118 research outputs found
Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes
This paper presents a nonparametric method for estimating the conditional
density associated to the jump rate of a piecewise-deterministic Markov
process. In our framework, the estimation needs only one observation of the
process within a long time interval. Our method relies on a generalization of
Aalen's multiplicative intensity model. We prove the uniform consistency of our
estimator, under some reasonable assumptions related to the primitive
characteristics of the process. A simulation example illustrates the behavior
of our estimator
Random coefficients bifurcating autoregressive processes
This paper presents a model of asymmetric bifurcating autoregressive process
with random coefficients. We couple this model with a Galton Watson tree to
take into account possibly missing observations. We propose least-squares
estimators for the various parameters of the model and prove their consistency
with a convergence rate, and their asymptotic normality. We use both the
bifurcating Markov chain and martingale approaches and derive new important
general results in both these frameworks
Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data
We present symmetry tests for bifurcating autoregressive processes (BAR) when
some data are missing. BAR processes typically model cell division data. Each
cell can be of one of two types \emph{odd} or \emph{even}. The goal of this
paper is to study the possible asymmetry between odd and even cells in a single
observed lineage. We first derive asymmetry tests for the lineage itself,
modeled by a two-type Galton-Watson process, and then derive tests for the
observed BAR process. We present applications on both simulated and real data
A general definition of influence between stochastic processes
We extend the study of weak local conditional independence (WCLI) based on a
measurability condition made by Commenges and G\'egout-Petit (2009) to a larger
class of processes that we call D'. We also give a definition related to the
same concept based on certain likelihood processes, using the Girsanov theorem.
Under certain conditions, the two definitions coincide on D'. These results may
be used in causal models in that we define what may be the largest class of
processes in which influences of one component of a stochastic process on
another can be described without ambiguity. From WCLI we can contruct a concept
of strong local conditional independence (SCLI). When WCLI does not hold, there
is a direct influence while when SCLI does not hold there is direct or indirect
influence. We investigate whether WCLI and SCLI can be defined via conventional
independence conditions and find that this is the case for the latter but not
for the former. Finally we recall that causal interpretation does not follow
from mere mathematical definitions, but requires working with a good system and
with the true probability
Modèles probabilistes pour l'initiation et la propagation de fissures
National audienceL'étude de la dégradation et du vieillissement des structures ou des matériels embarqués nécessite la modélisation de phénomènes mécaniques de fatigue. Cette modélisation conditionne les calculs de durées de vie et de probabilités d'occurrence d'événements redoutés et est donc particulièrement importante en ce qui concerne la sécurité. Même soumis à des régimes de fatigue contrôlés, les phénomènes d'initiation ou de propagation de fissures présentent un caractère aléatoire
Package 'armada' : A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependence
An R package, available on the CRAN. A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependenc
Network inference for truncated gaussian data
International audienc
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