On the applicability of maximum entropy to inexact reasoning

Paris, Jeffrey; Vencovská, Alena

doi:10.1016/0888-613x(89)90012-1

Cited by 50 publications

(31 citation statements)

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“…The study of note in this case which does not simply consider the convex hull of P * is [25]. 17 Paris & Vensovská have, of course, also found a natural way in which Maxent is uniquely rational for the purposes of estimating objective probabilities [21]. In a later paper [19, p. 275-276], Jeff Paris is somewhat more sympathetic towards CM for estimating objective probabilities.…”

Section: The Right Inference Process?mentioning

confidence: 99%

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Invariant Equivocation

Landes

Masterton

2016

Erkenn

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Objective Bayesians hold that degrees of belief ought to be chosen in the set of probability functions calibrated with one's evidence. The particular choice of degrees of belief is via some objective, i.e., not agentdependent, inference process that, in general, selects the most equivocal probabilities from among those compatible with one's evidence. Maximising entropy is what drives these inference processes in recent works by Williamson and Masterton though they disagree as to what should have its entropy maximised. With regard to the probability function one should adopt as one's belief function, Williamson advocates selecting the probability function with greatest entropy compatible with one's evidence while Masterton advocates selecting the expected probability function relative to the density function with greatest entropy compatible with one's evidence. In this paper we discuss the significant relative strengths of these two positions. In particular, Masterton's original proposal is further developed and investigated to reveal its significant properties; including its equivalence to the centre of mass inference process and its ability to accommodate higher order evidence.Keywords: Maximum Entropy, Objective Bayesianism, Inference Process, Centre of Mass, Language Invariance 1 Introduction "How should one form graded beliefs?" is a question that has long fascinated philosophers. The answer to this question is highly relevant throughout science, law, operational research and policy-making. Intuitively, it is obvious that one's evidence ought to matter when forming beliefs, whether graded or binary. The best way of caching out this ubiquitous intuition is, however, a matter of lively disagreement. The main philosophical protagonists in this debate are: the subjective Bayesians, who can be further subdivided into the radical (de Finetti This paper is concerned with objective Bayesianism. Objective Bayesians, like their subjective brethren, hold that one's degrees of belief ought to be consistent with one's evidence. However, in cases where the evidential constraints are satisfied by more than one probability function the objective Bayesians differ from the subjective Bayesians in holding that the choice of a particular probability function from those consistent with the evidential constraints ought to made 1 in an objective-i.e., agent-independent-manner. Typically, such a choice is made by applying an inference process that picks from among the probability functions consistent with the evidential constraints that function which is, in some sense, maximally equivocal. 1 Objective Bayesianism is (still!) a minority view with a relatively small but dedicated group of advocates. Even in this relatively small group there are disagreements. One such recent disagreement is that between Williamson [27] and Masterton [16] on how to understand maximal equivocation.We shall herein first rehearse Williamson's account in Section 2.1 and 2.2. Then we improve on Masterton's approach by reformulating it, Section 2...

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Section: The Right Inference Process?mentioning

confidence: 99%

“…What they are not is estimates of objective probabilities. emphasis original then Williamson's account (Maxent in Paris's terms) seems to be the clear objective Bayesian frontrunner, see [21,22,24].…”

Section: The Right Inference Process?mentioning

confidence: 99%

Invariant Equivocation

Landes

Masterton

2016

Erkenn

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“…The restricted notion S (or S L ) in the case of a single knowledge base or agent, i.e. when n = 1, is simply called an inference process and the properties of such inference processes have been extensively studied by Paris, Vencovská and others (see [5,11,12,13,15]). …”

Section: Formalizationmentioning

confidence: 99%

The irrelevant information principle for collective probabilistic reasoning

Adamčík¹,

Wilmers²

2014

Kybernetika

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“…maximum entropy, to these. Interestingly, the recommendation to maximize entropy (and minimize cross-entropy) also arise naturally in the context in the random-worlds approach; see section 6 of [2] for an extended discussion of the close relationship between the random-worlds method and maximum entropy (also early results in [19], where belief constraints are treated as if they arose from a large population of random worlds, and a criticism of this assumption in section 4 of [18]). In consequence, the randomworlds method can be applied to give the same solutions as we are prescribing.…”

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confidence: 99%

“…In particular, Kemeny's early contribution [15], the paper of Fagin [9] and the study of Zero-One Laws that it helped initiate (for a recent introduction see [7]), the work of Paris and Vencovská [19], [21], [18], of Shastri [26] and in particular the ambitious and wide-ranging development of Grove et al in [1], [2], [11], [12], [13].…”

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confidence: 99%