Related papers: Comment on: "Model uncertainty and missing data: A…

How do we know how much we know? Quantifying uncertainty associated with our modelling work is the only way we can answer how much we know about any phenomenon. With quantitative science now highly influential in the public sphere and the…

Uncertainty quantification of complex technical systems is often based on a computer model of the system. As all models such a computer model is always wrong in the sense that it does not describe the reality perfectly. The purpose of this…

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…

Economic evaluations from individual-level data are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. A critical problem in these analyses is that both effectiveness and…

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a…

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…

Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…

Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…

There are things we know, things we know we don't know, and then there are things we don't know we don't know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of…

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…

Trial-based economic evaluations are typically performed on cross-sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and…

Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…

We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…