Related papers: Bounding distributional errors via density ratios

Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances…

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…

Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…

Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…

Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under…

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit…

In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…

We obtain the optimal proxy variance for the sub-Gaussianity of Beta distribution, thus proving upper bounds recently conjectured by Elder (2016). We provide different proof techniques for the symmetrical (around its mean) case and the…

In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method.…