https://wiki.lesswrong.com/api.php?action=feedcontributions&user=Xadmin&feedformat=atomLesswrongwiki - User contributions [en]2020-11-28T23:39:27ZUser contributionsMediaWiki 1.31.10https://wiki.lesswrong.com/index.php?title=Bayesian&diff=7612Bayesian2011-09-03T11:54:28Z<p>Xadmin: /* Blog posts */</p>
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<div>{{wikilink|Bayesian}}<br />
The secret technical codeword that cognitive scientists use 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.<br />
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==Philosophy==<br />
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[[Classical statistics]] is a bucket of assorted methods; different "methods" may give different answers for whether, e.g., an experimental result is "statistically significant". In contrast, as the famous Bayesian E. T. Jaynes emphasized, probability theory is ''math'' and its results are ''theorems'', every theorem consistent with every other theorem; you cannot get two different results by doing the derivation two different ways.<br />
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So is the project of rationality solved? Indeed not. First, probability theory and decision theory are often too computationally expensive to run in practice - it wouldn't take a galaxy-sized computer, so much as an unphysical computer (much larger than the known universe). And second, it's not always clear how the math ''applies'' - even in theory, let alone the practice.<br />
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But we do know that violations of Bayesianism - even "unavoidable" violations due to lack of computing power - carry a price; a family of theorems demonstrates that anyone who does not choose according to consistent probabilities can be made to accept combinations of bets that are sure losses, or reject bets that are sure wins (the [[Dutch Book]] arguments); similarly, [[Cox's Theorem]] and its extensions show that anyone who obeys various "common-sensical" constraints on their betting probabilities must be representable in standard probability theory.<br />
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In other words, Bayesianism isn't just a good idea - ''it's the law'', and if you violate it, you'll pay ''some'' kind of price.<br />
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When cognitive psychologists identify a [[cognitive bias]], they know it's an ''error'' by comparison to the Bayesian gold standard.<br />
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==Math==<br />
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(Needs to be fleshed out.) For introductions see [[probability theory]], [[decision theory]], and [http://yudkowsky.net/rational/bayes this introduction] to [[Bayes' theorem]]. A widely lauded technical book on this subject is E. T. Jaynes's [http://www-biba.inrialpes.fr/Jaynes/prob.html "Probability Theory: The Logic of Science"].<br />
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==Other usages==<br />
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"Bayesian" in philosophical usage often describes someone who adheres to the [[Bayesian probability|Bayesian interpretation]] of probability, viewing probability as a level of certainty in a potential outcome or idea. This is in contrast to a [[frequentist]] who views probability as a representation of how frequently a particular outcome will occur over any number of trials.<br />
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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]]).<br />
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==Blog posts==<br />
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*{{lesswrongtag}}<br />
*[http://lesswrong.com/lw/1to/what_is_bayesianism/ What is Bayesianism]<br />
*[http://lesswrong.com/lw/mt/beautiful_probability/ Beautiful Probability], [http://lesswrong.com/lw/mu/trust_in_math/ Trust in Math], and [http://lesswrong.com/lw/na/trust_in_bayes/ Trust in Bayes]<br />
*[http://lesswrong.com/lw/oj/probability_is_in_the_mind/ Probability is in the Mind], [http://lesswrong.com/lw/s6/probability_is_subjectively_objective/ Probability is Subjectively Objective], and [http://lesswrong.com/lw/om/qualitatively_confused/ Qualitatively Confused]<br />
