gibbs in short), and the Sparse Compound Symmetry Gibbs (Sparse-CS-Gibbs) model. The Full-Gibbs is mainly to remind fully-connected models, and the other structures are useful to show how the model can be reduced in terms of complexity with sparsity and parsimony. All those models have been experimented, and the results arouse interest in those structures, in a sense that different structures help to reach different results in terms of Mean Squared Error (MSE) and Relative Root Mean Squared Error (RRMSE). For the Shallow Gibbs Network model, we have found the perfect learning framework : it is the $(l_1, \boldsymbol{\zeta}, \epsilon_{dbs})-\textbf{DBS}$ configuration, which is a combination of the \emph{Universal Approximation Theorem}, and the DBS optimization, coupled with the (\emph{dist})-Nearest Neighbor-(h)-Taylor Series-Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model [which in turn is a combination of the research of the Nearest Neighborhood for a good Train-Test association, the Taylor Approximation Theorem, and finally the Multivariate Interpolation Method]. It indicates that, with an appropriate number $l_1$ of neurons on the hidden layer, an optimal number $\zeta$ of DBS updates, an optimal DBS learnnig rate $\epsilon_{dbs}$, an optimal distance \emph{dist}$_{opt}$ in the research of the nearest neighbor in the training dataset for each test data $x_i^{\mbox{test}}$, an optimal order $h_{opt}$ of the Taylor approximation for the Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model once the {\bfseries DBS} has overfitted the training dataset, the train and the test error converge to zero (0). As the Potts Models and many random Partitions are based on a similarity measure, we open the door to find \emph{sufficient} invariants descriptors in any recognition problem for complex objects such as image; using \emph{metric} learning and invariance descriptor tools, to always reach 100\% accuracy. This is also possible with invariant networks that are also universal approximators. Our work closes the gap between the theory and the practice in artificial intelligence, in a sense that it confirms that it is possible to learn with very small error allowed.

This book provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It attempts to establish a gold standard for how a statistical analysis should proceed. The book illustrates relative belief theory using many examples and describes the strengths and weaknesses of the theory. The author also addresses fundamental statistical issues, including the meaning of probability, the role of subjectivity, the meaning of objectivity, and the role of infinity and continuity.