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Talks recorded on the
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- 05/18/2022, 14:00 Marina Friedrich
(Tinbergen Institute, Amsterdam) Room E554.
Sieve bootstrap inference for time-varying coefficient models
Abstract. We propose a sieve bootstrap framework to conduct
pointwise and simultaneous inference for time-varying coefficient regression
models based on a nonparametric local linear estimator. The asymptotic validity
of the sieve bootstrap in the presence of autocorrelation is established. We find
that it automatically produces a consistent estimation of nuisance parameters,
both at the interior and boundary points. In addition, we develop a bootstrap
test for parameter constancy and show that it is asymptotically correctly sized.
An extensive simulation study supports our findings. The proposed methods are
applied to assess the price development of CO2 certificates
in the European Emissions Trading System (EU ETS). We find evidence of time
variation in the relationship between allowance prices and their fundamental
price drivers. Working paper.
Slides.
- 05/4/2022, 14:00 Marion Borderon
(University of Vienna).
Room E554. Impact of climate change on human migration. Empirical Issues.
Abstract.
While there is general agreement in the scientific community that environmental
change could have a major impact on population distribution and migration patterns,
our knowledge of the nature and role of these impacts is still limited. Migration
decision processes are multifactorial, multi-scale and complex in nature, as can
be environmental change; involving therefore a significant number of challenges
when studying the nexus of both. Recent reviews of the literature highlight that
the current research field is mainly divided between detailed empirical case
studies on the micro level that often draw on self-reported environmental
information and with limited scope for generalization, and global and national
assessments on the macro level that do not sufficiently represent the local
situation. An interesting avenue is to harness survey data coupled with climate
or environmental data at the sub-national level in order to narrow the gap between
our theoretical knowledge and our capacity to empirically study the migration-climate
change nexus. Some examples of empirical approaches to the migration-climate
change nexus will be discussed.
- 05/2/2022, 14:00 (monday) Imma Curato
(University of Ulm).
Room E554. I
Light cones and supervised learning prediction tasks.
Abstract. Slides.
- 04/27/2022, 14:00 Pierre Jacob
(ESSEC, Cergy-Pontoise). Room E554.
Some methods based on couplings of Markov chain Monte Carlo algorithms.
Slides.
Abstract.
Markov chain Monte Carlo algorithms are commonly used to approximate a variety
of probability distributions. I will review the idea of coupling in the context
of Markov chains, and how this idea not only leads to theoretical analyses of
Markov chains but also to new Monte Carlo methods. In particular, the talk
will describe how coupled Markov chains can be used to obtain 1) unbiased
estimators of expectations and of normalizing constants, 2) non-asymptotic
convergence diagnostics for Markov chains, and 3) unbiased estimators of
the asymptotic variance of MCMC ergodic averages. The latter is based on novel
connections between the Poisson equation and coupled Markov chains.
- 04/13/2022, 14:00 Edouard Fouché
(KIT, Karlsruhe). Room E554.
Automated Decision Making for Sustainable Energy Systems.
Abstract.
Designing future energy systems under the ongoing green transition is one of the major challenges of the 21st century. In particular, with the increasing share of renewables and electric transportation, it has become highly challenging to coordinate operations between producers and consumers, as the grid must supply highly reliable and green power at any time. Grid operators, producers, and consumers must make optimal real-time decisions in the face of an ever-changing, distributed, and uncertain environment. Humans cannot reasonably make such decisions, i.e., decisions must be automated. While Automated Decision Making (ADM) has been of interest in Artificial Intelligence for over fifty years, existing techniques fall short regarding constraints of real-world applications, e.g., energy systems, in which uncertainties may be very diverse.
In this talk, I will present my vision to tackle this problem. Our goal is to develop new methods for data-driven decision making and respective tools to optimize the operation of large dynamic systems. We will particularly consider emerging energy systems, such as the so-called micro-grids and multi-modal networks; the interconnection between different energy carriers and networks offers new ways of coping with intermittent power generation and consumption. I will also present some of our previous contributions to ADM, such as our recent extensions of the Multi-Armed Bandit problem to a variable number of plays and non-stationary settings, as well as implications concerning knowledge discovery from massive streams of data.
Reference.
- 03/23/2022, 14:00 Federico Maddanu
(CYU Cergy-Pontoise). Forecasting highly persistent time series with
bounded spectrum processes. Slides.