*[http://lesswrong.com/lw/o5/the_second_law_of_thermodynamics_and_engines_of/ The Second Law of Thermodynamics, and Engines of Cognition], [http://lesswrong.com/lw/o6/perpetual_motion_beliefs/ Perpetual Motion Beliefs] and [http://lesswrong.com/lw/o7/searching_for_bayesstructure/ Searching for Bayes-Structure]<br />
*[http://lesswrong.com/lw/ul/my_bayesian_enlightenment/ My Bayesian Enlightenment]<br />
*[http://lesswrong.com/lw/k2/a_priori/ A Priori]<br />
*[http://lesswrong.com/lw/hk/priors_as_mathematical_objects/ Priors as Mathematical Objects]<br />
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*[http://lesswrong.com/lw/k1/no_one_can_exempt_you_from_rationalitys_laws/ No One Can Exempt You From Rationality's Laws]<br />
*[http://lesswrong.com/lw/l4/terminal_values_and_instrumental_values/ Terminal Values and Instrumental Values]<br />
*[http://lesswrong.com/lw/vo/lawful_uncertainty/ Lawful Uncertainty]<br />
*[http://lesswrong.com/lw/n3/circular_altruism/ Circular Altruism]<br />
*[http://lesswrong.com/lw/nc/newcombs_problem_and_regret_of_rationality/ Newcomb's Problem and Regret of Rationality]<br />
*[http://lesswrong.com/lw/sg/when_not_to_use_probabilities/ When (Not) To Use Probabilities]<br />
*[http://lesswrong.com/lw/qk/that_alien_message/ That Alien Message]<br />
*[http://lesswrong.com/lw/qg/changing_the_definition_of_science/ Changing the Definition of Science]<br />
*[http://www.gadgetsdotcom.com Gadgets]<br />
*[http://www.blognesian.com Blog ]<br />
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==See also==<br />
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*[[Bayes theorem]]<br />
*[[Bayesian probability]]<br />
*[[Priors]]<br />
*[[Rational evidence]]<br />
*[[Probability theory]]<br />
*[[Decision theory]]<br />
*[[Lawful intelligence]]<br />
*[[Bayesian Conspiracy]]<br />
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[[Category:Concepts]]<br />
[[Category:Jargon]]<br />
[[Category:Bayesian]]<br />
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{{cleanup}}</div>Xadminhttps://wiki.lesswrong.com/index.php?title=Aumann%27s_agreement_theorem&diff=7611Aumann's agreement theorem2011-09-03T11:54:15Z<p>Xadmin: /* Tags */</p>
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<div>{{wikilink}}<br />
'''Aumann's agreement theorem''', roughly speaking, says that two agents acting rationally (in a certain precise sense) and with [[common knowledge]] of each other's beliefs cannot agree to disagree. More specifically, if two people are genuine [[Bayesian]]s, share common [[priors]], and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.<br />
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==Blog posts==<br />
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*[http://lesswrong.com/lw/gr/the_modesty_argument/ The Modesty Argument] by [[Eliezer Yudkowsky]]<br />
*[http://www.overcomingbias.com/2006/12/agreeing_to_agr.html Agreeing to Agree] by [[Hal Finney]] (OB)<br />
*[http://www.overcomingbias.com/2007/01/the_coin_guessi.html The Coin Guessing Game] by [[Hal Finney]] (OB) - A toy problem illustrating the mechanics of Aumann agreement.<br />
*[http://lesswrong.com/lw/gq/the_proper_use_of_humility/ The Proper Use of Humility] by [[Eliezer Yudkowsky]]<br />
*[http://www.overcomingbias.com/2006/12/meme_lineages_a.html Meme Lineages and Expert Consensus] by [[Carl Shulman]] (OB)<br />
*[http://lesswrong.com/lw/1il/probability_space_aumann_agreement/ Probability Space & Aumann Agreement] by [[Wei Dai]]<br />
*[http://lesswrong.com/lw/i5/bayesian_judo/ Bayesian Judo] by [[Eliezer Yudkowsky]]<br />
*[http://dl.dropbox.com/u/34639481/Aumann_agreement_theorem.pdf A write-up of the proof of Aumann's agreement theorem](pdf) by [[Tyrrell McAllister]]<br />
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==See also==<br />
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*[[Disagreement]]<br />
*[[Modesty argument]]<br />
*[[Aumann agreement]]<br />
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==References==<br />
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*{{Cite journal<br />
