相关论文: Rigorous confidence intervals for critical probabi…

We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN)…

Model selection in the presence of intractable likelihoods remains a central challenge in Bayesian inference. Approximate Bayesian computation (ABC) provides a flexible likelihood-free framework, but its use for model choice is known to be…

Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized…

Lattices that can be represented in a kagome-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P_3, the probability that all three vertices in the triangle connect, and P_0, the…

Estimating the probability of the binomial distribution is a basic problem, which appears in almost all introductory statistics courses and is performed frequently in various studies. In some cases, the parameter of interest is a difference…

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…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form…

We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold…

Classical frequentist approaches to inference for the lasso emphasize exact coverage for each feature, which requires debiasing and severs the connection between confidence intervals and the original lasso estimates. To address this, in…

We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…

Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…

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…