de Finetti, B., 1974. Theory of Probability, vol. 1. John Wiley and Sons, New York NY.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....procedure analogous to quantum state tomography in Bayesian theory is the estimation of an unknown probability from the results of repeated trials on identically prepared systems. The way to eliminate unknown probabilities from this situation was introduced by Bruno de Finetti in the early 1930s [104]. His method was simply to focus on the equivalence of the repeated trials namely, that what is really important is that the systems are indistinguishable as far as probabilistic predictions are concerned. Because of this, any probability assignment p(x 1 , x 2 , xN ) for multiple ....

....paper is a bit of a transitionary one for me in that, since writing quant ph 0106166, I have become much more convinced of the consistency and value of the radically subjective Bayesian paradigm for probability theory. That is, I have become much more inclined to the view of Bruno de Finetti [104], say, than that of Edwin Jaynes [111] To that end, I have stopped calling probability distributions states of knowledge and been more true to the conception that they are states of belief whose cash value is determined by the way an agent will gamble in light of them. That is, a probability ....

B. de Finetti, Theory of Probability (Wiley, New York, 1990.

....out some consequences of applying the classic Dutch Book justi cation for rational belief being identi ed with probability in the context of alternate, non Tarskian, semantics. Whilst the formal version of the Dutch Book Theorem that we shall need is well know from the work of De Finetti, see [5] p90, our observations concerning the consequences of this theorem for characterizing rational belief functions in the context of certain alternate, non standard, semantics would, with the exception of a speci c earlier example due to Ja ray, 8] see also Regoli, 13] appear not to be widely ....

....1 ( V ( 0; T2) V ( 1 ( V ( 1 V ( 1; T3) V ( 0 ( V ( 0 V ( 0; T4) V ( 0 ( V ( 1 V ( 0: In this case V is nite since L is nite and every V 2 V is determined by its values on the propositional variables alone. Theorem 1 [4] [5] The function B 2 B is a probability function, that is satis es that for all ; 2 SL, P1) If j= then B( 1; if j= then B( 0 (P2) If j= then B( B( P3) B( B( B( B( if and only if there does not exist a Dutch Book against B. That is, there do ....

[Article contains additional citation context not shown here]

De Finetti, B., Theory of Probability, Vol.1, Wiley, New York, 1974.

....have been studied intensely. With regards to the first question, many researchers have suggested differentsetsof properties that should be satisfied by degrees of belief (e.g. Ramsey 1931, Cox 1946, Good Figure 1: The probability wheel: a tool for assessing probabilities. 1950, Savage 1954, DeFinetti 1970). It turns out that each set of properties leads to the same rules: the rules of probability. Although each set of properties is in itself compelling, the fact that different sets all lead to the rules of probability provides a particularly strong argument for using probability to measure ....

de Finetti, B. (1970). Theory of Probability. Wiley and Sons, New York.

....its subjective flavour, for the principle prevents subjective probability being bolstered into a logical interpretation. 1 Guess the number I am thinking of a particular natural number. For any natural number n, how confident are you that it is the one I am thinking of [Kolmogorov 1933] de Finetti 1970] A distinctive feature of this scenario is that the alternatives about which I am asking you to form beliefs constitute a countably infinite partition. There is no great conceptual difficulty in dealing with the infinite here perhaps you don t assign any credence to the event that I am ....

....p n Should we force him, against his own judgement, to assign practically the entire probability to some finite set of events, perhaps chosen arbitrarily Such limitations on the choice of the probabilities are altogether extraneous to the essence of the consistency condition. 122 [de Finetti 1970] 91 92 [de Finetti 1972] Suppose someone chooses his subjective probability distribution over a countable partition: Someone tells him that in order to be coherent he can choose the p i in any way he likes, so long as the sum = 1 (it is the same thing as in the finite case, anyway ) The ....

[Article contains additional citation context not shown here]

Bruno de Finetti: `Theory of probability', Wiley, 1974.

....# (1) where # is the document in question, # is the topic model and # Submission for CIKM 2002. Please do not cite or distribute this draft paper. is the i th term in the document. But to quote the famous probability theorist De Finetti, dependence is the norm rather than the contrary [2]. From our own understanding of natural language, we know that the assumption of term independence is a matter of mathematical convenience rather than a reality. For example, a document that contains the term Bin Laden is very likely to contain the terms Al Qaeda , Afghanistan , etc. ....

