Related papers: Choices and intervals
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…
We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…
A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional…
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…
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…
Gorman and Bedrick (2019) argued for using random splits rather than standard splits in NLP experiments. We argue that random splits, like standard splits, lead to overly optimistic performance estimates. We can also split data in biased or…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
We study a coarsening model describing the dynamics of interfaces in the one-dimensional Allen-Cahn equation. Given a partition of the real line into intervals of length greater than one, the model consists in constantly eliminating the…
We tackle the problem of building a prediction interval in heteroscedastic Gaussian regression. We focus on prediction intervals with constrained expected length in order to guarantee interpretability of the output. In this framework, we…