Related papers: Simple Confidence Intervals for MCMC Without CLTs
The purpose of this paper is to construct confidence intervals for the regression coefficients in high-dimensional Cox proportional hazards regression models where the number of covariates may be larger than the sample size. Our debiased…
We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…
In many high-risk machine learning applications it is essential for a model to indicate when it is uncertain about a prediction. While large language models (LLMs) can reach and even surpass human-level accuracy on a variety of benchmarks,…
Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the…
MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a…
Sensitivity analysis for measurement error can be applied in the absence of validation data by means of regression calibration and simulation-extrapolation. These have not been compared for this purpose. A simulation study was conducted…
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…
It is well known that the asymptotic variance of sample quantiles can be reduced under heterogeneity relative to the i.i.d. setting. However, asymptotically correct confidence intervals for quantiles are not yet available. We propose a…
This chapter describes several control variate methods for improving estimates of expectations from MCMC.
A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the…
Large Language Models (LLMs) have the impressive ability to perform in-context learning (ICL) from only a few examples, but the success of ICL varies widely from task to task. Thus, it is important to quickly determine whether ICL is…
Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in…
Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved…
It is common when using cross-section or panel data to assign each observation to a cluster and allow for arbitrary patterns of heteroskedasticity and correlation within clusters. For regression models, there are many ways to make…
We have made a Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) using the WMAP bispectrum and power spectrum. In our analysis, we have simultaneously constrained f_NL and cosmological parameters so that the…
Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model…
The following questions are discussed: ``Why confidence intervals are a hot topic?''; ``Are confidence intervals objective?''; ``What is the usefulness of coverage?''; ``How to obtain useful information from experiment?''; ``The confidence…