### Citations

280 | Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy
- Shore, Johnson
(Show Context)
Citation Context ... in order to isolate this Maxent solution, but that really was not the case.) Results characterizing Maxent in terms of “Rational Principles” had been obtained before, e.g., by Shore and Johnson, see =-=[3]-=-, but these had all assumed the choice of probability function to be the maximum point of some function F , the problem then being to characterize F . We made no such assumption, only that the agent w... |

241 |
least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems, The Annals of Statistics 19
- Csiszár, Why
- 1991
(Show Context)
Citation Context ...lity function to be the maximum point of some function F , the problem then being to characterize F . We made no such assumption, only that the agent was making some choice (Independently, Csiszár in =-=[4]-=- also gives a characterization of Maxent (and Least Squares etc.) without this assumption.) In a later paper, [5], the results of [1] were extended to much more general knowledge bases. Over my time o... |

65 |
A note on the inevitability of maximum entropy
- Paris, Vencovská
- 1990
(Show Context)
Citation Context ...se requirements/principles that we formulated left no choice as to what I could be, the principles forced I to be Maxent, i.e., I(K) = the solution to K which maximised the entropy, see, for example, =-=[1,2]-=-. (Actually we were subsequently accused of fabricating these principles in order to isolate this Maxent solution, but that really was not the case.) Results characterizing Maxent in terms of “Rationa... |

63 |
Information Theory and Statistical
- Jaynes
- 1957
(Show Context)
Citation Context ... degrees of belief. What they are not is estimates of objective probabilities. (There certainly are arguments for applying Maxent in the context of objective probabilities, for classic example(s) see =-=[10,11]-=-, but they are not the concern of this paper and should not be allowed to confuse the issues.) The answer 3/4 might look OK if one was trying to minimize the difference (TrueProb(p)− EstimatedProb(p))... |

39 | The well-posed problem.
- JAYNES
- 1973
(Show Context)
Citation Context ...nsidering here, the Principle of Insufficient Reason is associated with a number of paradoxes, in particular von Mises Water and Wine Paradox and Bertrand’s Stick and Circle Paradox. Interestingly in =-=[13]-=- Jaynes proposes a solution to this latter by considering essentially the sort of invariance under automorphisms that we detail here in the discrete case. Naturally this has not met with total accepta... |

23 |
Entropy and uncertainty.
- Seidenfeld
- 1986
(Show Context)
Citation Context ...Unfortunately, these delusions were not completely exorcized, hence this current attempt to hopefully save some souls from eternal darkness. Entropy 2014, 16 6188 2. Maxent and Language Dependence In =-=[7]-=-, and elsewhere, Teddy Seidenfeld (amongst many others. I have chosen this paper because of its especially wide influence) seemingly intends to criticize the Maxent inference process, ME say, for bein... |

23 | Representation Dependence in Probabilistic Inference.
- Halpern, Koller
- 2004
(Show Context)
Citation Context ...obability function satisfying K ′ with maximum entropy, despite K and K ′ “representing the same knowledge” (subsequently there have been various attempts to solve this general “problem”, for example =-=[8,9]-=-). He gives the following example of this. Consider a conventional die with faces marked 1 to 6. Let pi stand for The die lands with face i uppermost (1) He does not spell out what he takes the knowle... |

21 |
Common Sense and Maximum Entropy’, Synthèse 117(1): 75–93
- Paris
- 1998
(Show Context)
Citation Context ...onstraints can be replaced by ≤ without changing any of the results we shall need herein). Strictly speaking w here is a variable standing for a probability function on SL, that is a function w : SL→ =-=[0, 1]-=- satisfying, for θ, φ ∈ SL: (P1) |= θ ⇒ w(θ) = 1, (P2) θ |= ¬φ⇒ w(θ ∨ φ) = w(θ) + w(φ). On the face of it, this might seem like a very special and restricted context. Nevertheless, it is one which is ... |

14 | Maximum entropy and the glasses you are looking through
- Grünwald
(Show Context)
Citation Context ...obability function satisfying K ′ with maximum entropy, despite K and K ′ “representing the same knowledge” (subsequently there have been various attempts to solve this general “problem”, for example =-=[8,9]-=-). He gives the following example of this. Consider a conventional die with faces marked 1 to 6. Let pi stand for The die lands with face i uppermost (1) He does not spell out what he takes the knowle... |

11 |
Common sense and stochastic independence
- Paris, Vencovská
- 2001
(Show Context)
Citation Context ...such assumption, only that the agent was making some choice (Independently, Csiszár in [4] also gives a characterization of Maxent (and Least Squares etc.) without this assumption.) In a later paper, =-=[5]-=-, the results of [1] were extended to much more general knowledge bases. Over my time of working on this area I came to the opinion that Maxent is synonymous with “common sense”, at least in this limi... |

11 |
Why i am not an objective bayesian; some reflections prompted by rosenkrantz. Theory and Decision
- Seidenfeld
- 1979
(Show Context)
Citation Context ...ow be reconciled my resulting knowledge would be considerably more than just the above K ′. Entropy 2014, 16 6192 4. Maxent and Insufficient Reason In the above mentioned paper [7], and previously at =-=[12]-=- (p. 424), Seidenfeld appears to be thinking of Maxent as a souped up version of Laplace’s Principle of Insufficient Reason—that if there is no reason for two sentences/events to have different probab... |

6 | Bertrand’s paradox and the principle of indifference. Philosophy of Science 74 - Shackel |

5 | A resolution of Bertrand’s paradox - Marinoff - 1994 |

2 | Bertrand’s Paradox Revisited: Why Bertrand’s ‘Solutions - Rowbottom - 2013 |

1 | Solving the Hard Problem of Bertrand’s Paradox - Aerts, Bianci |

1 | On Bertrand’s Paradox - Bangu |

1 | Defusing Bertrand’s Paradox - Gyenis, Rédei |

1 | defense of Bertrand: The non-restrictiveness of reasoning by example - Klyve |

1 | Bangu’s random thoughts on Bertrand’s Paradox - Rowbottom, Shackel |