Related papers: Introducing shrinkage in heavy-tailed state space …

We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time…

We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet…

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

We adaptively estimate both changepoints and local outlier processes in a Bayesian dynamic linear model with global-local shrinkage priors in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We utilize a…

Bayesian methods are increasingly being applied to parameterize mechanistic process models used in environmental prediction and forecasting. In particular, models describing ecosystem dynamics with multiple states that are linear and…

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive…

This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…

Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…

Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at…

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Recent studies have shown that heavy tails can emerge in stochastic optimization and that the heaviness of the tails have links to the generalization error. While these studies have shed light on interesting aspects of the generalization…

Many systems such as autonomous vehicles and quadrotors are subject to parametric uncertainties and external disturbances. These uncertainties can lead to undesired performance degradation and safety issues. Therefore, it is important to…

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often…

Model updating of engineering systems inevitably involves handling both aleatory or inherent randomness and epistemic uncertainties or uncertainities arising from a lack of knowledge or information about the system. Addressing these…

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular…

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly…

We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests. These methods avoid the curse of…