Mauro Bernardi

A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities

This paper is of methodological nature, and deals with the foundations of Risk Assessment. Several international guidelines have recently recommended to select appropriate/relevant Hazard Scenarios in order to tame the consequences of (extreme) natural phenomena. In particular, the scenarios should be multivariate, i.e., they should take into account the fact that several variables, generally not independent, may be of interest. In this work, it is shown how a Hazard Scenario can be identified in terms of (i) a specific geometry and (ii) a suitable probability level. Several scenarios, as well as a Structural approach, are presented, and due comparisons are carried out. In addition, it is shown how the Hazard Scenario approach illustrated here is well suited to cope with the notion of Failure Probability, a tool traditionally used for design and risk assessment in engineering practice. All the results outlined throughout the work are based on the Copula Theory, which turns out to be a fundamental theoretical apparatus for doing multivariate risk assessment: formulas for the calculation of the probability of Hazard Scenarios in the general multidimensional case ( d≥2) are derived, and worthy analytical relationships among the probabilities of occurrence of Hazard Scenarios are presented. In addition, the Extreme Value and Archimedean special cases are dealt with, relationships between dependence ordering and scenario levels are studied, and a counter-example concerning Tail Dependence is shown. Suitable indications for the practical application of the techniques outlined in the work are given, and two case studies illustrate the procedures discussed in the paper.

Conditional risk based on multivariate hazard scenarios

We present a novel methodology to compute conditional risk measures when the conditioning event depends on a number of random variables. Specifically, given a random vector

Efficacy of biological agents administered as monotherapy in rheumatoid arthritis: a Bayesian mixed-treatment comparison analysis

(\mathbf {X},Y)

Sparse Networks Through Regularised Regressions

(X,Y), we consider risk measures that express the risk of Y given that

Approximate EM Algorithm for Sparse Estimation of Multivariate Location–Scale Mixture of Normals

\mathbf {X}

Multiple seasonal cycles forecasting model: the Italian electricity demand

X assumes values in an extreme multidimensional region. In particular, the considered risky regions are related to the AND, OR, Kendall and Survival Kendall hazard scenarios that are commonly used in environmental literature. Several closed formulas are considered (especially in the AND and OR scenarios). An application to spatial risk analysis involving real data is discussed.