B. De Finetti, Theory of Probability, 1:146-161, Wiley, London 1974.

....in this paper. In Section 3, we make our model as conservative as possible by representing the ignorance about the incompleteness mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities [14] This theory is a generalisation of the Bayesian theory of probability [3], with a closely related behavioural interpretation, and based on similar criteria of rationality. Because we are aware that readers may not be familiar with imprecise probability models, we present a brief discus But see the discussion by Walley in [14, Section 6.11] which has been a source ....

....to the set of all distributions, i.e. it makes all incompleteness mechanisms possible a priori. Our basic model follows from this as a necessary consequence, using the rationality requirement of coherence (a generalisation of the requirements of rationality in Bayesian probability theory [3]) We illustrate how our basic model works by addressing the Monty Hall puzzle, showing that the apparent paradox vanishes if the available knowledge about the incompleteness mechanism is properly modelled. We then apply our method for dealing with incomplete observations to the special case of a ....

[Article contains additional citation context not shown here]

B. de Finetti. Theory of Probability, volume 1. John Wiley & Sons, Chichester, 1974. English Translation of Teoria delle Probabilit a.

....lattice volume in a natural way so that all of R is covered. The resultant expression takes the form S h = exp [e h(x)#(x) d 1] d#(#) where # is a positive measure on fields that fulfills d#(#) #. As such we recognize S h as determined by a generalized Poisson process [3]. The parameter K may be chosen, e.g. to satisfy some normalization condition on the two point function. Elements 1 through 6 represent our recipe for resolving the ramifications of triviality. Frequently Asked Questions Why have we chosen P 4 as we have Elsewhere (see Chapter 8 in ....

B. DeFinetti, Theory of Probability, Vol. 2, (John Wiley & Sons, London, 1975).

....have been studied intensely. With regards to the first question, many researchers have suggested different sets of properties that should be satisfied by degrees of belief (e.g. Ramsey 1931, Cox 1946, Good Figure 1: The probability wheel: a tool for assessing probabilities. 1950, Savage 1954, DeFinetti 1970). It turns out that each set of properties leads to the same rules: the rules of probability. Although each set of properties is in itself compelling, the fact that different sets all lead to the rules of probability provides a particularly strong argument for using probability to measure ....

de Finetti, B. (1970). Theory of Probability. Wiley and Sons, New York.

.... follow from the algebraic rules of auxiliary functions F and G that we will soon adopt: Propositional limit assumption : G(x, F (#,x) #, F (x, S(S(x) x, and S(#) 3 Coherence, or Dutch Book avoidance We have now stated the common assumptions of most existing theories of plausibility[16, 14, 12, 34]. But more is required before probability appears as inevitable in a form we recognize. What is required is some means to derive constraints on sets of plausibilities of di#erent conditional statements. Without such constraints we can easily define plausibility measures that are not equivalent to ....

....a gambler can choose a combination which gives positive payo# in every situation seems to have made his bets from a globally incoherent set of beliefs. Several papers show, with important di#erences in detail, that every coherent belief set is equivalent to probability or robust probability theory[14, 12, 34, 25, 18, 9]. This type of argument has been used recently to criticize non Bayesian belief revision systems[39] However, there have also been arguments against this principle. One objection is related to possible complications with non linear utility functions [25, Discussion ] Another is related to the ....

[Article contains additional citation context not shown here]

B. de Finetti. Theory of Probability. London: Wiley, 1974.

....procedure analogous to quantum state tomography in Bayesian theory is the estimation of an unknown probability from the results of repeated trials on identically prepared systems. The way to eliminate unknown probabilities from this situation was introduced by Bruno de Finetti in the early 1930s [67]. His method was simply to focus on the equivalence of the repeated trials namely, that what is really of importance is that the systems are indistinguishable as far as probabilistic predictions are concerned. Because of this, any probability assignment p(x 1 ; x 2 ; xN ) for multiple ....

B. de Finetti, Theory of Probability (Wiley, New York,

.... in turn, storing incomplete information, which has strong links with work on non monotonic reasoning [55] imprecise information, which has been handled by various applications of fuzzy sets [168] and fuzzy logic [165, 166] and uncertain information, which has been dealt with using probability [48], possibility [40, 167] and Dempster Shafer theory [141] It should be noted, however, that the di erent forms of imperfection cannot be so cleanly seperated as this description suggests. For instance, the fact that data is imprecise will lead to queries that are made upon it returning answers ....

