Search results for "Theorem"
showing 10 items of 1250 documents
Directed random walk on the backbone of an oriented percolation cluster
2012
We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary discrete-time contact process. We prove a law of large numbers and an annealed central limit theorem (i.e., averaged over the realisations of the cluster) using a regeneration approach. Furthermore, we obtain a quenched central limit theorem (i.e.\ for almost any realisation of the cluster) via an analysis of joint renewals of two independent walks on the same cluster.
Bayesian joint modeling for assessing the progression of chronic kidney disease in children.
2016
Joint models are rich and flexible models for analyzing longitudinal data with nonignorable missing data mechanisms. This article proposes a Bayesian random-effects joint model to assess the evolution of a longitudinal process in terms of a linear mixed-effects model that accounts for heterogeneity between the subjects, serial correlation, and measurement error. Dropout is modeled in terms of a survival model with competing risks and left truncation. The model is applied to data coming from ReVaPIR, a project involving children with chronic kidney disease whose evolution is mainly assessed through longitudinal measurements of glomerular filtration rate.
Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks
2015
Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epide…
Bayesian Markov switching models for the early detection of influenza epidemics
2008
The early detection of outbreaks of diseases is one of the most challenging objectives of epidemiological surveillance systems. In this paper, a Markov switching model is introduced to determine the epidemic and non-epidemic periods from influenza surveillance data: the process of differenced incidence rates is modelled either with a first-order autoregressive process or with a Gaussian white-noise process depending on whether the system is in an epidemic or in a non-epidemic phase. The transition between phases of the disease is modelled as a Markovian process. Bayesian inference is carried out on the former model to detect influenza epidemics at the very moment of their onset. Moreover, t…
Bayesian joint ordinal and survival modeling for breast cancer risk assessment
2016
We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model. Time-to-event is modeled through a left-truncated proportionalhazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the …
An autoregressive approach to spatio-temporal disease mapping
2007
Disease mapping has been a very active research field during recent years. Nevertheless, time trends in risks have been ignored in most of these studies, yet they can provide information with a very high epidemiological value. Lately, several spatio-temporal models have been proposed, either based on a parametric description of time trends, on independent risk estimates for every period, or on the definition of the joint covariance matrix for all the periods as a Kronecker product of matrices. The following paper offers an autoregressive approach to spatio-temporal disease mapping by fusing ideas from autoregressive time series in order to link information in time and by spatial modelling t…
Prospective analysis of infectious disease surveillance data using syndromic information.
2014
In this paper, we describe a Bayesian hierarchical Poisson model for the prospective analysis of data for infectious diseases. The proposed model consists of two components. The first component describes the behavior of disease during nonepidemic periods and the second component represents the increase in disease counts due to the presence of an epidemic. A novelty of our model formulation is that the parameters describing the spread of epidemics are allowed to vary in both space and time. We also show how syndromic information can be incorporated into the model to provide a better description of the data and more accurate one-step-ahead forecasts. These real-time forecasts can be used to …
Large deviations results for subexponential tails, with applications to insurance risk
1996
AbstractConsider a random walk or Lévy process {St} and let τ(u) = inf {t⩾0 : St > u}, P(u)(·) = P(· | τ(u) < ∞). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time τ(u) is described as u → ∞. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for downwards skip-free processes like the classical compound Poisson insurance risk process where the formulation is in terms of total variation convergence. The ideas of the proof involve excursions and path decompositions for Mark…
Bayesian survival analysis with BUGS
2020
Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programmin…
Reassessing Accuracy Rates of Median Decisions
2007
We show how Bruno de Finetti''s fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the radiological diagnosis of asbestosis. Conditional exchangeability of individual radiologists'' diagnoses is recognized as more appropriate than independence which is commonly presumed. The FTP yields coherent bounds on probabilities of interest when available information is insufficient to determine a complete distribution. Further assertions that are natural to the problem motivate a partial ordering of conditional probabilities, extending the computation …