Related papers: Probability and Measurement Uncertainty in Physics…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
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…
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 inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…
In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
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…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
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,…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
The aim of this paper is to introduce a field of study that has emerged over the last decade called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…