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This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple…

Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become…

We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…

Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a…

The importance of quality measures in process mining has increased. One of the key quality aspects, generalization, is concerned with measuring the degree of overfitting of a process model w.r.t. an event log, since the recorded behavior is…

We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…

In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually…

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider a class of generalized coarsened procedures for confounding. At a…

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to…

Recently, we have witnessed the great success of the generalist model in natural language processing. The generalist model is a general framework trained with massive data and is able to process various downstream tasks simultaneously.…

This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…

Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with…

Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…