Related papers: Nonparametric Bayesian volatility learning under m…

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by…

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

We consider the models Y_{i,n}=\int_0^{i/n} \sigma(s)dW_s+\tau(i/n)\epsilon_{i,n}, and \tilde Y_{i,n}=\sigma(i/n)W_{i/n}+\tau(i/n)\epsilon_{i,n}, i=1,...,n, where W_t denotes a standard Brownian motion and \epsilon_{i,n} are centered i.i.d.…

The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…

Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…

Marginalising out uncertain quantities within the internal representations or parameters of neural networks is of central importance for a wide range of learning techniques, such as empirical, variational or full Bayesian methods. We set…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

There has been a surge in the interest of using machine learning techniques to assist in the scientific process of formulating knowledge to explain observational data. We demonstrate the use of Bayesian Hidden Physics Models to first…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and…

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the…

Modelling noisy data in a network context remains an unavoidable obstacle; fortunately, random matrix theory may comprehensively describe network environments effectively. Thus it necessitates the probabilistic characterisation of these…