Related papers: Rigorous confidence intervals for critical probabi…

We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx…

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…

We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

In this paper, we develop an exact method for computing the minimum coverage probability of Wald interval for estimation of binomial parameters. Similar approach can be used for other type of confidence intervals.

Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide…

The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard expansive empirical likelihood [Nordman et al. (2013)] methods for time series data are…

A C++ class was written for the calculation of frequentist confidence intervals using the profile likelihood method. Seven combinations of Binomial, Gaussian, Poissonian and Binomial uncertainties are implemented. The package provides…

Expected coverage and expected length of 90% upper and lower limit and 68.27% central intervals are plotted as functions of the true signal for various values of expected background. Results for several objective priors are shown, and…

We study Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations. Using the characteristic spatial Markov property or peeling process of these random lattices…

I calculated the exact site and bond percolation probability on lattice-like graphs for given dimension d: site percolation probability is 1/d and bond percolation probability is 0.5(d-1)^{-1/2}

A number of studies have suggested using comparisons between DNA sequences of closely related bacterial isolates to estimate the relative rate of recombination to mutation for that bacterial species. We consider such an approach which uses…

Based on the physical randomization of completely randomized experiments, Rigdon and Hudgens (2015) propose two approaches to obtaining exact confidence intervals for the average causal effect on a binary outcome. They construct the first…

Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…

Interferometers require accurate determination of the array configuration in order to produce reliable observations. A method is presented for finding the maximum-likelihood estimate of the telescope geometry, and of other instrumental…

Global sensitivity analysis is often impracticable for complex and time demanding numerical models, as it requires a large number of runs. The reduced-basis approach provides a way to replace the original model by a much faster to run code.…

Large language models (LLMs) excel at numerical estimation but struggle to correctly quantify uncertainty. We study how well LLMs construct confidence intervals around their own answers and find that they are systematically overconfident.…