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Séminaire Statistique

organisé par l'équipe Statistique

  • Julien Gibaud

    Identifiability of stochastic state-space models

    16 janvier 2026 - 11:00Salle de séminaires IRMA

    State-Space Models (SSMs) are deterministic or stochastic dynamical systems defined by two processes. The state process, which is not observed directly, models the transformation of the system states over time, while the observation process produces the observables on which model fitting and prediction are based. Ecology frequently uses stochastic SSMs to represent the imperfectly observed dynamics of population sizes or animal movement. However, several simulation-based evaluations of model performance suggest broad identifiability issues in ecological SSMs. Formal SSM identifiability is typically investigated using exhaustive summaries, which are simplified representations of the model. The theory on exhaustive summaries is largely based on continuous-time deterministic modelling and those for discrete-time stochastic SSMs have developed by analogy. While the discreteness of time does not constitute a challenge, finding a good exhaustive summary for a stochastic SSM is more difficult. The strategy adopted so far has been to create exhaustive summaries based on a transfer function of the expectations of the stochastic process. However, this evaluation of identifiability does not allow to take into account the possible dependency between the variance parameters and the process parameters. We show that the output spectral density plays a key role in stochastic SSM identifiability assessment. This allows us to define a new suitable exhaustive summary. Using several ecological examples, we show that usual ecological models are often theoretically identifiable, suggesting that most SSM estimation problems are due to practical rather than theoretical identifiability issues.

  • Marina Gomtsyan

    Variable selection methods in sparse GLARMA models

    23 janvier 2026 - 11:00Salle de séminaires IRMA

    We propose novel variable selection methods for sparse GLARMA (Generalised Linear Autoregressive Moving Average) models, which can be used for modelling discrete-valued time series. These models allow us to introduce some dependence in a Generalised Linear Model (GLM). The key idea behind our estimation procedure is first to estimate the coefficients of the ARMA part of the GLARMA model and then use a regularised approach, namely the Lasso, to estimate the regression coefficients of the GLM part of the model. Furthermore, we establish a sign-consistency result for the estimator of the regression coefficients in a sparse Poisson model without time dependence. The performance of our proposed methods was assessed on simulation studies in different frameworks and on several datasets in the field of molecular biology. Our approaches exhibit very good statistical performance, surpassing other methods in identifying non-null regression coefficients. Secondly, their low computational burden enables their application to relatively large datasets. Our proposed methods are implemented in R packages, which are publicly available on the Comprehensive R Archive Network (CRAN).

  • Jean-Armel Bra Kouadio

    Modèles autorégressifs modulés par une chaîne de Markov cachée avec innovations dépendantes

    6 février 2026 - 11:00Salle de séminaires IRMA

    Ces travaux portent sur l’estimation et l'inférence statistique des modèles de séries temporelles ARHMC (Autoregressive Hidden Markov Chain) à changements de régimes markoviens avec innovations dépendantes (i.e ARHMC(p) faibles). Nous avons développé des procédures d’estimation par la méthode des moments. Puis, nous avons établi les principales propriétés asymptotiques des estimateurs proposés. Nous avons également accordé une attention particulière à l'estimation de la matrice variance asymptotique de type sandwich. Pour le modèle ARHMC}(0) faible, nous construisons des tests portmanteau adaptés aux innovations dépendantes, permettant de tester l’adéquation du modèle et de sélectionner le nombre de régimes. Nous abordons également la prévision et le décodage de la chaîne cachée.

  • Yiye Jiang

    New sampling approaches for Shrinkage Inverse-Wishart distribution

    13 février 2026 - 11:00Salle de séminaires IRMA

    Covariance estimation has many applications, such as brain connectivity, portofolio allocation, to cite a few. Following a Bayesian approach, a typical covariance prior is the Inverse-Wishart distribution. However, a well-known issue of this prior is that it concentrates too little mass over covariance matrices with small eigengaps. To rebalance the mass, Berger et al. (2020, Annals of Statistics) proposed a more generic family, Shrinkage Inverse-Wishart, which thus offers a more flexible prior choice for covariance matrices. However, sampling from it remains challenging. The existing algorithm relies on a nested Gibbs sampler, which is slow and lacks rigorous theoretical convergence analysis. We propose a new algorithm based on the Sampling Importance Resampling method, which is significantly faster and comes with theoretical convergence guarantees. In this talk, we first derive the new sampling algorithm of Shrinkage Inverse-Wishart. Then we apply it to the inference of a Bayseian model of covariance estimation. We show inference results over a real data set of fMRI signals of rats.

  • Stéphane Lhaut

    Statistical Learning of Multivariate Extremes: finite sample analysis of tail risks

    20 février 2026 - 11:00Salle de séminaires IRMA

    Many problems in statistics (regression, classification, …) can be cast as specific instances of the general problem of minimizing a risk over a given class of functions. In practice, this risk is unknown and has to be estimated based on historical data. Statistical learning theory provides the tools to study the consistency properties of the solution to this empirical risk minimization procedure. In some problems, the tail of the covariate random vector plays a specific role in predicting the outcome. As such, it is of interest to study the tail risk arising from conditioning the risk on the covariate being larger than a threshold and letting this threshold tend to infinity. Making use of standard regular variation assumptions from extreme value analysis leads to the definition of tail risks based on the well-known angular measure for multivariate extremes. Studying the properties of empirical minimizers of such risks deserves special attention, and specific concentration tools have to be developed. We will explore these considerations mainly in the case of (tail) binary classification and propose new results for the general case.