Bayesian inference for power law processes with applications in repairable systems

Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a nonhomogeneous Poisson process with the power law process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of (β,η), where β is the elasticity of the mean number of events with respect to time and η is the mean number of events for the period in which the system was actually observed. It is shown that β and η are orthogonal and that the likelihood becomes proportional to a product of gamma densities. Therefore, the family of natural conjugate priors is also a product of gammas. The idea is extended to the case that several realizations of the same PLP are observed along overlapping periods of time. Some Monte Carlo simulations are provided to study the frequentist behavior of the Bayesian estimates and to compare them with the maximum likelihood estimates. The results are applied to a real problem concerning the determination of the optimal periodicity of preventive maintenance for a set of power transformers. Prior distributions are elicited for β and η based on their operational interpretation and engineering expertise.     

A Combined Monte Carlo and Possibilistic Approach to Uncertainty Propagation in Event Tree Analysis

In risk analysis, the treatment of the epistemic uncertainty associated to the probability of occurrence of an event is fundamental. Traditionally, probabilistic distributions have been used to characterize the epistemic uncertainty due to imprecise knowledge of the parameters in risk models. On the other hand, it has been argued that in certain instances such uncertainty may be best accounted for by fuzzy or possibilistic distributions. This seems the case in particular for parameters for which the information available is scarce and of qualitative nature. In practice, it is to be expected that a risk model contains some parameters affected by uncertainties that may be best represented by probability distributions and some other parameters that may be more properly described in terms of fuzzy or possibilistic distributions. In this article, a hybrid method that jointly propagates probabilistic and possibilistic uncertainties is considered and compared with pure probabilistic and pure fuzzy methods for uncertainty propagation. The analyses are carried out on a case study concerning the uncertainties in the probabilities of occurrence of accident sequences in an event tree analysis of a nuclear power plant.     

Robust linear mixed models for Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.     

Classification of biomedical signals for differential diagnosis of Raynaud's phenomenon

This paper discusses a supervised classification approach for the differential diagnosis of Raynaud's phenomenon (RP). The classification of data from healthy subjects and from patients suffering for primary and secondary RP is obtained by means of a set of classifiers derived within the framework of linear discriminant analysis. A set of functional variables and shape measures extracted from rewarming/reperfusion curves are proposed as discriminant features. Since the prediction of group membership is based on a large number of these features, the high dimension/small sample size problem is considered to overcome the singularity problem of the within-group covariance matrix. Results on a data set of 72 subjects demonstrate that a satisfactory classification of the subjects can be achieved through the proposed methodology.     

Unemployment and Search for Work: Exploratory Analyses of Labour Market Attachment using CPS-Type Data

Abstract. This paper deals with measuring unemployment and labour market attachment in Italy, on the basis of CPS-type survey data. It is shown that the size and rate of unemployment are highly sensitive to modest variations in the definition of unemployment. This motivates a different approach. Based on the answers to a set of questions on search for work, a cluster analysis is performed, which yields four well established groups. Comparing them with the official labour force classifications, two “grey areas” appear at the borders between employment, unemployment and inactivity, which are of some interest in interpreting labour market attachment.     

On the Intuition of Rank-Dependent Utility

Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rank-dependence and comonotonicity. It has been suggested that these concepts are technical tools that have no intuitive or empirical content. This paper describes such contents. As a result, rank-dependence and comonotonicity become natural concepts upon which preference conditions, empirical tests, and improvements in utility measurement can be based. Further, a new derivation of the rank-dependent models is obtained. It is not based on observable preference axioms or on empirical data, but naturally follows from the intuitive perspective assumed. We think that the popularity of the rank-dependent theories is mainly due to the natural concepts used in these theories.     

Ranking and Prioritization of Emergency Departments Based on Multi-indicator Systems

In this work we discuss how Emergency Departments (EDs) can be ranked on the basis of multiple indicators. This problem is of absolute relevance due to the increasing importance of EDs in regional healthcare systems and it is also complex as the number of indicators that have been proposed in the literature to measure ED performance is very high. Current literature faces this problem using synthetic (or numerically aggregated) indicators of a set of performance measures but, although simple, this solution has a number of drawbacks that make this choice inefficient: a compensation effect among the indicators; a high degree of subjectivism in the indicators weighting; opacity in the decision making; all the EDs are considered to be comparable. Indeed, the situations in which EDs are comparable (i.e. when all the performance of one ED are not lower than the performance indicators of the other) are a minority and incomparability is by itself a source of information that should be used to identify situations for which different policy actions should be designed. In this work we propose to use non compensatory composite indicators and partial ordering theory to rank and compare EDs giving value to the reasons of such an incomparability. These methods are applied on a case study of 19 EDs in an administrative region in Italy.     

Regret theory and risk attitudes

We examine risk attitudes under regret theory and derive analytical expressions for two components—the resolution and regret premiums—of the risk premium under regret theory. We posit that regret-averse decision makers are risk seeking (resp., risk averse) for low (resp., high) probabilities of gains and that feedback concerning the foregone option reinforces risk attitudes. We test these hypotheses experimentally and estimate empirically both the resolution premium and the regret premium. Our results confirm the predominance of regret aversion but not the risk attitudes predicted by regret theory; they also clarify how feedback affects attitudes toward both risk and regret.     

The role and significance of endogenous firing costs in a matching model with endogenous job destruction

Traditional models of the labor market assume fixed firing costs. This paper explores the implications of variable firing costs, building this new assumption into a matching model with endogenous job destruction. The available evidence on the outcomes of cases brought to labor courts suggests that firing costs are negatively related with labor market tightness. In such a case, we may no longer invoke “rigidities” on labor markets as the cause of their poor performance. Our model yields three interesting results. First, labor markets may have multiple equilibria that cannot be Pareto-ordered; each with its own configuration in terms of average duration of unemployment and filled jobs, as well as employment protection. Second, the variability of firing costs produces a positive externality affecting the stability properties of these equilibria. Finally, the two externalities affect the efficiency of the social optimum, modifying the Hosios [Hosios, A.J., 1990. On the efficiency of matching and related models of search and unemployment. Review of Economic Studies 57, 279–298] condition. We use these results to interpret the recent history of European unemployment.