Related papers: Comment on: "Model uncertainty and missing data: A…
Our comment on Garc\'ia-Donato et al. (2025). "Model uncertainty and missing data: An objective Bayesian perspective" explores a further extension of the proposed methodology. Specifically, we consider the sequential setting where…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…
Garcia-Donato et al. (2025) present a methodology for handling missing data in a model selection problem using an objective Bayesian approach. The current comment discusses an alternative, existing objective Bayesian method for this…
It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
The article by Garc{\'i}a-Donato and co-authors addresses the dual challenges of accounting for model uncertainty and missing data within the Gaussian regression frameworks from an objective Bayesian perspective. Thru the use of an…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
We begin by introducing the main ideas of the paper under discussion, and we give a brief description of the method proposed. Next, we discuss an alternative approach based on B-spline expansion, and lastly we make some comments on the…
Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…
We present a framework for generating multiple imputations for continuous data when the missing data mechanism is unknown. Imputations are generated from more than one imputation model in order to incorporate uncertainty regarding the…
Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…