Preface

Due to the huge advances in computational and modeling techniques, Bayesian methods are becoming an increasingly important tool for analyzing various types of data such as continuous, discrete and mixed data, time-series data, longitudinal data, cross-sectional data, categorical data, survival data, missing data, high/ultrahighdimensional data, and latent variable data. They are also widely applied in various fields such as industry, agriculture, economics, engineering, medicine, biological ecology, social science, data science, machine learning, and AI for statistical inferences such as a parameter or non-parameter estimation, hypothesis testing, and prediction.

A variety of Bayesian inference theories, methodologies, and computational techniques have been developed due to the requirements for analyzing complicated data and models. These include structural, semi-structured, and unstructured data, as well as models without likelihoods or having a computing hard likelihood, timesseries models, parametric or non/semi-parametric models, large-scale graphical or atmospheric models, network models, options pricing models, complex stochastic models, latent variable models, multilevel models, dynamic factor analysis models with/without time-varying parameters, high/ultrahigh-dimensional models, joint modeling of longitudinal and survival data, complex computer models, and causal inference models. Bayes factor computation, Bayesian variable selection, robust Bayesian inference, variational Bayesian inference, resampling, approximation of posterior distribution, approximate Bayesian computation, and debias methods are all of significance. But challenges remain with the development of AI and data mining requirements, such as how to balance computational time and statistical efficiency, design efficient Bayesian computational algorithms and robust sampling schemes for big/massive data, distributed data and streaming data, modeling and inference, while protecting privacy and guarding against malicious attacks.

This book, which features the work of five excellent researchers in theory, methods, models, algorithms and applications, has three sections and five chapters. Section I introduces the development of Bayesian inference, including theory, methods, algorithms and applications. Section II introduces Bayesian methods and includes two chapters. In Chapter 2, Professor Mohammad-Djafari Ali presents a Bayesian approach to solving inverse problems. In Chapter 3, Ph.D. candidate Ahmed Saadoon Mannaa investigates the prior data conflict by modeling the parameters in the prior distribution and comparing its standard deviation to that of the posterior distribution. A robust Bayesian method is presented that addresses the prior data conflict by using a set of prior distributions such as Weibull distribution and binomial distribution to identify the behavior of the estimators based on the estimation comparison of regular and robust Bayes methods via the integrated mean square error. The two chapters in Section III focus on the application of the hierarchical Bayesian method and optimized spectral acquisition in scattering experiments. In Chapter 4, Professor Bloetscher Frederick uses the hierarchical predictive Bayesian method to solve the challenge of

"what to do when you have a complex question with numerous variables that are not well understood?". In Chapter 5, Alessio De Francesco, Luisa Scaccia, Marin Boehm and Alessandro Cuusolo suggest a Bayesian inference approach based on real-time analysis of experimental data and implemented as a series of steps in which the spectral measurement is adjourned by summing to its successive acquisition runs, and the spectral modeling is upgraded.

I was invited to edit this book after the publication of *Bayesian Analysis for Hidden Markov Factor Analysis Models*, which I co-wrote with Yemao Xia, Xiaoqian Zeng, and Niansheng Tang, and my two previously edited books, *Bayesian Inference on Complicated Data* and *Data Clustering,* published in 2020 and 2022, respectively. I am very grateful to Ms. Karla Skuliber for her kind invitation to edit this book and for providing me the chance to work with these authors. I sincerely hope this book will be of great interest to statisticians, data analysts, data scientists, social scientists, biologists, ecologists, and AI and machine learning researchers.

> **Niansheng Tang** Department of Statistics, School of Mathematics and Statistics, Yunnan University at Chenggong Campus, Kunming, R. of China

Section 1

Introduction

Section 1 Introduction
