Likelihood inferences with interval-censored data

En l’anàlisi de la supervivència el problema de les dades censurades en un interval es tracta, usualment,via l’estimació per màxima versemblança. Amb l’objectiu d’utilitzar una expressió simplificada de la funció de versemblança, els mètodes estàndards suposen que les condicions que produeixen la censura no afecten el temps de fallada. En aquest article formalitzem les condicions que asseguren la validesa d’aquesta versemblança simplificada. Així, precisem diferents condicions de censura no informativa i definim una condició de suma constant anàloga a la derivada en el context de censura per la dreta. També demostrem que les inferències obtingudes amb la versemblançaa simplificada són correctes quan aquestes condicions són certes. Finalment, tractem la identificabilitat de la funció distribució del temps de fallada a partir de la informació observada i estudiem la possibilitat de contrastar el compliment de la condició de suma constant.

The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

An Interval Intelligent-based Approach for Fault Detection and Modelling

Not considered in the analytical model of the plant, uncertainties always dramatically decrease the performance of the fault detection task in the practice. To cope better with this prevalent problem, in this paper we develop a methodology using Modal Interval Analysis which takes into account those uncertainties in the plant model. A fault detection method is developed based on this model which is quite robust to uncertainty and results in no false alarm. As soon as a fault is detected, an ANFIS model is trained in online to capture the major behavior of the occurred fault which can be used for fault accommodation. The simulation results understandably demonstrate the capability of the proposed method for accomplishing both tasks appropriately

Dynamic diagnosis based on interval analytical redundancy relations and signs of the symptoms

A model-based approach for fault diagnosis is proposed, where the fault detection is based on checking the consistencyof the Analytical Redundancy Relations (ARRs) using an interval tool. The tool takes into account the uncertainty in theparameters and the measurements using intervals. Faults are explicitly included in the model, which allows for the exploitation of additional information. This information is obtained from partial derivatives computed from the ARRs. The signs in the residuals are used to prune the candidate space when performing the fault diagnosis task. The method is illustrated using a two-tank example, in which these aspects are shown to have an impact on the diagnosis and fault discrimination, since the proposed method goes beyond the structural methods

Efficient interval scoring rules

Scoring rules that elicit an entire belief distribution through the elicitation of point beliefsare time-consuming and demand considerable cognitive e¤ort. Moreover, the results are validonly when agents are risk-neutral or when one uses probabilistic rules. We investigate a classof rules in which the agent has to choose an interval and is rewarded (deterministically) onthe basis of the chosen interval and the realization of the random variable. We formulatean e¢ ciency criterion for such rules and present a speci.c interval scoring rule. For single-peaked beliefs, our rule gives information about both the location and the dispersion of thebelief distribution. These results hold for all concave utility functions.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

On the concept of optimality interval

The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind.This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a baseball player is 0.334, what is the minimum number of times he has been at bat? In this paper, we tackle somehow the inverse question: given a rational number P/Q, what is the set of all numbers for which P/Q is a `best approximation' of one or the other kind? We prove that inboth cases these `Optimality Sets' are intervals and we give aprecise description of their endpoints.

Paleozoic stratigraphy of the Central and Northern part of the Catalonian Coastal Ranges (NE Spain)

The Paleozoic stratigraphic succession in the Catalonian Coastal Ranges spans the interval from Cambrian(?) to Carboniferous, with only one break, separating the pre-Carboniferous part of the sequence from the Carboniferous. The oldest rocks exposed form a sequence of schists, fine grained sandstones, gneisses (laminar pre-Hercynian intrusions), marbles, orto- and para-amphibolites and calcsilicate rocks. comparison with other localities iuggests an Early Cambrian age (or perhaps in part older). Upwards the sequence becomes more monotonous andconsists only of schists (or slates where themetamorphic grade is lower) and thin fine-grained sandstone layers (Cambrian-Ordovician). Still higher in the sequence, an altemation of greywackes and slates is found, with interlayered mud-supported conglomerates at its lower part and acid volcanic rocks which occur throughout the whole sequence. This part of the sequence has provided the oldest faunas known in the Catalonian Coastal Ranges, which indicate the Caradoc. Finally, in its uppermost part, the Ordovician sequence contains some thin limestone layers that contain Ashgill faunas. The Silurian, from Llandovery to Lower Ludlow, consists of black graptolitic shales with dolerite sills, whilst the upper Ludlow, Pridolian and Devonian consist of nodular limestones and marls withpelagic and hemipelagic faunas. The youngest Devonian faunas found correspond in general to the Emsian. The existence of a gap at this point of the sequence suggests the possibility that part of the Devonian could have been eroded. The Carboniferous is characterized by a thick culm sequence (Visean to Westphalian?), resting on thin chert and limestone layers (Tournaisian and Visean). A comparison with neighbouring areas shows a similarity regarding succession and facies with other Paleozoic massifs around the Western Mediterranean.