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A Natural Law of Succession
, 1995
"... Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we presen ..."
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Cited by 35 (3 self)
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Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we present a new solution to this fundamental problem in statistics and demonstrate that our solution outperforms standard approaches, both in theory and in practice.
Inferring Sentenceinternal Temporal Relations
 In HLT 2004
, 2004
"... In this paper we propose a data intensive approach for inferring sentenceinternal temporal relations, which relies on a simple probabilistic model and assumes no manual coding. ..."
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Cited by 28 (1 self)
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In this paper we propose a data intensive approach for inferring sentenceinternal temporal relations, which relies on a simple probabilistic model and assumes no manual coding.
Binary induction and Carnap’s continuum
 In Proceedings of the 7th Workshop on Uncertainty Processing (WUPES
, 2006
"... We consider the problem of induction over languages with binary predicates and show that a natural generalization of Johnson’s Sufficientness Postulate eliminates all but two solutions. We discuss the historical context and connections to the unary case. 1 ..."
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Cited by 2 (0 self)
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We consider the problem of induction over languages with binary predicates and show that a natural generalization of Johnson’s Sufficientness Postulate eliminates all but two solutions. We discuss the historical context and connections to the unary case. 1
Munich, 2012
, 2012
"... I have commonly heard philosophers say that Goodman’s GRUE Paradox, [12], [13], spells the end of Carnap’s Inductive Logic Programme, see [1], [2], [3], [4], [7], [8]. 1 That may indeed be so if one intends it to be an applied subject, to be applicable to the problem of our assigning probabilities i ..."
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I have commonly heard philosophers say that Goodman’s GRUE Paradox, [12], [13], spells the end of Carnap’s Inductive Logic Programme, see [1], [2], [3], [4], [7], [8]. 1 That may indeed be so if one intends it to be an applied subject, to be applicable to the problem of our assigning probabilities in the real world, as I suppose was Carnap’s primary aim. However as Carnap
Pure Inductive Logic
"... Before a football match can begin the tradition is that the referee tosses a coin and one of the captains calls, heads or tails, whilst the coin is in the air. If the captain gets it right s/he picks which end to start playing at, or alternatively to have the kick off. There never seems to be an iss ..."
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Before a football match can begin the tradition is that the referee tosses a coin and one of the captains calls, heads or tails, whilst the coin is in the air. If the captain gets it right s/he picks which end to start playing at, or alternatively to have the kick off. There never seems to be an issue of which captain actually
6 The Johnson–Carnap Continuum
"... Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 2 to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bay ..."
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Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 2 to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the Johnson–Carnap continuum of inductive methods, as well as the Nix–Paris
ESTIMATION OF THE NUMBER OF SPECIES FROM A RANDOM
"... Dedicated to the memory of Thyagaraju Chelluri, a wonderful human being who would have become a fine mathematician had his life not been cut tragically short. Abstract. We consider the classical problem of estimating T, the total number of species in a population, from repeated counts in a simple ra ..."
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Dedicated to the memory of Thyagaraju Chelluri, a wonderful human being who would have become a fine mathematician had his life not been cut tragically short. Abstract. We consider the classical problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample and propose a new algorithm for treating it. In order to produce an estimator T ̂ we actually start from the estimation of a related quantity, the unobserved probability U. In fact, we first show that an estimation of T can be obtained by requiring compatibility between the Laplace addone (or addλ) estimator and the TuringGood estimator ÛTG of U; the estimators obtained in this way concide with those of ChaoLee and of HorvitzThompson, depending on λ. On the other hand, since the Laplace formula can be derived as the mean of a Bayesian posterior with a uniform (or Dirichlet) prior, we later modify the structure of the likelihood and, by requiring the compatibility of the new posterior with ÛTG, determine a modified Bayesian estimator T ̂ ′. The form of T ̂ ′ can be again related to that of ChaoLee, but provides a better justified term for their estimated variance. T ̂ ′ appears to be extremely effective in estimating T, for instance improving upon all existing estimators for the standard fully explicit Carothers data. In addition, we can derive estimations of the population distribution, confidence intervals for U and confidence intervals for T; these last appear to be the first in the literature not based on resampling. 1 2Keywords and phrases: simple random sample, unobserved species, unobserved probability, point estimator, confidence interval, Dirichlet prior, Bayesian posterior. 1.