Abstract.
Long memory models can be generalised by the Fractional equal-root
Autoregressive Moving Average (FerARMA) process, which displays short
memory for a suitable parameter's set. Consequently, the spectrum is bounded,
ensuring stationarity also for values of the memory parameter d larger than 0.5.
The FerARMA generalization is proposed here to forecast highly persistent
time series, as climate records of tree rings and paleo-temperature
reconstructions. The main advantage of a bounded spectrum allows for
more accurate predictions with respect to standard long memory models,
especially if a long-horizon is considered.
- 03/16/2022, 14:00 Federico Maddanu
(CYU Cergy-Pontoise)
with Tommaso Proietti
(Roma Torre Vergata). Time trends in atmospheric ethane. Slides.
Abstract.
Understanding the dynamics underlying ethane (C2H6) trends is of uttermost
importance in the context of climate change. We focus on time series of ethane
abundance in the atmosphere recorded at six ground-stations located in both
the Northern and Southern Hemispheres. The trend component is hidden by both
a strong persistent annual cycle and the large amount of missing data (about 70%). Our approach proposes a novel structural model where both the cycle and trend evolve stochastically and can be estimated via the Kalman filter methodology. The results suggest a global pattern in the dynamics of ethane trends in both the Northern and Southern Hemispheres.
- 03/9/2022, 14:00 Pierre-Olivier Goffard
(Laboratory SAF, ISFA, Lyon).
Sequential Monte Carlo samplers to fit and compare insurance loss models.
Slides.
Abstract.
Insurance loss distributions are characterized by a high frequency of small
amounts and a lower, but not insignificant, occurrence of large claim amounts.
Composite models, which link two probability distributions, one for the “belly”
and the other for the “tail” of the loss distribution, have emerged in the
actuarial literature to take this specificity into account. The parameters
of these models summarize the distribution of the losses. One of them
corresponds to the breaking point between small and large claim amounts.
The composite models are usually fitted using maximum likelihood estimation.
A Bayesian approach is considered in this work. Sequential Monte Carlo samplers
are used to sample from the posterior distribution and compute the posterior
model evidences to both fit and compare the competing models.
The method is validated via a simulation study and illustrated on insurance
loss datasets.
Reference.
- 02/23/2022, 14:00 Luca Rolla & Alessandro Giovannelli
(Roma Torre Vergata). Room E554.
The forecasting performance of the factor model with martingale difference errors.
Slides.
Abstract. We compare the forecasting performance of two
factor models for a
large set of macroeconomic and financial time series: (i) The standard
principal-component model used by Stock and Watson (2002) (ii) The factor
model with martingale difference errors recently introduced by Lee and Shao
(2018). The factor model with martingale difference errors allows to find a
linear transformation of the original series so that it is possible to
obtain a separation of the resulting variables, according to whether they
are conditionally mean independent upon past information or not. In terms
of prediction this feature of the model allows to achieve optimal results
in the mean squared error sense despite considering a smaller set of factors,
i.e., those factors that display some form of dependence in the conditional mean. We adopt the classical diffusion index (DI) approach proposed by Stock and Watson to compare the empirical performance of the two methods when forecasting a large dataset of macroeconomic and financial monthly time series for the U.S. economy.
- 02/16/2022, 14:00 Marie-Pierre Etienne
(AgroParistech, Rennes).
Statistical methods for understanding movement data.
Slides.
Abstract.
Movement of organisms is one of the main mechanisms who govern relations between species.
Advances in biologging open promising perspectives in the study of animal movements at numerous scales.
It is now possible to record time series of animal locations over extended areas and long durations
with a high spatial and temporal resolution. One question addressed with this sort of data is the
habitat preference selection, which can be defined as the relationship between the environmental
covariates and the stationnary distribution, known in ecology as resource selection function.
Using some ergodicity assumptions, it is possible to estimate this relationship
by long-term monitoring of an individual movement. We explore the use of Langevin model for
modelling animal movement in order to estimate the resource selection function.
Reference.
T Michelot, P Gloaguen, P G. Blackwell, M-P Étienne (2019)
The Langevin diffusion as a continuous-time model of animal movement and habitat selection.
Methods in Ecology and Evolution,
https://doi.org/10.1111/2041-210X.13275.
- 02/9/2022, 14:00 Laurence Reboul
(Aix-Marseille University, I2M). Room E554.
Estimation of Pickands dependence function of bivariate extremes under mixing conditions,
with M. Boutahar, I. Kchaou.
Slides.
Abstract.
- 06/30/2021, 14:00 Denys Pommeret
(Aix-Marseille University, I2M / laboratory SAF, ISFA).
Comparing copulas, with Yves Ngounou. Slides.
Abstract.
Copulas are still extensively studied and used to model the dependence of multivariate
observations. Many applications can be found in fields such as energy, environment or ecology.
In a one-sample case, there are many tests to compare an observed copula to a target copula.
In the two-sample case, Rémillard and Scaillet (2009) proposed a test to compare two nonparametric
copulas, that is to test H_{0}: C_{1 } = C_{2 },
where C_{1 } and C_{2 } are two copulas observed on two iid samples, which
may be paired. To our knowledge, there is no extension to the K sample case. However, the
increasing amount of data requires sometimes more comprehensive analyzes. It is in this sense that
we propose an equality test of K copulas simultaneously when K populations are observed.
We propose to test the following hypothesis: H_{0}: C_{1 } = C_{2 }= ⋯ = C_{K },
from K iid samples, possibly paired. It is therefore a generalization of Rémillard and
Scaillet (2009). However, we obtain the exact
asymptotic distribution of the test statistic and the convergence of the test. The idea of the test is to
transform the observations to uniform laws, then to use the decomposition of the density of the
copula in the Legendre polynomials orthogonal basis. Returning to the copula function we obtain
what are called copula coefficients which characterize each copula. The test then amounts to
simultaneously comparing these coefficients. We provide some illustrations of this method, in
particular we suggest a clustering algorithm to classify populations with similar forms of dependence.
Reference.
YI Ngounou B, D Pommeret (2020) Nonparametric estimation of copulas and copula densities
by orthogonal projections.
Arxiv-2010.15351.
- 06/23/2021, 14:00 Jüri Lember
(University of Tartu, Estonia).
An evolution model that satisfies detailed balance.
Abstract,
Slides.
Reference. J Lember, C Watkins (2020).
An Evolutionary Model that Satisfies Detailed Balance. Methodol. Comput. Appl. Probab.
doi.org/10.1007/s11009-020-09835-5.
- 06/9/2021, 14:00 Hansjörg Albrecher
(UNIL, Lausanne)
Asymptotic Analysis of the Greenwood Statistic and Extensions.
Abstract.
We revisit and unify the asymptotic analysis of the classical Greenwood
statistic comprising the ratio of
the sum of squares and the sum squared of independent and identically distributed
random variables with regularly varying tails. We discuss some of its application
areas and extend the analysis to the situation of arbitrary powers. Finally, we
study the robustness of the asymptotic expressions when some of the terms in
the statistic are dropped. Part of the talk is based on recent joint work with
Brandon Garcia-Flores.
References.
H Albrecher, S Ladoucette, J Teugels (2010). Asymptotics of the sample coefficient of variation and the sample dispersion.
JSPI, 140-2, 358-368.
Preprint.
H Albrecher, J Teugels (2007). Asymptotics analysis of a measure of variation.
Theor. Probability and Math. Statist. 74, 1–10.
- 6/2/2021, 14:00 Antonio Cuevas (Dept. Mat.
UAM, Madrid)
On the shape restrictions used in set estimation.
Abstract
Set estimation techniques deal with the problem of reconstructing a compact set S from a random sample of points.
Some shape restrictions on the target set S (often inspired on convexity-related notions) appear in a natural way in this context.
They are used at least in two ways: first, as a tool to simplify calculations when proving asymptotic results. Second, as a guide to construct natural estimators via the "hull paradigm" (the estimator is defined as the "minimal set" including the sample and fulfilling the assumed shape restriction). We will review here some recent contributions providing examples of both situations.
This talk is based on joint work with Alejandro Cholaquidis (Universidad de la República, Uruguay) and Catherine Aaron (Université de Clermont-Ferrand, France).
References.
C Aaron, A Cholaquidis, A Cuevas (2017).
Detection of low dimensionality and data denoising via set estimation techniques.
Electronic Journal of Statistics, 11, 4596-4628.
