Related papers: On Existence Theorems for Conditional Inferential …
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional…
Existing frameworks for probabilistic inference assume the quantity of interest is the parameter of a posited statistical model. In machine learning applications, however, often there is no statistical model/parameter; the quantity of…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…
A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory…
Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
Building models that generalize across physical systems without retraining remains a central challenge in computational science. Here we introduce In-Context Modeling (ICM), a retrain-free paradigm that infers physical relationships…
Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper we provide a general procedure for inference…
Inference in current domains of application are often complex and require us to integrate the expertise of a variety of disparate panels of experts and models coherently. In this paper we develop a formal statistical methodology to guide…
Written with respect to an appropriate Poisson structure, a partially integrable Hamiltonian system is viewed as a completely integrable system with parameters. Then, the theorem on quasi-periodic stability in Ref. [1] (the KAM theorem) can…
Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects…
Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire…