Related papers: Plausibility functions and exact frequentist infer…
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
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…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
Besides the classical motivation of fusing evidence from multiple sources, modern inferential procedures based on randomization, resampling, and data splitting often introduce analyst-generated multiplicity, where aggregating outputs across…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
Probabilistic programming languages aim to describe and automate Bayesian modeling and inference. Modern languages support programmable inference, which allows users to customize inference algorithms by incorporating guide programs to…
This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…