David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Let be n events in a probability space, and suppose that we have only partial information about the distribution: The probabilites of the events themselves, and their pair intersections. With this partial information we cannot, usually, deternine the probability of an event B in the algebra generated by the 's, but we can obtain lower and upper bounds. This is done by a linear program related to the correlation polytope c(n), a structure introduced in , . In the first part of the paper I demonstrate how laws of large numbers (for sequences of events which are not necessarily independent) can be proved, using only the duality theorem of linear programming. These include the weak law of large numbers (necessary and sufficient condition) and various sufficient conditions for strong laws. The connection between these laws and the facet structure of the correlation polytope is established. In the second part of the paper I consider a more general case. Assume that our information consists of the values of the probabilities of all intersections of the 's up to size k, k < n. The techniques of linear programming lead naturally to an application of the theory of polynomial approximation in estimating the size of various events. In particular, I prove an approximate version of the central limit theorem.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Ranald R. Macdonald (2000). The Limits of Probability Modelling: A Serendipitous Tale of Goldfish, Transfinite Numbers, and Pieces of String. [REVIEW] Mind and Society 1 (2):17-38.
Maurizio Negri (2010). A Probability Measure for Partial Events. Studia Logica 94 (2):271 - 290.
David Atkinson & Jeanne Peijnenburg (2010). Justification by Infinite Loops. Notre Dame Journal of Formal Logic 51 (4):407-416.
Timothy O'Connor (2005). The Metaphysics of Emergence. Noûs 39 (4):658-678.
Hong Yu Wong (2005). The Metaphysics of Emergence. Noûs 39 (4):658 - 678.
Stanley Paluch (1968). The Covering Law Model of Historical Explanation. Inquiry 11 (1-4):368 – 387.
Jaegwon Kim (1989). Honderich on Mental Events and Psychoneural Laws. Inquiry 32 (March):29-48.
Peter Milne (2008). Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events. Studia Logica 90 (3):425 - 453.
Vladimir Doljenko (2008). Dialectics Process - Harmony of Life. Proceedings of the Xxii World Congress of Philosophy 9:85-92.
Added to index2010-12-22
Total downloads21 ( #82,873 of 1,102,934 )
Recent downloads (6 months)1 ( #297,435 of 1,102,934 )
How can I increase my downloads?