Please connect before the talk by using **
Zoom Calendar,** *click on the event of interest to obtain the
corresponding Zoom link (click to obtain the details of the event of interest).*
and
seminaries will be recorded on the **
Ecodep Youtube Channel.**

- __3/31/2021, 15:00__** Frederic Barraquand ** (IMB Bordeaux)
Inferring species interactions using Granger causality and convergent cross mapping. Slides

__Abstract__. How to reliably infer interactions between species from time series of their population densities is a long-standing goal of statistical ecology. Usually this inference is done using multivariate (linear) autoregressive models, defining interactions through Granger causality: x causes y whenever x helps predicting future y values. However, the entangled nature of nonlinear ecological systems has suggested an alternative causal inference method based on attractor reconstruction, convergent cross mapping, which is increasingly popular in ecology. Here, we compare the two methods. They uncover interactions with surprisingly similar performance for predator-prey cycles, 2-species chaotic or stochastic competition, as well as 10- and 20-species networks. Thus, contrary to intuition, linear Granger causality remains useful to infer interactions in highly nonlinear ecological networks. We conclude on inevitable similarities between Granger-causal methods and convergent cross mapping due to interaction definitions, and provide suggestions to improve many-species interaction inference.

**Reference.**
F Barraquand, C Picoche, M Detto, F Hartig (2019). Inferring species interactions using Granger causality and convergent cross mapping.
https://arxiv.org/abs/1909.00731

- __3/24/2021, 14:00__** Benjamin Poignard **
(Riken AIP, Osaka) An introduction to sparsity: modelling, properties and applications.

__Abstract__. The application domains of sparse modelling have been substantially widened by the availability of high-dimensional data. In particular, high-dimensional statistical modelling is concerned with the significantly large number of parameters to estimate. To tackle the over-fitting issue, penalised/regularized estimation methods have been gaining much attention. In this talk, I will introduce the concept of sparsity together with the standard penalisation methods for sparse modelling and the implications in terms of statistical properties. To illustrate the relevance of sparse modelling, I will present some applications to models that typically suffer from the so-called curse of dimensionality.

**References.**
B Poignard, J-D Fermanian (2021). High-dimensional penalized arch processes.
Econometric Reviews
Volume 40, 2021 - Issue 1.

B Poignard, M Asai (2020). A Penalised OLS Framework for High-Dimensional
Multivariate Stochastic Volatility Models.
Papers In Economics
& Business, Discussion Paper 20-02.

- __3/10/2021, 16:00__** Julien Randon-Furling ** (Paris 1, Panthéon Sorbonne)
Convex Hulls of Random Walks.

__Abstract__.
This talk will cover a range of results on the convex hull of random walks in the plane and
in higher dimension:
expected perimeter length in the planar case, expected number of faces on the boundary,
expected d-dimensional volume, and other geometric properties of such random convex polytopes.
Applications in ecology include estimations of animals' home ranges and minimal habitat sizes in conservation parks.

**References.**
J Randon-Furling, D Zaporozhets (2020).
Convex hulls of several multidimensional Gaussian random walkls.
arXiv:2007.02768.

J Randon-Furling, F Wespi (2017).
Facets on the convex hull of *d*-dimensional Brownian and Lévy motion..
Physical Review E.

SN Majumdar, A Comtet, J Randon-Furling (2010).
Random convex hulls and extreme value statistics.
Journal of Statistical Physics.

- __1/27/2021, 15:00__** Benjamin Bobbia ** (CYU & Univ. Franche-Comté)
Extreme quantile regression: A coupling approach and Wasserstein distance. Slides

__Abstract__.
In this work, we develop two coupling approaches for extreme quantile regression. We
consider i.i.d copies of Y in R and X in R^d and we want an estimation of the conditional
quantile of Y given X = x of order 1- alpha for a very small alpha > 0.

We introduce the proportional tail model, strongly inspired by the heteroscedastic
extremes developed by Einmahl, de Haan and Zhou. The main assumption is that the
tail distribution of Y is asymptotically proportional to the conditional tail of Y given
X = x. We propose and study estimators of both model parameters and conditional
quantile, which are studied by coupling methods.

**References.**
B Bobbia, C Dombry, D Varron (2020). The coupling method in extreme value theory.
https://arxiv.org/pdf/1912.03155

B Bobbia, C Dombry, D Varron (2020).
Extreme quantile regression in a proportional tail framework.
https://arxiv.org/pdf/2002.01740

- __12/2/2020, 16:00__** Rolando Rebolledo**
(University of Valparaiso) Open-system approach to ecological networks.
Abstract,
** Talk,** and
** Slides.**

**Reference.**
R Rebolledo, SA Navarrete, S Kéfi, S Rojas, PA Marquet.
An Open-System Approach to Complex Biological Networks.
SIAM Journal on Applied Mathematics, 79(2):619–640, 2019.

- __11/25/2020, 16:00,__** Félix Cheysson** (Agro-Paristech Paris)
Properties of Hawkes processes. **Talk,
Slides.**

__Abstract__. Hawkes processes are a family of stochastic processes for which the
occurrence of any event increases the probability of further events occurring. When count
data are only observed in discrete time, we propose a spectral approach for the estimation
of Hawkes processes, by means of Whittle's parameter estimation method. To get asymptotic
properties for the estimator, we prove alpha-mixing properties for the series of counts,
using the Galton-Watson properties of the cluster representation of Hawkes processes.
Simulated datasets and an application to the incidence of measles in France illustrate
the performances of the estimation, notably of the Hawkes excitation function, even when
the time between observations is large.

- __11/18/2020, 16:00,__** Marc Lavielle**
(Inria & CMAP, Polytechnique) Modelling the COVID 19 pandemic requires a model...
but also data! **Talk,
Slides**.

__Abstract.__
I will present in this talk some models for different Covid-19 data. I will first propose a
SIR-type model for the data provided by the Johns-Hopkins University for several countries:
these are the daily numbers of confirmed cases and deaths. The same model is used for all
countries but the parameters of the model change from one country to another to reflect
differences in dynamics. In particular, the model incorporates a time-dependent transmission
rate, whose variations are thought to be related to the public health measures taken by the
country in question.

I will then present a model for French hospital data provided by Santé Publique France: daily
numbers of hospitalization, admissions in intensive care units, deaths and hospital
discharges.

The proposed models may seem relatively simple, but it must be understood that they
do not pretend to describe the spread of the pandemic in a precise and detailed way.
Their role is to adjust the available data and provide reliable forecasts: their
complexity is therefore adjusted to the amount of information available in the data.
Indeed, very few parameters are needed to properly describe the outcome of interest
and the prediction proves to be stable over time.
Two interactive web applications are available to visualize the data and the adjusted
models:

http://shiny.webpopix.org/covidix/app1/
for JHU data,

http://shiny.webpopix.org/covidix/app3/
for SPF data.