Introduction to Bayesian Estimation and Copula Models of Dependence

Due to the recent progress of communication tools and the globalization of the world economy and information space, our physical lives, economical existences, and information fields are becoming more and more interrelated. Many processes that were successfully modelled in the past by probability and statistical methods assuming independent behavior of the components are becoming more and more intertwined. Brownian motion and Newtonian mechanics are still utilized, but they often fail to serve as good models for many complicated systems with component interactions. This explains an increased interest to model statistical dependence whether it be dependence of physical lives in demography and biology, dependence of financial markets, or dependence between the components of a complex engineering system.  This book is structured in two parts: the first four chapters form the first part of the book which can be used aspresents a general introduction to Bayesian statistics with a clear emphasis on the parametric estimation; and the following four chapters stress statistical models of dependence with a focus of copulas.  Copulas provide an attractive alternative to traditional tools such as correlation analysis or Cox’s proportional hazards. The key factor in the popularity of copulas is their applicability to risk management and their ability to model entire joint distribution functions that are not limited to moments. This allows for the treatment of non-linear dependence including joint tail dependence, which extends far beyond the standard analysis of correlation. The limitations of more traditional correlation-based approaches to modeling risks were felt around the world during the last financial crisis, i.e. copulas found their way into Basel Accord II documents regulating the world banking system, Bayesian methods are mentioned in recent FDA recommendations, etc.