Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Thu, 08 May 2025 11:45:49 -0700 Received: from [192.168.123.254] (port=58360 helo=web.lojban.org) by fe3e2dc928fd with smtp (Exim 4.96) (envelope-from ) id 1uD6Ff-0037nC-0T for jbovlaste-admin@lojban.org; Thu, 08 May 2025 11:45:49 -0700 Received: by web.lojban.org (sSMTP sendmail emulation); Thu, 08 May 2025 18:45:46 +0000 From: "Apache" To: ByronJohnsonFP@gmail.com Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word pabykanpystika -- By bairyn Date: Thu, 8 May 2025 18:45:46 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / In jbovlaste, the user bairyn has edited a definition of "pabykanpystika" in the language "English". Differences: 5,5c5,7 < --- > This is evidence as understood in a Bayesian framework, arising from Bayes' theorem. Evidence, in terms of Bayes' rule, updates degrees of belief by decomposing the update of the probability / magnitude to the posterior (afterwards) probability of the belief into its prior (before) probability and (multiplied by) the likelihood ratio. The likelihood ratio represents how much better the belief predicts the evidence (how likely is the evidence if the hypothesis is true?) than not-belief predicts the hypothesis (how likely is the evidence if the hypothesis is false?). It is derived mathematically from probability theory. > > ni'o This formulation uses Bayes' rule formulation, not the Bayes' theorem style. They are equivalent, but Bayes' rule allows separation of the evidence strength from the prior odds, providing for an intuitive form of just newOdds ＝ oldOdds ⋅ evidenceStrength, since it uses odds, except in the likelihood ratio (the likelihood ratio is evidenceStrength), the numerator and the denominator are probabilities (it's a ratio of probabilities, but otherwise it's in terms of odds). The Bayes' Theorem style, an equivalent formula, does not use odds but only probability. Old Data: Definition: $x_1=s_1$ is Bayesian evidence for belief / prediction / hypothesis $x_2=k_2$, with evidence magnitude / strength (and direction), as a likelihood ratio as odds, $x_3=s_3=p_1$ since the hypothesis predicts the evidence to degree / with probability $x_4=p_2$ and since not-hypothesis predicts the evidence to degree / with probability $x_5=p_3$, updating $x_6=k_1$'s belief strength / odds / confidence to posterior odds / new confidence $x_7=k_3$ from prior odds / old confidence $x_8=s_2$; $x_1$ is evidence for $x_2$ with evidence strength and direction $x_3$ due to how much better (or worse) the hypothesis predicts the evidence (amount $x_4$) than not-hypothesis predicts the evidence (amount $x_5$), according to knowledge / truth / subjective probability judge / assigner / evaluator $x_6$, who after accounting for the evidence has odds in the hypothesis $x_7$ after prior odds $x_8$. Notes: Jargon: Gloss Keywords: Place Keywords: New Data: Definition: $x_1=s_1$ is Bayesian evidence for belief / prediction / hypothesis $x_2=k_2$, with evidence magnitude / strength (and direction), as a likelihood ratio as odds, $x_3=s_3=p_1$ since the hypothesis predicts the evidence to degree / with probability $x_4=p_2$ and since not-hypothesis predicts the evidence to degree / with probability $x_5=p_3$, updating $x_6=k_1$'s belief strength / odds / confidence to posterior odds / new confidence $x_7=k_3$ from prior odds / old confidence $x_8=s_2$; $x_1$ is evidence for $x_2$ with evidence strength and direction $x_3$ due to how much better (or worse) the hypothesis predicts the evidence (amount $x_4$) than not-hypothesis predicts the evidence (amount $x_5$), according to knowledge / truth / subjective probability judge / assigner / evaluator $x_6$, who after accounting for the evidence has odds in the hypothesis $x_7$ after prior odds $x_8$. Notes: This is evidence as understood in a Bayesian framework, arising from Bayes' theorem. Evidence, in terms of Bayes' rule, updates degrees of belief by decomposing the update of the probability / magnitude to the posterior (afterwards) probability of the belief into its prior (before) probability and (multiplied by) the likelihood ratio. The likelihood ratio represents how much better the belief predicts the evidence (how likely is the evidence if the hypothesis is true?) than not-belief predicts the hypothesis (how likely is the evidence if the hypothesis is false?). It is derived mathematically from probability theory. ni'o This formulation uses Bayes' rule formulation, not the Bayes' theorem style. They are equivalent, but Bayes' rule allows separation of the evidence strength from the prior odds, providing for an intuitive form of just newOdds ＝ oldOdds ⋅ evidenceStrength, since it uses odds, except in the likelihood ratio (the likelihood ratio is evidenceStrength), the numerator and the denominator are probabilities (it's a ratio of probabilities, but otherwise it's in terms of odds). The Bayes' Theorem style, an equivalent formula, does not use odds but only probability. Jargon: Gloss Keywords: Place Keywords: You can go to to see it.