scholarly journals THE THEORY OF SPECTRUM EXCHANGEABILITY

2014 ◽  
Vol 8 (1) ◽  
pp. 108-130
Author(s):  
E. HOWARTH ◽  
J. B. PARIS
Keyword(s):  
Probability Function ◽  
Inductive Logic ◽  
Probability Functions ◽  
Homogeneous Functions ◽  
Finite Structures ◽  
Spectrum Exchangeability

AbstractSpectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown1 that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language L is the set of sentences of L which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures for L, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.

A Modified Supervaluationist Framework for Decision-Making

2021 ◽  
Vol 12 (2) ◽  
pp. 175-191
Author(s):  
Jonas Karge ◽  
Keyword(s):  
Decision Making ◽  
Probability Function ◽  
Imprecise Probabilities ◽  
Adequate Account ◽  
Alternative Account ◽  
Semantic Approach ◽  
Probability Functions ◽  
Degree Of Belief ◽  
The Way

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework.

scholarly journals Isochrone Probability Functions for Old Stellar Systems

1999 ◽  
Vol 190 ◽  
pp. 345-346
Author(s):  
Peter A. Bergbusch
Keyword(s):  
Probability Function ◽  
Stellar Populations ◽  
Stellar Systems ◽  
Probability Functions ◽  
Luminosity Functions ◽  
Distance Relation

The isochrone probability function (IPF) is derived from the slope of the mass–distance relation on an isochrone in where the distance along the isochrone is computed with respect to some arbitrary, well-defined point. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations.

scholarly journals Nonconstant Sum Red-And-Black Games with Bet-Dependent Win Probability Function

2007 ◽  
Vol 44 (2) ◽  
pp. 547-553 ◽  
Author(s):  
Laura Pontiggia
Keyword(s):  
Probability Function ◽  
Positive Probability ◽  
Probability Functions

In this paper we investigate a class of N-person nonconstant sum red-and-black games with bet-dependent win probability functions. We assume that N players and a gambling house are engaged in a game played in stages, where the player's probability of winning at each stage is a function f of the ratio of his bet to the sum of all the players' bets. However, at each stage of the game there is a positive probability that all the players lose and the gambling house wins their bets. We prove that if the win probability function is super-additive and it satisfies f(s)f(t)≤f(st), then a bold strategy is optimal for all players.

scholarly journals TRIANGULATING NON-ARCHIMEDEAN PROBABILITY

2018 ◽  
Vol 11 (3) ◽  
pp. 519-546 ◽  
Author(s):  
HAZEL BRICKHILL ◽  
LEON HORSTEN
Keyword(s):  
Representation Theorem ◽  
Probability Function ◽  
Good Sense ◽  
Specific Kind ◽  
Probability Functions ◽  
Popper Functions

AbstractWe relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.

scholarly journals Discussion on D.C.M. Dickson & H.R. Waters Multi-Period Aggregate Loss Distributions for a Life Portfolio

1999 ◽  
Vol 29 (2) ◽  
pp. 311-314 ◽  
Author(s):  
Bjørn Sundt
Keyword(s):  
Positive Integer ◽  
Probability Function ◽  
The Other ◽  
Positive Probability ◽  
Probability Functions ◽  
Counting Distribution ◽  
Aggregate Loss ◽  
Image Position ◽  
Bold Face ◽  
Compound Probability

In the present discussion we point out the relation of some results in Dickson & Waters (1999) to similar results in Sundt (1998a, b).We shall need some notation. For a positive integer m let m be the set of all m × 1 vectors with positive integer-valued elements and m+ = m ~ {0}. A vector will be denoted by a bold-face letter and each of its elements by the corresponding italic with a subscript denoting the number of the elements; the subscript · denotes the sum of the elements. Let m0 be the class of probability functions on m with a positive probability at 0 and m+ the class of probability functions on m+. For j = 1,…, m we introduce the m × 1 vector ej where the jth element is one and all the other elements zero. We make the convention that summation over an empty range is equal to zero.Let g ∈ m0 be the compound probability function with counting distribution with probability function v ∈ 10 and severity distribution with probability function h ∈ m+; we shall denote this compound probability function by v V h. Sundt (1998a) showed thatwhere φv denotes the De Pril transform of v, given byMotivated by (2) Sundt (1998a) defined the De Pril transform φg of g byThis defines the De Pril transform for all probability functions in m0. Insertion of (2) in (3) givesand by solving φg(X) we obtainSundt (1998a) studies the De Pril transform defined in this way and found in particular that it is additive for convolutions.

scholarly journals Probability Functions of Order Statistics from Discrete Uniform Distribution

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Ayse Metin KarakaÅŸ ◽  
S. Çalik
Keyword(s):  
Order Statistics ◽  
Uniform Distribution ◽  
Probability Function ◽  
Probability Functions ◽  
Discrete Uniform Distribution ◽  
Discrete Uniform

In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.

Nonconstant Sum Red-And-Black Games with Bet-Dependent Win Probability Function

2007 ◽  
Vol 44 (02) ◽  
pp. 547-553 ◽  
Author(s):  
Laura Pontiggia
Keyword(s):  
Probability Function ◽  
Positive Probability ◽  
Probability Functions

In this paper we investigate a class of N-person nonconstant sum red-and-black games with bet-dependent win probability functions. We assume that N players and a gambling house are engaged in a game played in stages, where the player's probability of winning at each stage is a function f of the ratio of his bet to the sum of all the players' bets. However, at each stage of the game there is a positive probability that all the players lose and the gambling house wins their bets. We prove that if the win probability function is super-additive and it satisfies f(s)f(t)≤f(st), then a bold strategy is optimal for all players.

scholarly journals Two New Models for the Two-Person Red-And-Black Game

2010 ◽  
Vol 47 (01) ◽  
pp. 97-108 ◽  
Author(s):  
May-Ru Chen ◽  
Shoou-Ren Hsiau
Keyword(s):  
Nash Equilibrium ◽  
Probability Function ◽  
Positive Probability ◽  
Probability Functions ◽  
New Models

In a two-person red-and-black game, each player holds an integral amount of chips. At each stage of the game, each player can bet any integral amount in his possession, winning the chips of his opponent with a probability which is a function of the ratio of his bet to the sum of both players' bets and is called a win probability function. Both players seek to maximize the probability of winning the entire fortune of his opponent. In this paper we propose two new models. In the first model, at each stage, there is a positive probability that two players exchange their bets. In the second model, the win probability functions are stage dependent. In both models, we obtain suitable conditions on the win probability functions such that it is a Nash equilibrium for the subfair player to play boldly and for the superfair player to play timidly.

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