Tim Bedford

Bio: Tim Bedford is an academic researcher from University of Strathclyde. The author has contributed to research in topics: Reliability (statistics) & Bayes' theorem. The author has an hindex of 26, co-authored 135 publications receiving 4806 citations. Previous affiliations of Tim Bedford include Delft University of Technology.

Vines: A new graphical model for dependent random variables

Abstract: A new graphical model, called a vine, for dependent random variables is introduced. Vines generalize the Markov trees often used in modelling high-dimensional distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence.

Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

Abstract: A vine is a new graphical model for dependent random variables Vines generalize the Markov trees often used in modeling multivariate distributions They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence A general formula for the density of a vine dependent distribution is derived This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions The so-called ‘canonical vines’ built on highest degree trees offer the most efficient structure for Gibbs sampling

Probabilistic Risk Analysis: Foundations and Methods

Abstract: Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible. The authors discuss the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgement and uncertainty propagation. The relationship of risk analysis with decision making is highlighted in chapters on influence diagrams and decision theory. Finally, the difficulties of choosing metrics to quantify risk, and current regulatory frameworks are discussed.

Probabilistic Risk Analysis: Probabilistic risk analysis

Abstract: Probabilistic risk analysis (PRA), also called quantitative risk analysis (QRA) or probabilistic safety analysis (PSA), is currently being widely applied to many sectors, including transport, construction, energy, chemical processing, aerospace, the military, and even to project planning and financial management. In many of these areas PRA techniques have been adopted as part of the regulatory framework by relevant authorities. In other areas the analytic PRA methodology is increasingly applied to validate claims for safety or to demonstrate the need for further improvement. The trend in all areas is for PRA to support tools for management decision making, forming the new area of risk management . Since PRA tools are becoming ever more widely applied, and are growing in sophistication, one of the aims of this book is to introduce the reader to the main tools used in PRA, and in particular to some of the more recent developments in PRA modeling. Another important aim, though, is to give the reader a good understanding of uncertainty and the extent to which it can be modeled mathematically by using probability. We believe that it is of critical importance not just to understand the mechanics of the techniques involved in PRA, but also to understand the foundations of the subject in order to judge the limitations of the various techniques available. The most important part of the foundations is the study of uncertainty. What do we mean by uncertainty? How might we quantify it?

Pair-copula constructions of multiple dependence

Abstract: Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically.

Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

Abstract: A vine is a new graphical model for dependent random variables Vines generalize the Markov trees often used in modeling multivariate distributions They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence A general formula for the density of a vine dependent distribution is derived This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions The so-called ‘canonical vines’ built on highest degree trees offer the most efficient structure for Gibbs sampling