| author = Robert J. Aumann<br />
| title = Agreeing to Disagree<br />
| year = 1976<br />
| journal = The Annals of Statistics<br />
| issn = 00905364<br />
| volume = 4<br />
| issue = 6<br />
| pages = 1236-1239<br />
}} ([http://www.ma.huji.ac.il/~raumann/pdf/Agreeing%20to%20Disagree.pdf PDF])<br />
*{{Cite journal<br />
| author = Tyler Cowen and Robin Hanson<br />
| title = Are Disagreements Honest?<br />
| year = 2004<br />
}} ([http://hanson.gmu.edu/deceive.pdf PDF], [http://www.newmedia.ufm.edu/gsm/index.php?title=Are_Disagreements_Honest%3F Talk video])<br />
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==Tags==<br />
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*{{lesswrongtag|aumann|majoritarianism|disagreement|modesty}}<br />
*[http://www.overcomingbias.com/tag/disagreement Overcoming Bias posts on "Disagreement"]<br />
* [http://www.gadgetsdotcom.com Gadgets] <br />
* [http://www.blognesian.com blog ]<br />
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[[Category:Theorems]]</div>Xadminhttps://wiki.lesswrong.com/index.php?title=Bayesian_probability&diff=7610Bayesian probability2011-09-03T11:53:48Z<p>Xadmin: /* Blog posts */</p>
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<div>{{wikilink|Bayesian probability}}<br />
'''Bayesian probability''' represents a level of certainty relating to a potential outcome or idea. This is in contrast to a [[Wikipedia:Frequentist_inference|frequentist]] probability that represents the frequency with which a particular outcome will occur over any number of trials.<br />
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An [[Wikipedia:Event (probability theory)|event]] with Bayesian probability of .6 (or 60%) should be interpreted as stating "With confidence 60%, this event contains the true outcome", whereas a frequentist interpretation would view it as stating "Over 100 trials, we should observe event X approximately 60 times."<br />
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The difference is more apparent when discussing ideas. A frequentist will not assign probability to an idea, either it is true or false and it cannot be true 6 times out of 10.<br />
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==Blog posts==<br />
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*[http://lesswrong.com/lw/1to/what_is_bayesianism/ What is Bayesianism?]<br />
*[http://lesswrong.com/lw/s6/probability_is_subjectively_objective/ Probability is Subjectively Objective]<br />
*[http://lesswrong.com/lw/oj/probability_is_in_the_mind/ Probability is in the Mind]<br />
*[http://lesswrong.com/lw/sg/when_not_to_use_probabilities/ When (Not) To Use Probabilities]<br />
*{{lesswrongtag|Probability}}<br />
*[http://www.gadgetsdotcom.com Gadgets]<br />
*[http://www.blognesian.com Blog ]<br />
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==See also==<br />
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*[[Priors]]<br />
*[[Bayesian]]<br />
*[[Bayes' theorem]]<br />
*[[Mind projection fallacy]]<br />
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==External links==<br />
*[http://www.astro.cornell.edu/staff/loredo/bayes/index.html BIPS]: Bayesian Inference for the Physical Sciences<br />
*[[Wikipedia:Maximum entropy thermodynamics|Maximum entropy thermodynamics]]<br />
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{{stub}}<br />
[[Category:Concepts]]<br />
[[Category:Bayesian]]</div>Xadminhttps://wiki.lesswrong.com/index.php?title=Bias&diff=7609Bias2011-09-03T11:53:11Z<p>Xadmin: /* Blog posts on the concept of "bias" */</p>
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<div>{{wikilink|Bias|List of cognitive biases}}<br />
<br />
As used here, the term "bias" or "cognitive bias" refers to a specific, predictable error pattern in the human mind. The [[heuristics and biases]] program in cognitive psychology has documented hundreds of reproducible errors - often ''huge'' errors. This continues to be a highly active area of investigation in cognitive psychology.<br />
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Understanding cognitive biases and trying to defend against their effects has been a basic theme of [[Less Wrong]] since the days it was part of [[Overcoming Bias]].<br />
