Related papers: Non-parametric estimation of conditional densities…
This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to…
Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
We study an unbiased estimator for the density of a sum of random variables that are simulated from a computer model. A numerical study on examples with copula dependence is conducted where the proposed estimator performs favourably in…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows'…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T: \delta = 1_{Y \leq T}.…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…