相关论文: Bounding Means of Discrete Distributions

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…

A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…

Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…

The distribution of frequency counts of distinct words by length in a language's vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that…

Aleatoric uncertainty quantification seeks for distributional knowledge of random responses, which is important for reliability analysis and robustness improvement in machine learning applications. Previous research on aleatoric uncertainty…

We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two…

In analyzing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first…

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally…

We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…

This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…

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…

Data discretization, also known as binning, is a frequently used technique in computer science, statistics, and their applications to biological data analysis. We present a new method for the discretization of real-valued data into a finite…

Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…