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Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…
The generation of multi-step density forecasts for non-Gaussian data mostly relies on Monte Carlo simulations which are computationally intensive. Using aggregated wind power in Ireland, we study two approaches of multi-step density…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…
Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
We introduce and study a variational framework for the analysis of empirical risk based inference for dynamical systems and ergodic processes. The analysis applies to a two-stage estimation procedure in which (i) the trajectory of an…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
This study seeks to advance the understanding and prediction of stock market return uncertainty through the application of advanced deep learning techniques. We introduce a novel deep learning model that utilizes a Gaussian mixture…
An MCMC simulation method based on a two stage delayed rejection Metropolis-Hastings algorithm is proposed to estimate a factor multivariate stochastic volatility model. The first stage uses kstep iteration towards the mode, with k small,…
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 describes an approach to simultaneously identify clusters and estimate cluster-specific regression parameters from the given data. Such an approach can be useful in learning the relationship between input and output when the…