Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived. The impact of these equivalence results is that it justifies the use of the Euler scheme instead of the discretized diffusion process for inference purposes.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1216 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Approximation of epidemic models by diffusion processes and their statistical inference

Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating $(Z(t))$. First, \previous results on the approximation of density-dependent $SIR$-like models by diffusion processes with small diffusion coefficient $\frac{1}{\sqrt{N}}$, where $N$ is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number $n$ of observations, which corresponds to the epidemic context, and for $N\rightarrow \infty$. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as $R_0$ (the basic reproduction number), $N$, $n$ are investigated on simulations. Two models, $SIR$ and $SIRS$, corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.Comment: 30 pages, 10 figure

The future of research and innovation policies : Is the intermediate layer what we thought it would be ?

Présentation pdf consultable sur Internet : http://www.utwente.nl/mb/steps/news/bestanden/presentations_Arie_symposium_2011/laredo.pd

Knowledge circulation and the valorisation of technologies

Présentation pdf consultable sur Internet : http://www.madrimasd.org/informacionidi/madrimasd-tv/seminario-valorizacion-tecnologias/docs/Conferencia-inagural_Philippe-Laredo.pd

Understanding the emergence and deployment of “nano” S&T

As an introduction to the special issue on “emerging nanotechnologies”, this paper puts in perspective contemporary debates and challenges about nanotechnology. It presents an overview of diverse analyses and expectations about this presumably revolutionary set of technological, scientific and industrial developments. Three main lines of argument can then be delineated: first of all, the degree of cumulativeness of science and technologies and the respective roles of newcomers and incumbents in the industrial dynamics; second the knowledge dynamics in nanotechnologies, especially the linkages by science and technology and third the role of institutions (network, geographic agglomeration and job market). It finally discusses methodologies to delineate the field of nanotechnologies and to collect data. For more informations: http: //www.nanoeconomics.eu/Nanotechnology; Industrial dynamics; Science policy; Institution

THE NEXT GENERATION IN STI STUDIES : KEYNOTE FOR THE 50TH YEAR OF SCIENCE AND INNOVATION STUDIES AT THE UNIVERSITY OF MANCHESTER NOVEMBER 4, 2017

International audienc

Dimensions of internationalisation – universities at home and abroad: A position Paper

Educational activities have not been exempt from the trends towards globalisation of economic and cultural activity. The environment in which universities operate is characterised by finance, goods, services, knowledge and cultural activities flowing across borders in the context of worldwide markets, multinational organisations and competition. Most pertinent is the growing movement of people, temporary and permanent. Analysts of the international activities of universities regularly distinguish between internationalisation and the wider context of globalisation. In this chapter we shall define internationalisation as the sum total of the practices universities develop to adapt to this new context

Changing patterns of public research funding in France

In this paper, we critically assess the specificity of the French research system and of its funding mode, which is accepted in most of the literature on the subject. We show that this interpretation is largely a result of the use of categories for the analysis of public funding that are not really suited to the French case. We thus develop two new categories: joint laboratories as a distinct organisational structure between public research organisations and universities; and human resources funding as a description of the specific allocation mode of CNRS (Centre National de la Recherche Scientifique) to the joint laboratories, which we consider as more similar to project funding than to core funding. We then show that the French system has changed fundamentally in the last two decades, moving towards a system much nearer to other European countries than normally assumed, albeit following a distinct evolutionary trajectory based on the gradual restructuring of existing instruments. In methodological terms, this underlines the importance of adapting the categories for the analysis of funding systems to the specificities of each national contex

Parametric inference for discrete observations of diffusion processes with mixed effects

Pré-publication, Document de travail HAL Id : hal-01332630, version 1Stochastic differential equations with mixed effects provide means to model intraindividual and in-terindividual variability in biomedical experiments based on longitudinal data. We consider N i.i.d. stochastic processes (Xi(t), t ∈ [0, T ]), i = 1,. .. , N , defined by a stochastic differential equation with linear mixed effects. We consider a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behaviour of estimators under the double asymptotic framework: the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within the fixed time interval [0, T ]. The estimation method is assessed on simulated data for various models comprised in our framework

A diffusion representation of the nonparametric iid experiment on a interval

We consider a diffusion model of small variance type with positive drift function varying in a nonparametric set. We investigate discrete versions of this continuous model with respect to statistical equivalence, in the sense of the asymptotic theory of experiments. It is shown that the collection of level crossing times for a uniform grid of levels is asymptotically equivalent to the continuous model in the sense of Le Cam's deficiency distance, when the discretization step decreases with the noise intensity ε. It follows that in the continuous diffusion model, the statistic of level crossing times is asymptotically sufficient. Since the level crossing times obey a nonparametric regression model with independent data, a further asymptotic equivalence can be established, leading to a simple Gaussian signal-in-white noise problem. When the drift density ƒ is also a probability density, this in turn is asymptotically equivalent to i.i.d. data with density ƒ on the unit interval