Related papers: Recursive Construction of Confidence Regions
Supervised learning of time series data has been extensively studied for the case of a categorical target variable. In some application domains, e.g., energy, environment and health monitoring, it occurs that the target variable is…
Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…
This is a method for discrete event simulation specified by survival analysis. It presents a sequence of steps. First, hazard rates from survival analysis specify the rates of a set of counting processes. Second, those counting processes…
Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…
The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this…
Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.
The reliability of concurrent and distributed systems often depends on some well-known techniques for fault tolerance. One such technique is based on checkpointing and rollback recovery. Checkpointing involves processes to take snapshots of…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…
The simulation of crack initiation and propagation in an elastic material is difficult, as crack paths with complex topologies have to be resolved. Phase-field approach allows to simulate crack behavior by circumventing the need to…
We consider a linear regression model with regression parameter beta=(beta_1,...,beta_p) and independent and identically N(0,sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel.…
Existing conformal prediction algorithms estimate prediction intervals at target confidence levels to characterize the performance of a regression model on new test samples. However, considering an autonomous system consisting of multiple…
Sentiment signals derived from sparse news are commonly used in financial analysis and technology monitoring, yet transforming raw article-level observations into reliable temporal series remains a largely unsolved engineering problem.…
This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…