more from this thinker     |     more from this text

Single Idea 16837

[filed under theme 14. Science / C. Induction / 6. Bayes's Theorem ]

Full Idea

In p(H|E) = p(E|H)p(H)/p(E), the left side is the 'posterior' probability of H given E, p(E|H) is the 'likelihood' of E given H, and the others are the 'priors' of H and E. Moving from right to left is known as 'conditionalization'.

Gist of Idea

Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising'

Source

Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian')

Book Ref

Lipton,Peter: 'Inference to the Best Explanation (2nd ed)' [Routledge 2004], p.103

The 19 ideas with the same theme [equation showing probability of an inductive truth]:

14280 The probability of two events is the first probability times the second probability assuming the first [Bayes]
22656 Trying to assess probabilities by mere calculation is absurd and impossible [James]
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
19155 Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson]
2751 Probabilities can only be assessed relative to some evidence [Dancy,J]
2798 Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]
2799 Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
16802 Bayes seems to rule out prior evidence, since that has a probability of one [Lipton]
16803 Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton]
16801 A hypothesis is confirmed if an unlikely prediction comes true [Lipton]
16837 Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton]
16839 Explanation may be an important part of implementing Bayes's Theorem [Lipton]
6372 Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz]
17600 Bayesian inference is forced to rely on approximations [Thagard]
14990 Bayes produces weird results if the prior probabilities are bizarre [Sider]
6798 Bayesianism claims to find rationality and truth in induction, and show how science works [Bird]
22178 If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
17943 Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
22365 The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger]