Related papers: Inversion Copulas from Nonlinear State Space Model…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional…

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…

In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation…

Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…

With insurers benefiting from ever-larger amounts of data of increasing complexity, we explore a data-driven method to model dependence within multilevel claims in this paper. More specifically, we start from a non-parametric estimator for…

State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent…

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges,…

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation…

To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate…

This paper considers a linear regression model with an endogenous regressor which arises from a nonlinear transformation of a latent variable. It is shown that the corresponding coefficient can be consistently estimated without external…

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density…

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…

Most common parametric families of copulas are totally ordered, and in many cases they are also positively or negatively regression dependent and therefore they lead to monotone regression functions, which makes them not suitable for…

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…

We introduce new estimates and tests of independence in copula models with unknown margins using $\phi$-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the…

In this paper, we propose a new method to calculate the mode functions in the noncommutative power-law inflation model. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied are generated inside…

We consider a model of inflation consisting a single fluid with a time-dependent equation of state. In this phenomenological picture, two periods of inflation are separated by an intermediate non-inflationary stage which can be either a…