A Cholaquidis, A Cuevas (2020). Set estimation under biconvexity restrictions.
ESAIM: Probability and Statistics, 24, 770-788.
- 5/5/2021, 14:00 Kamila Kare (SAMM, Paris 1, Panthéon-Sorbonne)
Data Driven Model Selection for Same-Realization Predictions in Autoregressive Processes.
Slides.
Abstract. This paper is about the one-step ahead prediction of the future of observations
drawn from an infinite-order autoregressive AR(∞) process.It aims to design penalties
(completely data driven)
ensuring that the selected model verifies the efficiency property but in the non asymptotic framework.
We present an oracle inequality with a leading constant equal to one. Moreover, we also show that the
excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered
collection.
To achieve these results, we needed to overcome the dependence difficulties by following a classical
approach which consists in restricting to a set where the empirical covariance matrix is equivalent
to the theoretical one. We show that this event happens with probability larger than
1-c_{0}/n^{3} with c_{0}>0.
The proposed data driven criteria are based on the minimization of the penalized criterion akin
to the Mallows's C_{p}. Monte Carlo experiments are performed to highlight the obtained results.
Reference.
K Kare (2021). Data Driven Model Selection for Same-Realization Predictions in Autoregressive Processes.
Hal Preprint.
- 4/28/2021, 14:00 Alexander Kreiss (KU Leuven)
Non-Parametric Modelling of Interactions Among Vertices in Dynamic Networks.
Slides.
Abstract. We will consider dynamic networks in which the vertices (the actors) can interact
with each other along the edges of the network. We assume that over the observation period [0,T]
the number of vertices remains fixed while the edges between them may change randomly over time.
The occurrence of interactions between the actors is modelled by specifying a Cox-Type model
which allows for additional, time-varying covariates. Our interest lies in non-parametrically estimating
the (possibly) time-varying effect of the covariates on the interactions. To this end, we introduce a
kernel-based local likelihood estimator and study its asymptotic (as the network grows) performance.
Moreover, we introduce two test statistics which evaluate the fit of the non-parametric compared to parametric models. From a theoretical point of view a particular challenge when handling this type of data is that neighboring actors in the network influence each other and cannot be treated as independent. We introduce therefore weak dependence measures on dynamic networks based on correlation, mixing and temporal m-dependence. The results are illustrated on bike sharing data.
This is partially joint work with Enno Mammen (Heidelberg) and Wolfgang Polonik (UC Davis).
References.
A Kreiß, E Mammen, W Polonik (2019) Nonparametric inference for continuous-time event counting and link-based dynamic network models.
https://doi.org/10.1214/19-EJS1588.
A Kreiß (2019) Correlation bounds, mixing and m-dependence under random time-varying network distances with an application to Cox-Processes.
https://arxiv.org/abs/1906.03179.
A Kreiß, E Mammen, W Polonik (2021) Testing For a Parametric Baseline-Intensity in Dynamic Interaction Networks.
https://arxiv.org/abs/2103.14668.
- 4/7/2021, 14:00 Diu Tran (University of Jyväskylä, Helsinki)
Statistical inference for Vasicek-type model driven by Hermite processes.
Slides.
Abstract. Let Z denote a Hermite process of order q >= 1 and self-similarity parameter
H ∈ (1/2, 1).
This process is H-self-similar, has stationary increments and exhibits long-range dependence.
When q = 1, it corresponds
to the well-known fractional Brownian motion, whereas it is not Gaussian as soon as q >= 2.
In the talk, we deal with a Vasicek-type model driven by Z, of the form dX_{t} = a(b − X_{t})dt + dZ_{t}.
This model includes the fractional Vasicek model and Hermite-driven Ornstein-Uhlenbeck process.
Here, a > 0 and b ∈ R are considered as unknown drift parameters.
We provide estimators for a and b based on
continuous-time observations. For all possible values of H and q, we prove strong consistency and we analyze the asymptotic fluctuations.
This is a first step to estimate parameters of a stochastic equation driven by a Hermite process. Joint work with Prof.
Ivan Nourdin from University of Luxembourg.
Reference. I Nourdin, D Tran (2019): Statistical inference for Vasicek-type model driven by Hermite processes.
Stoch. Proc. Appl., 129, no. 10, pp. 3774-3791.
ArXiv.
- 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.
Slides.
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.
Slides.
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.