Stylianos Georgiadis

Uncertainty Management and Sensitivity Analysis

Uncertainty is always there and LCA is no exception to that. The presence of uncertainties of different types and from numerous sources in LCA results is a fact, but managing them allows to quantify and improve the precision of a study and the robustness of its conclusions. LCA practice sometimes suffers from an imbalanced perception of uncertainties, justifying modelling choices and omissions. Identifying prevalent misconceptions around uncertainties in LCA is a central goal of this chapter, aiming to establish a positive approach focusing on the advantages of uncertainty management. The main objectives of this chapter are to learn how to deal with uncertainty in the context of LCA, how to quantify it, interpret and use it, and how to communicate it. The subject is approached more holistically than just focusing on relevant statistical methods or purely mathematical aspects. This chapter is neither a precise statistical method description, nor a philosophical essay about the concepts of uncertainty, knowledge and truth, although you will find a little bit of both. This chapter contains (1) an introduction of the essential terminology and concepts of relevance for LCA; (2) a discussion of main sources of uncertainty and how to quantify them; (3) a presentation of approaches to calculate uncertainty for the final results (propagation); (4) a discussion of how to use uncertainty information and how to take it into account in the interpretation of the results; and finally (5) a discussion of how to manage, communicate and present uncertainty information together with the LCA results.

First hitting probabilities for semi markov chains and estimation

ABSTRACT We first consider a stochastic system described by an absorbing semi-Markov chain (SMC) with finite state space, and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible SMC. In the latter case, a non-parametric estimator for the first hitting probability is proposed and the asymptotic properties of strong consistency and asymptotic normality are proven. Finally, a numerical application on a five-state system is presented to illustrate the performance of this estimator.

Nonparametric Estimation of Interval Reliability for Discrete-Time Semi-Markov Systems

In this article, we consider a repairable discrete-time semi-Markov system with finite state space. The measure of the interval reliability is given as the probability of the system being operational over a given finite-length time interval. A nonparametric estimator is proposed for the interval reliability, and the asymptotic properties of the strong consistency and the asymptotic normality for this estimator are proved. A numerical application concerning a four-state semi-Markov system is also presented.

Nonparametric Estimation of the Stationary Distribution of a Discrete-Time Semi-Markov Process

In this article, we consider a discrete-time semi-Markov process with finite state space and an observation censored at an arbitrary fixed time. Some intermediate results concerning the empirical estimation of the mean recurrence times of the embedded Markov process and the mean sojourn times of the semi-Markov process are given. We study two nonparametric estimators for the stationary distribution of the semi-Markov process and examine their asymptotic properties, such as strong consistency and asymptotic normality, as the length of the observation tends to infinity. Finally, a numerical application is presented to illustrate the comparison of the two estimators.

On the Weak Convergence of an Empirical Estimator of the Discrete-Time Semi-Markov Kernel

In this chapter, we consider the discrete-time semi-Markov processes with finite state space and the empirical estimator of the semi-Markov kernel. The basic definitions concerning the semi-Markov processes are presented. We study the weak convergence of the empirical estimator of the discrete-time semi-Markov kernel. Next, we present the corresponding weak convergence theorem for the empirical estimator of some related measures. The proofs of our results are based on semimartingales.