ESOBE 2026

Title: Inferring model structure from data: MCMC for DAGs

Abstract: Inferring a directed acyclic graph (DAG) given data is computationally challenging. Current state-of-the-art MCMC methods for graph inference efficiently scan the space by first considering a restricted search space and iteratively expand the space until a stopping criterion is met. We estimate the error introduced from current methods that use restricted spaces compared to the full space and develop a novel MCMC method that reduces this error. The new adaptive algorithm allows for either expansion or contraction of the search space at any iteration. Extensive numerical experiments demonstrate the efficiency of the new algorithm and compare its performance with existing methods.

Title: Gaussian Invariant Markov Chain Monte Carlo

Abstract: We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second-order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that Gaussian invariant sampling can lead to ergodic estimators with significantly improved statistical efficiency. This is due to a remarkable property of Gaussian invariance that allows us to obtain exact analytical solutions to the Poisson equation for Gaussian targets. These solutions can be used to construct efficient and easy-to-use control variates for variance reduction of estimators under any intractable target. We demonstrate the new samplers and estimators in several examples, including high-dimensional targets in latent Gaussian models, where we compare against several advanced methods and obtain state-of-the-art results. We also provide theoretical results regarding geometric ergodicity and an optimal scaling analysis that shows the dependence of the optimal acceptance rate on the Gaussianity of the target.

Title: Multivariate extreme joint dependencies using nonparametric copulas

Abstract: We propose a novel multivariate copula model capable of capturing both central and tail dependence in joint probability distributions. Accurately modeling dependence structures, particularly in the joint tails, is crucial for applications in risk management, such as macroeconomics and finance. Our approach adopts a Bayesian nonparametric framework to construct a random copula model based on infinite partitions of unity. Specifically, we define a hierarchical prior over an infinite partition of the unit hypercube, which admits a stick-breaking representation and yields an infinite mixture of products of independent beta densities. Leveraging this stick-breaking formulation, we develop a Gibbs sampling algorithm for posterior inference. In our empirical analysis, we evaluate the proposed model using both simulated data and real datasets involving insurance claims and portfolio returns. We compare its ability to capture central and tail dependence against several parametric and nonparametric benchmark copula models. The results demonstrate that our model consistently outperforms competing approaches in both simulated and real-world scenarios.