Search

Hymenoscyphus fraxineus is an invasive forest fungal pathogen that induces severe dieback in European ash populations. The spread of the disease has been closely monitored in France by the forest health survey system. We have developed a mechanisticstatistical model that describes the spread of the disease. It takes into account climate (summer temperature and spring rainfall), pathogen population dynamics (foliar infection, Allee effect induced by limited sexual partner encounters) and host density. We fitted this model using available disease reports. We estimated the parameters of our model, first identifying the appropriate ranges for the parameters, which led to a model reduction, and then using an adaptive multiple importance sampling algorithm for fitting. The model reproduces well the propagation observed in France over the last 20 years. In particular, it predicts the absence of disease impact in the south-east of the country and its weak development in the Garonne valley in south-west France. Summer temperature is the factor with the highest overall effect on disease spread, and explains the limited impact in southern France. Among the different temperature indices tested, the number of summer days with temperatures above 28{\textdegree}C gave the best qualitative behavior and the best fit. In contrast, the Allee effect and the heterogeneity of spring precipitation did not strongly affect the overall expansion of H. fraxineus in France and could be neglected in the modeling process. The model can be used to infer the average annual dispersal of H. fraxineus in France.

We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean telomere length and its age. We study its Malthusian's behaviour and provide numerical simulations to understand the influence of biologically relevant parameters.

We propose a new methodology for selecting and ranking covariates associated with a variable of interest in a context of high-dimensional data under dependence but few observations. The methodology successively intertwines the clustering of covariates, decorrelation of covariates using Factor Latent Analysis, selection using aggregation of adapted methods and finally ranking. Simulations study shows the interest of the decorrelation inside the different clusters of covariates. We first apply our method to transcriptomic data of 37 patients with advanced non-small-cell lung cancer who have received chemotherapy, to select the transcriptomic covariates that explain the survival outcome of the treatment. Secondly, we apply our method to 79 breast tumor samples to define patient profiles for a new metastatic biomarker and associated gene network in order to personalize the treatments.

We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which covariates are involved in the model. In this framework, we deal with L1-penalised regression models. To handle the choice of the penalty parameter to perform variable selection, we develop a new method based on the knockoffs idea. This revisited knockoffs method is general, suitable for a wide range of regressions with various types of response variables. Besides, it also works when the number of observations is smaller than the number of covariates and gives an order of importance of the covariates. Finally, we provide many experimental results to corroborate our method and compare it with other variable selection methods., Comment: arXiv admin note: text overlap with arXiv:1805.10097

We propose a new centered autologistic spatio-temporal model for binary data on a lattice. The centering allows the interpretation of the autoregression coefficients in separating the large scale structure of the model corresponding to an expected mean and the small-scale structure corresponding to the auto-correlation. We discuss the existence of the joint law of the process and show by simulation the interest of this kind of centering. We propose and show the efficiency of the maximum pseudo-likelihood estimator and also a method to choose the best structure of neighborhood. Method is applied to model and fit epidemiological data about Esca disease on a vineyard of the Bordeaux region.

We consider the problem of variable selection when the response is ordinal, that is an ordered categorical variable. In particular, we are interested in selecting quantitative explanatory variables linked with the ordinal response variable and we want to determine which predictors are relevant. In this framework, we choose to use the polytomous ordinal logistic regression model using cumulative logits which generalizes the logistic regression. We then introduce the Lasso estimation of the regression coefficients using the Frank-Wolfe algorithm. To deal with the choice of the penalty parameter, we use the stability selection method and we develop a new method based on the knockoffs idea. This knockoffs method is general and suitable to any regression and besides, gives an order of importance of the covariates. Finally, we provide some experimental results to corroborate our method. We then present an application of this regression method for network inference of zero-inflated variables and use it in practice on real abundance data in an agronomic context., Comment: This article is an old version of arXiv:1907.03153

As part of optimizing the reliability, Thales Optronics now includes systems that examine the state of its equipment. The aim of this paper is to use hidden Markov Model to detect as soon as possible a change of state of optronic equipment in order to propose maintenance before failure. For this, we carefully observe the dynamic of a variable called "cool down time" and noted Tmf, which reflects the state of the cooling system. Indeed, the Tmf is an indirect observation of the hidden state of the system. This one is modelled by a Markov chain and the Tmf is a noisy function of it. Thanks to filtering equations, we obtain results on the probability that an appliance is in degraded state at time $t$, knowing the history of the Tmf until this moment. We have evaluated the numerical behavior of our approach on simulated data. Then we have applied this methodology on our real data and we have checked that the results are consistent with the reality. This method can be implemented in a HUMS (Health and Usage Monitoring System). This simple example of HUMS would allow the Thales Optronics Company to improve its maintenance system. This company will be able to recall appliances which are estimated to be in degraded state and do not control to soon those estimated in stable state., Comment: 11 pages, 9 figures

A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the dependence structure within genealogical trees. Its main new feature is the joint use of all available information from several data sets instead of single data set estimation, to avoid the drawbacks of low accuracy for estimators or low power for tests on small single-trees. The data is modeled by an asymmetric bifurcating autoregressive process and possibly missing observations are taken into account by modeling the genealogies with a two-type Galton-Watson process. Least-squares estimators of the unknown parameters of the processes are given and symmetry tests are derived. Results are applied on real data of Escherichia coli division and an empirical study of the convergence rates of the estimators and power of the tests is conducted on simulated data.

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.

This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. The paper is illustrated by a numerical example.

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.

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.

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

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.

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events are observed exactly. A heuristic likelihood can be written for such models, at least for Markov models; however, a formal proof is not easy and has not been given yet. We present a general class of possibly non-Markov multistate models which can be represented naturally as multivariate counting processes. We give a rigorous derivation of the likelihood based on applying Jacod's formula for the full likelihood and taking conditional expectation for the observed likelihood. A local description of the likelihood allows us to extend the result to a more general coarsening observation scheme proposed by Commenges & G\'egout-Petit. The approach is illustrated by considering models for dementia, institutionalization and death.

We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic processes, as in Aalen (1987); then we define direct and indirect influence. We propose a definition of causal influence using the concepts of ``physical system''. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of this paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for HIV load and CD4 counts. We show its inadequacy to capture causal influences while on the contrary known mechanisms of HIV infection can be expressed directly through a system of differential equations., Comment: 43 pages, 3 figures

We develop a study of ignorability and conditions thereof for likelihood inference in the framework of stochastic processes. We define a coarsening model for processes which includes discrete-time observations as well as censored continuous-time observations and applies to continuous state-space processes as well as counting processes. For preparing the work we recall formulas for manipulating marginal and conditional likelihood ratios (which can apply to stochastic processes). Ignorability is defined in terms of local equality of two likelihood ratios. We give static conditions of ignorability and then dynamical conditions which are more interpretable. We illustrate the use of the dynamical conditions of ignorability in problems of censoring, missing data and joint modelling., Comment: 31 pages, 2 figures