David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
When combining information from multiple sources and attempting to estimate the probability of a conclusion, we often find ourselves in the position of knowing the probability of the conclusion conditional on each of the individual sources, but we have no direct information about the probability of the conclusion conditional on the combination of sources. The probability calculus provides no way of computing such joint probabilities. This paper introduces a new way of combining probabilistic information to estimate joint probabilities. It is shown that on a particular conception of objective probabilities, clear sense can be made of second-order probabilities (probabilities of probabilities), and these can be related to combinatorial theorems about proportions in finite sets as the sizes of the sets go to infinity. There is a rich mathematical theory consisting of such theorems, and the theorems generate corresponding theorems about secondorder probabilities. Among the latter are a number of theorems to the effect that certain inferences from probabilities to probabilities, although not licensed by the probability calculus, have probability 1 of producing correct results. This does not mean that they will always produce correct results, but the set of cases in which the inferences go wrong form a set of measure 0. Among these inferences are some enabling us to reasonably estimate the values of joint probabilities in a wide range of cases. A function called the Y-function is defined. The central theorem is the Y-Theorem, which tells us that if we know the individual probabilities for the different information sources and estimate the joint probability using the Y-function, the second-order probability of getting the right answer is 1. This mathematical result is tested empirically using a simple multi-sensor example. The Y-theorem agrees with Dempster's rule of combination in special cases, but not in general.
|Keywords||No keywords specified (fix it)|
|Categories||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
Sven Ove Hansson (2010). Past Probabilities. Notre Dame Journal of Formal Logic 51 (2):207-223.
Henry E. Kyburg Jr (1992). Getting Fancy with Probability. Synthese 90 (2):189 - 203.
Henry E. Kyburg (1992). Getting Fancy with Probability. Synthese 90 (2):189-203.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Paul Weirich (1983). Conditional Probabilities and Probabilities Given Knowledge of a Condition. Philosophy of Science 50 (1):82-95.
John Pollock (2011). Reasoning Defeasibly About Probabilities. Synthese 181 (2):317 - 352.
Added to index2009-01-28
Total downloads27 ( #100,874 of 1,700,363 )
Recent downloads (6 months)6 ( #105,649 of 1,700,363 )
How can I increase my downloads?