Related papers: Connections between statistical practice in elemen…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…
Suppose you are told that taking a statin will reduce your risk of a heart attack or stroke by 3% in the next ten years, or that women have better emotional intelligence than men. You may wonder how accurate the 3% is, or how confident we…
High energy physics aims to understand the fundamental laws of particles and their interactions at both the largest and smallest scales of the universe. This typically means probing very high energies or large distances or using…
Unobserved effect modifiers can induce bias when generalizing causal effect estimates to target populations. In this work, we extend a sensitivity analysis framework assessing the robustness of study results to unobserved effect…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted…
The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more…
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\it the…
This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
Criteria for defining errors of a physical theory are formulated. It is shown that the Special Theory of Relativity (STR) has a solid mathematical basis. An enormous amount of experiments carried out in particle physics use beams of…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Different methods to extract the temperature and density in heavy ion collisions are compared using a statistical model tailored to reproduce many experimental features at low excitation energy. The model assumes a sequential decay 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…
Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population,…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…