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A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…
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…
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
In nature, active inference agents must learn how observations of the world represent the state of the agent. In engineering, the physics behind sensors is often known reasonably accurately and measurement functions can be incorporated into…
Mistakes/uncertainties in object detection could lead to catastrophes when deploying robots in the real world. In this paper, we measure the uncertainties of object localization to minimize this kind of risk. Uncertainties emerge upon…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
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…
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant 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…
A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This…