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==Starting points==<br />
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*Daniel Kahneman's [http://nobelprize.org/nobel_prizes/economics/laureates/2002/kahneman-lecture.html Nobel prize acceptance speech], where he summarizes the work for which he won the prize;<br />
*[[Wikipedia:List of cognitive biases]]; <br />
*Kahneman et al's [http://www.amazon.com/Judgment-under-Uncertainty-Heuristics-Biases/dp/0521284147 three] [http://www.amazon.com/Choices-Values-Frames-Daniel-Kahneman/dp/0521627494/ref=pd_bxgy_b_text_b edited] [http://www.amazon.com/Heuristics-Biases-Psychology-Intuitive-Judgment/dp/0521796792/ref=pd_bxgy_b_img_c volumes] of research on heuristics and biases (this is the best solid source, but requires obtaining hard-copy books, and is slower reading);<br />
*Eliezer's introductory book chapter [http://intelligence.org/upload/cognitive-biases.pdf Cognitive biases affecting judgment of existential risks] (available online).<br />
*Cialdini's book [http://www.amazon.com/Influence-Practice-Robert-B-Cialdini/dp/0205609996/ref=sr_1_3?ie=UTF8&s=books&qid=1239074671&sr=1-3 Influence: Science and Practice] (at once contentful and full of engaging anecdotes and cartoons, but, again, requires actually obtaining a book);<br />
*[http://psychology.wikia.com/wiki/Category:Cognitive_biases Psychology Wiki's list of Cognitive Biases]<br />
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==Blog posts on the concept of "bias"==<br />
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*[http://www.overcomingbias.com/2006/11/what_exactly_is.html What exactly is bias?] by [[Nick Bostrom]]<br />
*[http://www.overcomingbias.com/2006/11/to_the_barricad.html To the barricades! Against ... what exactly?] by [[Robin Hanson]]<br />
*[http://lesswrong.com/lw/gp/whats_a_bias_again/ ...What's a bias, again?] by [[Eliezer Yudkowsky]]<br />
*[http://www.overcomingbias.com/2006/11/the_big_four_ec.html Are The Big Four Econ Errors Biases?] by [[Robin Hanson]]<br />
*[http://www.overcomingbias.com/2006/11/incautious_defe.html In cautious defense of bias] by [[Paul Gowder]]<br />
*[http://www.overcomingbias.com/2006/12/seen_vs_unseen_.html Seen vs. Unseen Biases] by [[Robin Hanson]]<br />
*[http://lesswrong.com/lw/he/knowing_about_biases_can_hurt_people/ Knowing About Biases Can Hurt People] by [[Eliezer Yudkowsky]] - Knowing about common biases doesn't help you obtain truth if you only use this knowledge to attack beliefs you don't like.<br />
* [http://www.gadgetsdotcom.com Gadgets]<br />
* [http://www.blognesian.com Blog ]<br />
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==Blog posts about known cognitive biases==<br />
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*[http://lesswrong.com/lw/hw/scope_insensitivity/ Scope Insensitivity] - The human brain can't represent large quantities: an environmental measure that will save 200,000 birds doesn't conjure anywhere near a hundred times the emotional impact and willingness-to-pay of a measure that would save 2,000 birds.<br />
*[http://lesswrong.com/lw/hz/correspondence_bias/ Correspondence Bias], also known as the fundamental attribution error, refers to the tendency to attribute the behavior of others to intrinsic dispositions, while excusing one's own behavior as the result of circumstance.<br />
*Confirmation bias, or [http://lesswrong.com/lw/iw/positive_bias_look_into_the_dark/ Positive Bias] is the tendency to look for evidence that confirms a hypothesis, rather than disconfirming evidence.<br />
*[http://lesswrong.com/lw/il/hindsight_bias/ Hindsight Bias] describes the tendency to seem much more likely in hindsight than could have been predicted beforehand.<br />
*[http://lesswrong.com/lw/jg/planning_fallacy/ Planning Fallacy] - We tend to plan envisioning that everything will go as expected. Even assuming that such an estimate is accurate conditional on everything going as expected, things will ''not'' go as expected. As a result, we routinely see outcomes worse then the ''ex ante'' worst case scenario.<br />
