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The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q. With random walk…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…
This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…
In random sequential adsorption (RSA), objects are deposited on a substrate randomly, irreversibly, and sequentially. Attempts of deposition that lead to an overlap with previously deposited objects are discarded. The process continues…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Spatial autoregressive combined (SAC) model has been widely studied in the literature for the analysis of spatial data in various areas such as geography, economics, demography, regional sciences. This is a linear model with scalar…
Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial…
Sequential design of real and computer experiments via Gaussian Process (GP) models has proven useful for parsimonious, goal-oriented data acquisition purposes. In this work, we focus on acquisition strategies for a GP model that needs to…
As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in…
We propose to learn a probabilistic motion model from a sequence of images. Besides spatio-temporal registration, our method offers to predict motion from a limited number of frames, useful for temporal super-resolution. The model is based…
Surrogate safety measures can provide fast and pro-active safety analysis and give insights on the pre-crash process and crash failure mechanism by studying near misses. However, validating surrogate safety measures by connecting them to…