....pieces of information. 4.3. 2 Probabilistic logics The classic paper on reasoning combining logic and probability is due to Nilsson [107] though unbeknownst to him he was restating for an arti cial intelligence audience work that was originally carried out by Smith [147] and de Finetti [48]. The paper considers the consequence of combining the probabilities assigned to P and P Q when the two are combined using modus ponens. In general the probabilities on a set of sentences do not completely determine the underlying joint distribution so that it is only possible to determine the ....

[Article contains additional citation context not shown here]

de Finetti, B. (1974) Theory of Probability, Wiley, New York.

....this fact into consideration, some of the problems associated with subjective probabilities disappear. 1 Introduction In the Bayesian approach to reasoning under uncertainty, probability is viewed as a subjective notion. While the Bayesian approach has strong theoretical foundations (see, e.g. De Finetti (1974); Savage (1954) and typically performs well in practice, several aspects of the interpretation of subjective probability remain controversial and problematic. In order to deal with such concerns, one may attempt to define the meaning of subjective probabilities in non probabilistic terms. In this ....

....to such researchers, that (a) the problem of making overly strong inferences can be rigorously shown to exist (see Example 6) but that (b) this problem can in principle be solved, too. The Meaning of the Meaning of Subjective Probability Two classic approaches (due to Savage (1954) and De Finetti (1974)) define the meaning of subjective probability by giving a precise answer to the following question: Behavior Question What does the statement Agent s subjective distribution is P entail in terms of behavior of the Agent if the Agent s task is to make decisions and or predictions about the ....

[Article contains additional citation context not shown here]

De Finetti, B. 1974. Theory of Probability. A critical introductory treatment.

....has access only to the actions of the expert, for example his betting behavior or verbal reports, which are inextricably linked to utility as well as belief. Various elicitation aids have been designed to extract beliefs from actions, including lotteries, scoring rules [6] and promissory notes [2] This task is underconstrained, though, and any one of a continuous family of belief utility pairs offers an equally valid explanation for a particular behavior. Elicitation devices based on monetary incentives actually reveal risk neutral probabilities, or the probabilities at which a ....

.... actually reveal risk neutral probabilities, or the probabilities at which a risk neutral agent would choose the same actions, which may differ significantly from true probabilities [3,4] The modeler seeks to describe the joint distribution across a set of S binary, uncertain events, Z = fA 1 ; A 2 ; AS g. Let Omega = f 1 ; 2 ; 2 Sg be the set of all 2 S possible joint outcomes of the events, also called the atomic states. The expert has a subjective probability distribution Pr over Omega and utility u(y) for y dollars, which may in general depend on the state. Let ....

[Article contains additional citation context not shown here]

B. de Finetti. Theory of Probability. J. Wiley, New York, 1974.

....sequence is de ned by (i) k) Tr k 1 (k 1) for all k, where Tr k 1 denotes the partial trace over the (k 1)th system, and (ii) each (k) is invariant under permutations of the k systems on which it is de ned. This de nition is the quantum generalization of de Finetti s [14] de nition of exchangeable sequences of classical random variables. A state (N) is exchangeable if and only if it can be written in the form (N) Z d p( N ; 5) where d is a measure on density operator space, and p( is a normalized generating function, R d p( 1. This ....

....in the form (N) Z d p( N ; 5) where d is a measure on density operator space, and p( is a normalized generating function, R d p( 1. This is a consequence of the quantum de Finetti theorem, the quantum version of the fundamental representation theorem due to de Finetti [14] The quantum 4 theorem was rst proved by Hudson and Moody [15] after pioneering work by St rmer [16] for an elementary proof see Ref. 17] How, in general, do we pick p( d To our knowledge, there is no universal rule for this task, although there exist a number of proposals for unbiased ....