*[http://lesswrong.com/lw/ji/conjunction_fallacy/ Conjunction Fallacy] - Elementary probability theory tells us that the probability of one thing (we write P(A)) is necessarily greater than or equal to the <i>conjunction</i> of that thing <i>and</i> another thing (write P(A&B)). However, in the psychology lab, subjects' judgments do not conform to this rule. This is [http://lesswrong.com/lw/jj/conjunction_controversy_or_how_they_nail_it_down/ not an isolated artifact] of a particular study design. Debiasing [http://lesswrong.com/lw/jk/burdensome_details/ won't be as simple] as practicing specific questions, it requires certain general habits of thought.<br />
*[http://lesswrong.com/lw/jx/we_change_our_minds_less_often_than_we_think/ We Change Our Minds Less Often Than We Think] - we all change our minds occasionally, but we don't constantly, honestly reevaluate every decision and course of action. Once you think you believe something, the chances are good that you already do, for better or worse.<br />
*[http://lesswrong.com/lw/k3/priming_and_contamination/ Priming and Contamination] - Even slight exposure to a stimulus is enough to change the outcome of a decision or estimate. See also [http://lesswrong.com/lw/3b/never_leave_your_room/ Never Leave Your Room] by Yvain, and [http://lesswrong.com/lw/4e/cached_selves/ Cached Selves] by Salamon and Rayhawk.<br />
*[http://lesswrong.com/lw/k4/do_we_believe_everything_were_told/ Do We Believe <i>Everything</i> We're Told?] - Some experiments on priming suggest that mere exposure to a view is enough to get one to passively accept it, at least until it is specifically rejected.<br />
*[http://lesswrong.com/lw/ke/illusion_of_transparency_why_no_one_understands/ Illusion of Transparency] - Everyone knows what their own words mean, but experiments have confirmed that we systematically overestimate how much sense we are making to others.<br />
*[http://lesswrong.com/lw/kf/selfanchoring/ Self-Anchoring] - Related to contamination and the illusion of transparancy, we "anchor" on our own experience and underadjust when trying to understand others.<br />
*[http://lesswrong.com/lw/lg/the_affect_heuristic/ Affect Heuristic] - Positive and negative emotional impressions exert a greater effect on many decisions than does rational analysis.<br />
*[http://lesswrong.com/lw/lh/evaluability_and_cheap_holiday_shopping/ Evaluability] - It's difficult for humans to evaluate an option except in comparison to other options. Poor decisions result when a poor category for comparison is used. Includes an application for cheap gift-shopping.<br />
*[http://lesswrong.com/lw/li/unbounded_scales_huge_jury_awards_futurism/ Unbounded Scales, Huge Jury Awards, and Futurism] - Without a metric for comparison, estimates of, e.g., what sorts of punative damages should be awarded, or when some future advance will happen, vary widely simply due to the lack of a scale.<br />
*[http://lesswrong.com/lw/lj/the_halo_effect/ The Halo Effect] - Positive qualities <i>seem</i> to correlate with each other, whether or not they ''actually'' do.<br />
*[http://lesswrong.com/lw/m9/aschs_conformity_experiment/ Asch's Conformity Experiment] - The unanimous agreement of surrounding others can make subjects disbelieve (or at least, fail to report) what's right before their eyes. The addition of just one dissenter is enough to dramatically reduce the rates of improper conformity.<br />
*[http://lesswrong.com/lw/my/the_allais_paradox/ The Allais Paradox] (and [http://lesswrong.com/lw/mz/zut_allais/ subsequent] [http://lesswrong.com/lw/n1/allais_malaise/ followups]) - Offered choices between gambles, people make decision-theoretically inconsistent decisions. <br />
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==See also==<br />
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*[[Heuristics and biases]], [[Heuristic]]<br />
*[[Debiasing]], [[Dangerous knowledge]]<br />
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==Not to be confused with==<br />
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*[[Statistical bias]]<br />
*[[Inductive bias]]<br />
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[[Category:Concepts]]<br />
[[Category:Biases]]</div>Xadmin