Related papers: Nonparametric Bayesian volatility estimation for g…
We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…
This paper presents a novel approach to stochastic volatility (SV) modeling by utilizing nonparametric techniques that enhance our ability to capture the volatility of financial time series data, with a particular emphasis on the…
Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…
Inferring a decision maker's utility function typically involves an elicitation phase where the decision maker responds to a series of elicitation queries, followed by an estimation phase where the state-of-the-art is to either fit the…
In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
This paper discusses the efficient Bayesian estimation of a multivariate factor stochastic volatility (Factor MSV) model with leverage. We propose a novel approach to construct the sampling schemes that converges to the posterior…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…
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…