Related papers: The bilateral generalized inverse Gaussian process…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
Several characterizations of the Generalized Inverse Gaussian (GIG) distribution have been proposed in the literature, especially over the past two decades. These characterization theorems are surveyed, and two new characterizations are…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density…
In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real…
We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent…
We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and…
In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly…
The generalized inverse Gaussian-Poisson (GIGP) distribution proposed by Sichel in the 1970s has proved to be a flexible fitting tool for diverse frequency data, collectively described using the item production model. In this paper, we…
Many inverse problems focus on recovering a quantity of interest that is a priori known to exhibit either discontinuous or smooth behavior. Within the Bayesian approach to inverse problems, such structural information can be encoded using…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
Gaussian process regression can flexibly represent the posterior distribution of an interest parameter given sufficient information on the likelihood. However, in some cases, we have little knowledge regarding the probability model. For…
Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each $10$-minute lag: the Gamma distribution, the inverse Gamma distribution, the…
In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as…
We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…