[Article contains additional citation context not shown here]

B. de Finetti, Theory of Probability (Wiley, New York, 1990).

....M 0, there is a state (N M) of N M subsystems that is invariant under permutations of the subsystems and that satis es 3 (N) tr M ( N M) 21,22] The expansion (10) is then unique. This is the quantum version of the fundamental representation theorem due to de Finetti [23]; for an elementary proof of the quantum theorem see Ref. 24] The signi cance of part (ii) of the de nition of exchangeability given above is illustrated by the GHZ state GHZ = j GHZ ih GHZ j, where j GHZ i = j000i j111i) p 2. This threeparticle state is invariant under permutations ....

B. de Finetti, Theory of Probability (Wiley, New York, 1990).

....nonprobabilistic part of classical decision theory, then one is e ectively introducing probabilities at the same time. Indeed, once one realizes that quantum theory deals with uncertain outcomes, one is forced to introduce probabilities as they provide the only language for quantifying uncertainty [3,5,6,9,10]. From this point of view, the most powerful and compelling derivation of the quantum probability rule is Gleason s theorem. Gleason s theorem: 7,11,12] Assume there is a function f from the onedimensional projectors acting on a Hilbert space of dimension greater than 2 to the unit interval, ....

B. de Finetti, Theory of Probability, Vols. I and II (Wiley, New York, 1972).

....prediction consists of two numbers, E i and D i 0; roughly, E i is the Bookmaker s expectation of X i , and D i is his expectation of the accuracy L i : X i Gamma E i ) 2 (measured by the Brier scoring rule, see Dawid [1] of the prediction E i . Along the lines of Chapter 3 of de Finetti [2] we give an operative interpretation to the numbers E i and D i as follows. Before X i is disclosed, the Bookmaker lets the Statistician buy any amount, positive or negative, of X i tickets for E i each and L i tickets for D i each. An X i ticket (resp. L i ticket) is a contract which ....

B. de Finetti. Theory of probability. Vol. 1. London: Wiley (1974)

....have different levels of probability, depending whether we think that they are more likely to be true or false (see Fig. 1) The concept of probability is then simply a measure of the degree of belief that an event will 1 occur. This is the kind of definition that one finds in Bayesian books[3, 4, 5, 6, 7] and the formulation cited here is that given in the ISO Guide to Expression of Uncertainty in Measurement [2] of which we will talk later. At first sight this definition does not seem to be superior to the combinatorial or the frequentistic ones. At least they give some practical rules to ....

....of probability 1=2 for each of the results in tossing a coin is only acceptable if: the coin is regular; it does not remain vertical (not impossible when playing on the beach) it does not fall into a manhole; etc. The subjective point of view is expressed in a provocative way by de Finetti s[5] PROBABILITY DOES NOT EXIST . 3 We will talk later about the influence of a priori beliefs on the outcome of an experimental investigation. 14 3 Conditional probability and Bayes theorem 3.1 Dependence of the probability from the status of information If the status of information changes, ....

[Article contains additional citation context not shown here]

B. de Finetti, "Theory of probability", J. Wiley & Sons, 1974.

....which only assume the value 0 and 1; and the constant gambles, which will be denoted by the unique value they assume in R. The set of all gambles is denoted by L( 7 A positive linear functional P on L( with P (1) 1 is called a linear prevision. Such a P is a prevision in the sense of de Finetti [7], and P (X) can be interpreted as a fair price for the gamble X . The set of all linear previsions with domain L( is denoted by P. Also assume that with the phenomenon of interest, there is associated a true linear prevision P T describing the uncertainty associated with it, but that the ....

B. de Finetti. Theory of Probability, volume 1. John Wiley & Sons, Chichester, 1974. English Translation of Teoria delle Probabilita.

....also more compelling. 1 Introduction The normative claim of Bayesianism is that every type of uncertainty should be described as probability. Bayesianism has been quite controversial in both the statistics and the uncertainty management communities. It developed as subjective Bayesianism, in [5, 11] Recently, the information based family of justifications, initiated in [3] and continued in [1] have been discussed in [12, 6, 13] We will try to find assumptions that are strong enough to strictly imply Bayesianism and at the same time convincing in a subjective way (common sense) In ....

....is no completion satisfying associativity, symmetry and strict monotonicity. A simple case where the partially specified function triples satisfy the laws, but no completion over the support points does so, is the following: Assume the partial specification satisfies F (x4 , x4 ) a (1) F (x3 , x5 ) a (2) F (x2 , x4) b (3) F (x1 , x5) b (4) F (x4 , x6) c (5) F (x3 , x7) c (6) F (x2 , x6) d (7) F (x1 , x8) d (8) Here we have assumed that the x i quantities are ordered increasingly in the open interval (0, 1) but the quantities a, b, c and d can have any values. If the ....

