# Bayesianism

TagLast edit: 18 Jun 2023 6:11 UTC by

Bayesianism is the broader philosophy inspired by Bayes’ theorem. The core claim behind all varieties of Bayesianism is that probabilities are subjective degrees of belief—often operationalized as willingness to bet.

This stands in contrast to other interpretations of probability, which attempt greater objectivity. The frequentist interpretation of probability has a focus on repeatable experiments; probabilities are the limiting frequency of an event if you performed the experiment an infinite number of times.

Another contender is the propensity interpretation, which grounds probability in the propensity for things to happen. A perfectly balanced 6-sided die would have a 16 propensity to land on each side. A propensity theorist sees this as a basic fact about dice not derived from infinite sequences of experiments or subjective viewpoints.

Note how both of these alternative interpretations ground the meaning of probability in an external objective fact which cannot be directly accessed.

As a consequence of the subjective interpretation of probability theory, Bayesians are more inclined to apply Bayes’ Theorem in practical statistical inference. The primary example of this is statistical hypothesis testing. Frequentists take the application of Bayes’ Theorem to be inappropriate, because “the probability of a hypothesis” is meaningless: a hypothesis is either true or false; you cannot define a repeated experiment in which it is sometimes true and sometimes false, so you cannot assign it an intermediate probability.

## Bayesianism & Rationality

Bayesians conceive rationality as a technical codeword used by cognitive scientists to mean “rational”. Bayesian probability theory is the math of epistemic rationality, Bayesian decision theory is the math of instrumental rationality. Right up there with cognitive bias as an absolutely fundamental concept on Less Wrong.

## Other usages

The term “Bayesian” may also refer to an ideal rational agent implementing precise, perfect Bayesian probability theory and decision theory (see, for example, Aumann’s agreement theorem).

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26 Jan 2024 3:58 UTC
13 points

# Prob­a­bil­ity is in the Mind

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129 points

# Search­ing for Bayes-Structure

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60 points

# What is Bayesi­anism?

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115 points

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166 points

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69 points

# Bayesian Injustice

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122 points
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51 points

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104 points

# Lawful Uncertainty

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98 points

# Cir­cu­lar Altruism

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83 points

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31 Jan 2008 19:36 UTC
144 points

# When (Not) To Use Probabilities

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63 points

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22 May 2008 5:55 UTC
356 points

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30 points

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205 points

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69 points

# Beau­tiful Probability

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102 points

# Trust in Math

15 Jan 2008 4:25 UTC
22 points

# Trust in Bayes

29 Jan 2008 23:12 UTC
38 points

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14 Jul 2008 9:16 UTC
40 points

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14 Mar 2008 17:01 UTC
59 points

# My Bayesian Enlightenment

5 Oct 2008 16:45 UTC
67 points

# A Priori

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80 points

# Bayesian Punishment

27 Oct 2023 3:24 UTC
1 point

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20 points

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25 Feb 2024 14:17 UTC
93 points
(kevindorst.substack.com)

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12 Dec 2023 18:31 UTC
−7 points
(tiplur-bilrex.tlon.network)

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16 Sep 2023 16:31 UTC
14 points
(kevindorst.substack.com)

# ra­tio­nal­is­tic prob­a­bil­ity(lit­ter­ally just throw­ing shit out there)

4 Oct 2023 17:46 UTC
−30 points

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11 Feb 2024 17:42 UTC
54 points

# Mir­a­cles and why not to be­lieve them

16 Nov 2022 12:07 UTC
4 points