By Glenn Shafer
Both in technology and in useful affairs we cause through combining evidence basically inconclusively supported by means of proof. development on an summary realizing of this means of mixture, this ebook constructs a brand new concept of epistemic chance. the idea attracts at the paintings of A. P. Dempster yet diverges from Depster's standpoint by way of picking out his "lower possibilities" as epistemic chances and taking his rule for combining "upper and decrease chances" as primary.
The ebook opens with a critique of the well known Bayesian conception of epistemic likelihood. It then proceeds to advance an alternative choice to the additive set services and the guideline of conditioning of the Bayesian idea: set features that want basically be what Choquet known as "monotone of order of infinity." and Dempster's rule for combining such set features. This rule, including the assumption of "weights of evidence," ends up in either an intensive new conception and a greater figuring out of the Bayesian idea. The publication concludes with a quick remedy of statistical inference and a dialogue of the constraints of epistemic chance. Appendices include mathematical proofs, that are fairly user-friendly and infrequently rely on arithmetic extra complex that the binomial theorem.
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METHODS OP PROOF.!. multiplicand; product. this Multiply the multiplier by the product must be the same as the first MULTIPLICATION. The same 2. NOTE. as when the multiplier does not exceed 12. For proof by casting out the REMARK. Although it is 35 9's, see Art. 105. OPERATION. custom- use the figures of the multiary in regular order beginning with plier units, it will give the same product to to use them in any order, observing that the right-hand figure of each partial product must be placed under the figure of the multiplier which produces _ 235 738 492 1230 product by product by 2 product by 57810 product by 2 3 5 30 5 it.
4. 119. Of what number is 103 both the divisor and the 10609. quotient? 5. What is the nearest number to 53815, that divided by 375 without a remainder? farmer bought 25 acres of land for $2675 6. 19 acres of it cost? A I bought 15 horses, at $75 a head head must I sell them to gain $210 ? 7. A : at can be 54000. : what did $2033. how much per $89. locomotive has 391 miles to run in 11 hours: after running 139 miles in 4 hours, at what rate per hour must 36 miles. the remaining distance be run?
DIVISION. In the following, multiply itself, also B by itself: and B. A. B. Ans. 10355. 13. 4986 5369. 14. 3973 4308. 15. 23798 47329 59635. Ans. 83433. 65931. Ans. 113260. 16. 17. If is by difference of the products by the difference of divide the A A 47 Ans. 8281. 25 acres produce 1825 bushels of wheat, how much 73 bushels. that per acre 18. 19. filled How many How many times 1024 in 1048576? 1024 times. sacks, each containing 55 pounds, can be 37 sacks. pounds of flour? with 2035 How many pages in a book of 7359 lines, each page lines?
A Mathematical Theory of Evidence by Glenn Shafer