Related papers: A practical, effective calculation of gamma differ…

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…

Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the…

We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…

With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…

Our goal is to evaluate the accuracy of a black-box classification model, not as a single aggregate on a given test data distribution, but as a surface over a large number of combinations of attributes characterizing multiple test data…

This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…

Mamba has demonstrated excellent performance in various time series forecasting tasks due to its superior selection mechanism. Nevertheless, conventional Mamba-based models encounter significant challenges in accurately predicting stock…

We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…

The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and…

Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…

The diffusion model has long been plagued by scalability and quadratic complexity issues, especially within transformer-based structures. In this study, we aim to leverage the long sequence modeling capability of a State-Space Model called…

Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…

Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…

Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…