TagLast edit: 18 Jun 2023 6:11 UTC by tgrecojs

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.

See also: Bayes theorem, Bayesian probability, Radical Probabilism, Priors, Rational evidence, Probability theory, Decision theory, Lawful intelligence, Bayesian Conspiracy.

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).

Ap­prox­i­mately Bayesian Rea­son­ing: Knigh­tian Uncer­tainty, Good­hart, and the Look-Else­where Effect

RogerDearnaley26 Jan 2024 3:58 UTC
13 points
0 comments11 min readLW link

Prob­a­bil­ity is in the Mind

Eliezer Yudkowsky12 Mar 2008 4:08 UTC
129 points
195 comments6 min readLW link

Search­ing for Bayes-Structure

Eliezer Yudkowsky28 Feb 2008 22:01 UTC
60 points
48 comments5 min readLW link

What is Bayesi­anism?

Kaj_Sotala26 Feb 2010 7:43 UTC
115 points
217 comments4 min readLW link

The Se­cond Law of Ther­mo­dy­nam­ics, and Eng­ines of Cognition

Eliezer Yudkowsky27 Feb 2008 0:48 UTC
166 points
72 comments9 min readLW link

Per­pet­ual Mo­tion Beliefs

Eliezer Yudkowsky27 Feb 2008 20:22 UTC
69 points
44 comments3 min readLW link

Bayesian Injustice

Kevin Dorst14 Dec 2023 15:44 UTC
122 points
10 comments6 min readLW link

Pri­ors as Math­e­mat­i­cal Objects

Eliezer Yudkowsky12 Apr 2007 3:24 UTC
51 points
20 comments4 min readLW link

No One Can Ex­empt You From Ra­tion­al­ity’s Laws

Eliezer Yudkowsky7 Oct 2007 17:24 UTC
119 points
52 comments3 min readLW link

Ter­mi­nal Values and In­stru­men­tal Values

Eliezer Yudkowsky15 Nov 2007 7:56 UTC
104 points
45 comments10 min readLW link

Lawful Uncertainty

Eliezer Yudkowsky10 Nov 2008 21:06 UTC
98 points
57 comments4 min readLW link

Cir­cu­lar Altruism

Eliezer Yudkowsky22 Jan 2008 18:00 UTC
83 points
310 comments4 min readLW link

New­comb’s Prob­lem and Re­gret of Rationality

Eliezer Yudkowsky31 Jan 2008 19:36 UTC
144 points
616 comments10 min readLW link

When (Not) To Use Probabilities

Eliezer Yudkowsky23 Jul 2008 10:58 UTC
63 points
46 comments6 min readLW link

That Alien Message

Eliezer Yudkowsky22 May 2008 5:55 UTC
356 points
174 comments10 min readLW link

Chang­ing the Defi­ni­tion of Science

Eliezer Yudkowsky18 May 2008 18:07 UTC
30 points
30 comments2 min readLW link

My cur­rent LK99 questions

Eliezer Yudkowsky1 Aug 2023 22:48 UTC
205 points
38 comments5 min readLW link

The role of Bayesian ML in AI safety—an overview

Marius Hobbhahn27 Jan 2023 19:40 UTC
30 points
6 comments10 min readLW link

Neu­ral un­cer­tainty es­ti­ma­tion re­view ar­ti­cle (for al­ign­ment)

Charlie Steiner5 Dec 2023 8:01 UTC
69 points
1 comment11 min readLW link

Beau­tiful Probability

Eliezer Yudkowsky14 Jan 2008 7:19 UTC
102 points
123 comments6 min readLW link

Trust in Math

Eliezer Yudkowsky15 Jan 2008 4:25 UTC
22 points
51 comments3 min readLW link

Trust in Bayes

Eliezer Yudkowsky29 Jan 2008 23:12 UTC
38 points
28 comments8 min readLW link

Prob­a­bil­ity is Sub­jec­tively Objective

Eliezer Yudkowsky14 Jul 2008 9:16 UTC
40 points
72 comments11 min readLW link

Qual­i­ta­tively Confused

Eliezer Yudkowsky14 Mar 2008 17:01 UTC
59 points
82 comments4 min readLW link

My Bayesian Enlightenment

Eliezer Yudkowsky5 Oct 2008 16:45 UTC
67 points
65 comments7 min readLW link

A Priori

Eliezer Yudkowsky8 Oct 2007 21:02 UTC
80 points
133 comments4 min readLW link

Bayesian Punishment

Rob Lucas27 Oct 2023 3:24 UTC
1 point
1 comment6 min readLW link

On Hav­ing No Clue

Chris_Leong1 Nov 2023 1:36 UTC
20 points
11 comments1 min readLW link

Ide­olog­i­cal Bayesians

Kevin Dorst25 Feb 2024 14:17 UTC
93 points
4 comments10 min readLW link

A de­sign con­cept for su­per­in­tel­li­gent ma­chines (and Pop­per’s cri­tique of in­duc­tion)

tiplur-bilrex12 Dec 2023 18:31 UTC
−7 points
6 comments1 min readLW link

Po­lariza­tion is Not (Stan­dard) Bayesian

Kevin Dorst16 Sep 2023 16:31 UTC
14 points
6 comments7 min readLW link

ra­tio­nal­is­tic prob­a­bil­ity(lit­ter­ally just throw­ing shit out there)

NotaSprayer ASprayer4 Oct 2023 17:46 UTC
−30 points
8 comments2 min readLW link

How do you ac­tu­ally ob­tain and re­port a like­li­hood func­tion for sci­en­tific re­search?

Peter Berggren11 Feb 2024 17:42 UTC
54 points
3 comments1 min readLW link

Mir­a­cles and why not to be­lieve them

mruwnik16 Nov 2022 12:07 UTC
4 points
0 comments2 min readLW link

Fore­act­ing agents

B Jacobs8 Dec 2023 19:57 UTC
4 points
0 comments13 min readLW link

[Question] Bayesian Reflec­tion Prin­ci­ples and Ig­no­rance of the Future

crickets25 Jan 2024 19:00 UTC
5 points
3 comments1 min readLW link
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