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The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…
Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of…
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…
This article, produced as a result of the Symposium on Statistical Inference, is an introduction to the literature on the function of expertise, judgment, and choice in the practice of statistics and scientific research. In particular,…
A coordinate system is a foundation for every quantitative science, engineering, and medicine. Classical physics and statistics are based on the Cartesian coordinate system. The classical probability and hypothesis testing theory can only…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
Clinical trials are considered as the golden standard for medical device validation. However, many sacrifices have to be made during the design and conduction of the trials due to cost considerations and partial information, which may…
We develop a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. By…
Epidemiologists increasingly use causal inference methods that rely on machine learning, as these approaches can relax unnecessary model specification assumptions. While deriving and studying asymptotic properties of such estimators is a…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based…
To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causal representation learning. The other approach is to build…
Mathematical models connect theory with the real world through data, enabling us to interpret, understand, and predict complex phenomena. However, scientific knowledge often extends beyond what can be empirically measured, offering valuable…
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…
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…
Breiman (2001) proposed to statisticians awareness of two cultures: 1. Parametric modeling culture, pioneered by R.A.Fisher and Jerzy Neyman; 2. Algorithmic predictive culture, pioneered by machine learning research. Parzen (2001), as a…