Related papers: On split sample and randomized confidence interval…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
This article deals with the spatio-temporal sensors deployment in order to maximize detection probability of an intelligent and randomly moving target in an area under surveillance. Our work is based on the rare events simulation framework.…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
We propose a method for estimating disparity confidence intervals in stereo matching problems. Confidence intervals provide complementary information to usual confidence measures. To the best of our knowledge, this is the first method…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation…
Conformal Prediction (CP) is a distribution-free framework for constructing statistically rigorous prediction sets. While popular variants such as CD-split improve CP's efficiency, they often yield prediction sets composed of multiple…
Certifiable robustness gives the guarantee that small perturbations around an input to a classifier will not change the prediction. There are two approaches to provide certifiable robustness to adversarial examples: a) explicitly training…
This paper concerns differentially private Bayesian estimation of the parameters of a population distribution, when a statistic of a sample from that population is shared in noise to provide differential privacy. This work mainly addresses…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the…
In this manuscript, a purely data driven statistical regularization method is proposed for extracting the information from big data with randomly distributed noise. Since the variance of the noise maybe large, the method can be regarded as…
The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information.…