Plenary talks

Maria Kateri
RWTH Aachen University
Germany

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Enrique Lopez Droguett 
UCLA
USA

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Luis E. Nieto-Barajas   
ITAM
Mexico

Title: Markov Processes in Survival Analysis

Abstract: In this talk we present some discrete and continuous Markov processes that have shown to be useful in survival analysis and other biostatistics applications. Both discrete and continuous time processes are used to define Bayesian nonparametric prior distributions. The discrete time processes are constructed via latent variables in a hierarchical fashion, whereas the continuous time processes are based on Lévy increasing additive processes. To avoid discreteness of the implied random distributions, these latter processes are further used as mixing measures of the parameters in a particular kernel, which lead to the so-called Lévy-driven processes. We include univariate and multivariate settings, regression models and cure rate models.

Bruno Tuffin
INRIA Rennes
France

Title: Importance Sampling for the Rare Event Simulation of Reliability Models

Abstract: Monte Carlo simulation methods are often the only tools to get an estimation of performance measures of complex systems. When dealing with the specific class of reliability, we typically require the estimation of probability of order 10^{-9} or even less. It is for example the case of one considers the probability of a failure of nuclear plant, the probability of ruin of an insurance company, the saturation probability in telecommunications… In this case, the crude Monte simulation method, which simply means simulating the system model as many times as possible to obtain the rare event a sufficient number of times is computationally inefficient. Specific methods have been developed in the literature for this rare context, mainly grouped into two classes, importance sampling and importance splitting (also called subset simulation).

During this talk, we are going to review the most efficient application of importance sampling on two types of reliability models: static and dynamic ones. Static models mean that we do not have a stochastic model evolving with time; the system typically has a huge space of states decomposed into two classes, where the system works and where the systems not operational. We often then look at the probability that the systems is down. Dynamic reliability models have components subject to failures and repairs, potentially grouped; we are here interested in the probability of failure of the whole system at a given time, over an interval of time, or the mean time to failure. In each case, we will describe how importance sampling can be applied and discuss the robustness of the estimators with respect to some rarity parameter. We will also discuss the determination of quantile of time to failure, of particular importance for warranty setup for example.