Related papers: Diffusion Copulas: Identification and Estimation

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model…

In this paper, we consider distributed simultaneous state and parameter estimation for a class of nonlinear systems, for which the augmented model comprising both the states and the parameters is only partially observable. Specifically, we…

We introduce a universal diffusion-based downscaling framework that lifts deterministic low-resolution weather forecasts into probabilistic high-resolution predictions without any model-specific fine-tuning. A single conditional diffusion…

Deep generative models offer powerful tools for multivariate data analysis, but their black-box architectures are often unidentified and difficult to interpret. We introduce the Deep Discrete Encoder (DDE) Copula, an identifiable and…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…

The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains foundational in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its…

The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…

Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus…

We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives,…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…