Related papers: On computing distributions of products of random v…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes…
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many…
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…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…