Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts

We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general assumptions on the division rate $B(x),$ its solution converges towards an oscillatory function,explicitely given by the projection of the initial state on the space generated by the countable set of the dominant eigenvectors of the operator. Despite the lack of hypo-coercivity of the operator, the proof relies on a general relative entropy argument in a convenient weighted $L^2$ space, where well-posedness is obtained via semigroup analysis. We also propose a non-dissipative numerical scheme, able to capture the oscillations

Online Sequential Monte Carlo smoother for partially observed stochastic differential equations

This paper introduces a new algorithm to approximate smoothed additive functionals for partially observed stochastic differential equations. This method relies on a recent procedure which allows to compute such approximations online, i.e. as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. This online smoother cannot be used directly in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that a similar algorithm may still be defined for partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. We prove that this estimator is consistent and its performance are illustrated using data from two models

Random effects compound Poisson model to represent data with extra zeros

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and predict species counts (discrete data) or abundance distributions (continuous data). Standard methods for modeling such data include mixture and two-part conditional models. Conversely to these methods, the stochastic models proposed here behave coherently with regards to a change of scale, since they mimic the harvesting of a marked Poisson process in the modeling steps. Random effects are used to account for inhomogeneity. In this paper, model design and inference both rely on conditional thinking to understand the links between various layers of quantities : parameters, latent variables including random effects and zero-inflated observations. The potential of these parsimonious hierarchical models for zero-inflated data is exemplified using two marine macroinvertebrate abundance datasets from a large scale scientific bottom-trawl survey. The EM algorithm with a Monte Carlo step based on importance sampling is checked for this model structure on a simulated dataset : it proves to work well for parameter estimation but parameter values matter when re-assessing the actual coverage level of the confidence regions far from the asymptotic conditions.Comment: 4

Asymptotic behavior of the local score of independent and identically distributed random sequences

AbstractLet (Xn)n⩾1 be a sequence of real random variables. The local score is Hn=max1⩽i<j⩽n(Xi+⋯+Xj). If (Xn)n⩾1 is a “good” Markov chain under its invariant measure, the Xi are centered, we prove that Hn/n converges in distribution to B1∗ when n→+∞, where B1∗=max0⩽u⩽1|Bu| and (Bu,u⩾0) is a standard Brownian motion, B0=0. If (Xn)n⩾1 a sequence of i.i.d. random variables, E(X1)=δ/n and Var(X1)=σ2>0, we prove the convergence of Hn/n to σξδ/σ where ξγ=max0⩽u⩽1{(B(u)+γu)−min0⩽s⩽u(B(s)+γs)}. We approximate the probability distribution function of ξγ and we determine the asymptotic behavior of P(ξγ⩾a),a→+∞

Construction the Statistics Distributions for Characterizing the Transfer Factors of Metals from Soil to Plant (TFsp) Using Bayesian Method

Plants have the faculty of  levy the metals in the soil. The consumption of this plants can represent in some situations a health risk to be assessed. The transfer of contaminants from soil to food crops is a major route connecting the soil contamination to human exposure. The Transfer Factors Soil-Plant (TFsp) (the ratio between the concentration of contaminants in plants and the concentration of contaminants in the soil) is a value commonly used in the assessment of exposure and health risks. This research use the BAPPET database (database contents the informations of elements metal traces plants and vegetables). The goal of this research is for define the variable that influent the variability of TFsp and for characterizing their effects from their posteriors distributions using bayesian methods, Metropolis-Hastings. There are 3 metals (Cd, As and Pb), 4 plant types (leaf, fruit, root and tuber) and 2 analysis (using 4 plant types and 3 plant types, without tuber) with 4 models of analysis of varians (ANOVA, using normal and lognormal distribution for likelihood) that used in this research. The results of analysis for 4 plant types is chosing the model II with lognormal distribution for likelihood (yi ~ LN(µi, σi2)) for the best model and for 3 plant types is chosing the model IV with lognormal distribution for likelihood (yi ~ LN(µi, σ2), µi = µ + αi + Bj + δk, Bj ~ N(0, σB2)) for the best model. The contains of metal Cd, As and Pb in leaf has the highest risk for the health because that has the biggest posterior mean of TFsp

Low prevalence of chronic kidney disease in Far-East Asian populations: impact of the ethnicity factor?

peer reviewe

Approximation of the distribution of the supremum of a centered random walk. Application to the local score.

We determine the rate of convergence of the distribution function of the one-sided supremum of a centered random walk to its limit

stop Smoking Help: A Need

peer reviewedToday the smoker carries a risk of mortality 70% higher compared to the nonsmoker. In Belgium active smoking is indisputably the most important cause of avoidable death. In 2004 it appears that 27% of the belgian population was smoking. This review describes the comorbidity associated with active tobacco consumption and defines the concepts of dependence and smoking cessation. It also identifies the three factors which determine the success of smoking cessation, i.e. the degree of nicotinic dependence, the presence of anxio-depressive disorders and the importance of the motivation to the stop