tailieunhanh - Handbook of Statistics Vol 25

Fisher and Mahalanobis described Statistics as the key technology of the twentieth century. Since then Statistics has evolved into a field that has many applications in all sciences and areas of technology, as well as in most areas of decision making such as in health care, business, federal statistics and legal proceedings. Applications in statistics such as inference for Causal effects, inferences about the spatio- temporal processes, analysis of categorical and survival data sets and countless other functions play an essential role in the present day world. In the last two to three decades, Bayesian Statistics has emerged as one. | Preface Fisher and Mahalanobis described Statistics as the key technology of the twentieth century. Since then Statistics has evolved into a field that has many applications in all sciences and areas of technology as well as in most areas of decision making such as in health care business federal statistics and legal proceedings. Applications in statistics such as inference for Causal effects inferences about the spatio- temporal processes analysis of categorical and survival data sets and countless other functions play an essential role in the present day world. In the last two to three decades Bayesian Statistics has emerged as one of the leading paradigms in which all of this can be done in a unified fashion. There has been tremendous development in Bayesian theory methodology computation and applications in the past several years. Bayesian statistics provides a rational theory of personal beliefs compounded with real world data in the context of uncertainty. The central aim of characterizing how an individual should make inferences or act in order to avoid certain kinds of undesirable behavioral inconsistencies and consequent are all successfully accomplished through this process. The primary theory of Bayesian statistics states that utility maximization should be the basis of rational decision-making in conjunction with the Bayes theorem which acts as the key to the basis in which the beliefs should fit together with changing evidence scenario. Undoubtedly it is a major area of statistical endeavor which has hugely increased its profile both in context of theories and applications. The appreciation of the potential for Bayesian methods is growing fast both inside and outside the statistics community. The first encounter with Bayesian ideas by many people simply entails the discovery that a particular Bayesian method is superior to classical statistical methods on a particular problem or question. Nothing succeeds like success and this observed superiority .