Related papers: Simple Confidence Intervals for MCMC Without CLTs

Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…

Sample size determination for cluster randomised trials (CRTs) is challenging as it requires robust estimation of the intra-cluster correlation coefficient (ICC). Typically, the sample size is chosen to provide a certain level of power to…

Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…

The relevance condition of Integrated Conditional Moment (ICM) estimators is significantly weaker than the conventional IV's in at least two respects: (1) consistent estimation without excluded instruments is possible, provided endogenous…

Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference…

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

This paper introduces a first implementation of a novel likelihood-ratio-based approach for constructing confidence intervals for neural networks. Our method, called DeepLR, offers several qualitative advantages: most notably, the ability…

This paper develops conformal inference methods to construct a confidence interval for the frequency of a queried object in a very large discrete data set, based on a sketch with a lower memory footprint. This approach requires no knowledge…

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of…

Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…

Using concentration inequalities, we give non-asymptotic confidence intervals for estimates obtained by Markov chain Monte Carlo (MCMC) simulations, when using the approximation $\mathbb{E}_{\pi} f\approx (1/(N-t_0))\cdot \sum_{i=t_0+1}^N…

Fast robust methods for calculating likelihoods from CMB observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximation,…

In the deployment of large language models (LLMs), accurate confidence estimation is critical for assessing the credibility of model predictions. However, existing methods often fail to overcome the issue of overconfidence on incorrect…

We provide the asymptotic distribution of the major indexes used in the statistical literature to quantify disparate treatment in machine learning. We aim at promoting the use of confidence intervals when testing the so-called group…

We contribute to bridging the gap between large- and finite-sample inference by studying confidence sets (CSs) that are both non-asymptotically valid and asymptotically exact uniformly (NAVAE) over semi-parametric statistical models. NAVAE…

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to…

We introduce three notions of multivariate median bias, namely, rectilinear, Tukey, and orthant median bias. Each of these median biases is zero under a suitable notion of multivariate symmetry. We study the coverage probabilities of…

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…

The study explores mitigating overconfidence bias in LLMs to improve their reliability. We introduce a knowledge transfer (KT) method utilizing chain of thoughts, where "big" LLMs impart knowledge to "small" LLMs via detailed, sequential…