[Article contains additional citation context not shown here]

B. de Finetti, Theory of Probability, London:Wiley, 1974.

....(only) to the outcomes of repeated experiments. Since uncertainty is related to knowledge, probability is only meaningful as long as there are human beings interested in knowing (or forecasting) something, no matter if the events considered are in some sense determined, or known by other people. [7] Since fortunately we do not share identical states of information, we are in different conditions of uncertainty. Probability is therefore only and always conditional probability, and depends on the different subjects interested in it (and hence the name subjective) This point of view about ....

....Jeffreys priors) While perceiving that probabilities cannot represent only frequencies, they [subjective Bayesians] still regard sampling probabilities as representing frequencies of random variables . 20] The name random variable is avoided by the most authoritative subjective Bayesians [7] and the terms uncertain (aleatoric) numbers and aleatoric vectors (form multi dimensional cases) are currently used. Even the idea of repeated events is rejected [7] as every event is unique, though one might think of classes of analogous events to which we can attribute the same ....

[Article contains additional citation context not shown here]

B. de Finetti, Theory of Probability (J. Wiley & Sons, 1974).

....risk measures, notably V aR, from the perspective of imprecise previsions. The theory of imprecise previsions has been extensively studied by P. Walley [9] previous work on the topic includes [12] and the pioneering paper [7] The theory generalizes de Finetti s approach to precise previsions [3], is extremely general and flexible and includes also other uncertainty measures as special cases, for instance belief functions or 2 monotone lower probabilities. We show in this paper that it can also be applied to risk measures. To be more precise, after introducing in Section 2.1 a ....

....# N, for each X 0 , X 1 , X n # D, for each s 0 , s 1 , s n real and non negative, defining G = # n i=1 s i (P (X i ) X i ) s 0 (P (X 0 ) X 0 ) it is sup G # 0. This definition generalizes to imprecise previsions the coherence principle introduced by de Finetti [3] for (precise) previsions 1 and probabilities. It also includes the definition of coherent upper probability, which is obtained when each X # D is the indicator function E of some event E ( E is the random number which is equal to 1 if E is true, to 0 if E is false) The theory of ....

B. de Finetti. Theory of Probability, volume 1. Wiley, London, 1974.

No context found.

de Finetti, B., 1974. Theory of Probability, vol. 1. John Wiley and Sons, New York NY.

No context found.

De Finetti, B. (1974). Theory of Probability (2 volumes). Wiley, Chichester.

No context found.

B. de Finetti. Theory of probability. Vol. 1-2. John Wiley & Sons Ltd., Chichester, 1990. Reprint of the 1975 translation. S. Deerwester, S. Dumais, T. Landauer, G. Furnas, and R. Harshman. Indexing by latent semantic analysis. Journal of the American Society of Information Science, 41(6):391--407, 1990.

No context found.

B. de Finetti. Theory of Probability. London:Wiley, 1974.

No context found.

B. de Finetti. Theory of Probability (vol. 1), Wiley, 1974.

No context found.

DE FINETTI, B. Theory of Probability, vol. 1. John Wiley & Sons, Chichester, 1974. English Translation of Teoria delle Probabilit a.

No context found.

De Finetti, B. Theory of Probability, 1:146-161, Wiley, London 1974.

No context found.

B. de Finetti. Theory of Probability. London:Wiley, 1974.

No context found.

De Finetti, B. Theory of Probability, 1:146-161, Wiley, London 1974.

No context found.

B. de Finetti. Theory of Probability. John Wiley & Sons, Chichester, 1974.

No context found.

B. de Finetti, Theory of Probability, vol. 1 and 2 (John Wiley & Sons, London, New York, Sydney, Toronto, 1974.

No context found.

B. de Finetti. Theory of Probability. J. Wiley, New York, 1974.

No context found.

de Finetti, B.: 1974, Theory of Probability. New York: Wiley.

No context found.

B. de Finetti. Theory of Probability. Wiley, New York, 1974.

No context found.

DeFinetti, B. (1990). Theory of Probability, 2 vols. New York: Wiley.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC