2,415,182 research outputs found
Cooperative Interval Games Arising from Airport Situations with Interval Data
This paper deals with the research area of cooperative interval games arising from airport situations with interval data. We also extend to airport interval games some results from classical theory.cooperative interval games;concave games;airport games;cost games;interval data
Generation interval contraction and epidemic data analysis
The generation interval is the time between the infection time of an infected
person and the infection time of his or her infector. Probability density
functions for generation intervals have been an important input for epidemic
models and epidemic data analysis. In this paper, we specify a general
stochastic SIR epidemic model and prove that the mean generation interval
decreases when susceptible persons are at risk of infectious contact from
multiple sources. The intuition behind this is that when a susceptible person
has multiple potential infectors, there is a ``race'' to infect him or her in
which only the first infectious contact leads to infection. In an epidemic, the
mean generation interval contracts as the prevalence of infection increases. We
call this global competition among potential infectors. When there is rapid
transmission within clusters of contacts, generation interval contraction can
be caused by a high local prevalence of infection even when the global
prevalence is low. We call this local competition among potential infectors.
Using simulations, we illustrate both types of competition.
Finally, we show that hazards of infectious contact can be used instead of
generation intervals to estimate the time course of the effective reproductive
number in an epidemic. This approach leads naturally to partial likelihoods for
epidemic data that are very similar to those that arise in survival analysis,
opening a promising avenue of methodological research in infectious disease
epidemiology.Comment: 20 pages, 5 figures; to appear in Mathematical Bioscience
On Sharp Identification Regions for Regression Under Interval Data
The reliable analysis of interval data (coarsened data) is one of the
most promising applications of imprecise probabilities in statistics. If one
refrains from making untestable, and often materially unjustified, strong
assumptions on the coarsening process, then the empirical distribution
of the data is imprecise, and statistical models are, in Manskiās terms,
partially identified. We first elaborate some subtle differences between
two natural ways of handling interval data in the dependent variable of
regression models, distinguishing between two different types of identification
regions, called Sharp Marrow Region (SMR) and Sharp Collection
Region (SCR) here. Focusing on the case of linear regression analysis, we
then derive some fundamental geometrical properties of SMR and SCR,
allowing a comparison of the regions and providing some guidelines for
their canonical construction.
Relying on the algebraic framework of adjunctions of two mappings between
partially ordered sets, we characterize SMR as a right adjoint and
as the monotone kernel of a criterion function based mapping, while SCR
is indeed interpretable as the corresponding monotone hull. Finally we
sketch some ideas on a compromise between SMR and SCR based on a
set-domained loss function.
This paper is an extended version of a shorter paper with the same title,
that is conditionally accepted for publication in the Proceedings of
the Eighth International Symposium on Imprecise Probability: Theories
and Applications. In the present paper we added proofs and the seventh
chapter with a small Monte-Carlo-Illustration, that would have made the
original paper too long
Bayesian semiparametric inference for multivariate doubly-interval-censored data
Based on a data set obtained in a dental longitudinal study, conducted in
Flanders (Belgium), the joint time to caries distribution of permanent first
molars was modeled as a function of covariates. This involves an analysis of
multivariate continuous doubly-interval-censored data since: (i) the emergence
time of a tooth and the time it experiences caries were recorded yearly, and
(ii) events on teeth of the same child are dependent. To model the joint
distribution of the emergence times and the times to caries, we propose a
dependent Bayesian semiparametric model. A major feature of the proposed
approach is that survival curves can be estimated without imposing assumptions
such as proportional hazards, additive hazards, proportional odds or
accelerated failure time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS368 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- ā¦