Related papers: On Some Problems of Confidence Region Construction

This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…

We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the…

The remarkably long-standing problem of cryptography is to generate completely secure key. It is widely believed that the task cannot be achieved within classical cryptography. However, there is no proof in support of this belief. We…

Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…

In this work it is pointed out that some physical theories, even being themselves falsifiable, predict the existence of regions of spacetime which are not falsifiable with relation to each other due to their impossibility of mutually…

We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate where the mean is the sum of a known background and an unknown non-negative signal. We point out that the intervals do not have…

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…

In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general…

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed.

While certified robustness is widely promoted as a solution to adversarial examples in Artificial Intelligence systems, significant challenges remain before these techniques can be meaningfully deployed in real-world applications. We…

Providing assurances for self-adaptive systems is challenging. A primary underlying problem is uncertainty that may stem from a variety of different sources, ranging from incomplete knowledge to sensor noise and uncertain behavior of humans…

We describe a general method for the construction of a confidence region for the two parameters of the Negative Binomial Distribution. This is achieved by expanding the sampling distribution of Method-of-Moments estimators, using the…

Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be…

Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This…

The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact…

Biometric systems, while offering convenient authentication, often fall short in providing rigorous security assurances. A primary reason is the ad-hoc design of protocols and components, which hinders the establishment of comprehensive…

Several sources of uncertainty have to be taken into account in the analysis and design of CPS. The set of parameters used in the model of the physical plant of a CPS may be uncertain due, for example, to manufacturing processes that are…

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter \theta, i.e. we want to construct a confidence set for theta that contains…

High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…