Related papers: Exact adaptive confidence intervals for linear reg…
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…
The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the…
In large-scale prediction problems, exhaustively following up on all test units is often impractical and inefficient, motivating a selective reporting strategy that fulfills the dual requirements of informativeness and trustworthiness.…
Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the…
Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…
Small area estimation (SAE) improves estimates for local communities or groups, such as counties, neighborhoods, or demographic subgroups, when data are insufficient for each area. This is important for targeting local resources and…
This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under…
We consider a linear regression model with regression parameter beta=(beta_1,...,beta_p) and independent and identically N(0,sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…
Conformal prediction (CP) is a method for constructing a prediction interval around the output of a fitted model, whose validity does not rely on the model being correct--the CP interval offers a coverage guarantee that is…
Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…
What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…
We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…
We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $\chi^2$…
This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the…
We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…
When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may…
Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate…
This article illustrates how indirect or prior information can be optimally used to construct a prediction region that maintains a target frequentist coverage rate. If the indirect information is accurate, the volume of the prediction…