The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer). Evidential probability, also called Bayesian probability, can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap). There are also evidential interpretations of probability covering groups, which are often labelled as 'intersubjective' (proposed by Gillies and Rowbottom).

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (42)
MATH-131: Probability and statistics
Le cours présente les notions de base de la théorie des probabilités et de l'inférence statistique. L'accent est mis sur les concepts principaux ainsi que les méthodes les plus utilisées.
MGT-484: Applied probability & stochastic processes
This course focuses on dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We will also study applications in q
MATH-232: Probability and statistics (for IC)
A basic course in probability and statistics
Show more
Related lectures (501)
Bias and Variance in Estimation
Discusses bias and variance in statistical estimation, exploring the trade-off between accuracy and variability.
Interval Estimation: Method of Moments
Covers the method of moments for estimating parameters and constructing confidence intervals based on empirical moments matching distribution moments.
Estimators and Confidence Intervals
Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.
Show more
Related publications (201)

Technosignatures Longevity and Lindy's Law

Claudio Grimaldi

The probability of detecting technosignatures (i.e., evidence of technological activity beyond Earth) increases with their longevity, or the time interval over which they manifest. Therefore, the assumed distribution of longevities has some bearing on the ...
Bristol2024

A FEM modelling workflow to simulate THM effects in the rock around nuclear waste packages

Matthias Timothee Stanislas Wojnarowicz

High-level waste, stemming from nuclear electricity generation poses significant environmental and safety concerns. Currently, high-level wastes are stored in interim facilities needing constant monitoring and waiting for a definitive solution. Deep geolog ...
EPFL2024

Bimanual dynamic grabbing and tossing of objects onto a moving target

Aude Billard, Michael Bosongo Bombile

Bimanual grabbing and tossing of packages onto trays or conveyor belts remains a human activity in the industry. For robots, such a dynamic task requires coordination between two arms and fast adaptation abilities when the tossing target is moving and subj ...
2023
Show more
Related concepts (18)
Bayesian statistics
Bayesian statistics (ˈbeɪziən or ˈbeɪʒən ) is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials.
Bayes' theorem
In probability theory and statistics, Bayes' theorem (beɪz or beɪzɪz ; alternatively Bayes' law or Bayes' rule), and occasionally Bayes's theorem, named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.
Bayesian epistemology
Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality.
Show more
Related MOOCs (4)
Neuronal Dynamics - Computational Neuroscience of Single Neurons
The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.
Neuronal Dynamics - Computational Neuroscience of Single Neurons
The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.
Selected Topics on Discrete Choice
Discrete choice models are used extensively in many disciplines where it is important to predict human behavior at a disaggregate level. This course is a follow up of the online course “Introduction t
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.