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Who is Elias and why isn't that question addressed on this page? Michael Hardy 03:40, 23 Jan 2005 (UTC)
Classicalecon ( talk · contribs) added "Implied probability" values to some of the entries of the table. I removed them because the article did not explain what "implied probability" was supposed to mean, and also because "implied probability" is not really accurate.
Ideally one picks a universal code to use so that a symbol which takes n bits to encode has a probability as close to 1/(n^2) as possible. This is not limited to this particular code; it's a basic fact of compression. If a symbol occurs 1/2 of the time, its optimal encoding is in 1 bit. If a symbol occurs 1/4 of the time, its optimal encoding is in 2 bits; if 1/8 of the time, in 3 bits; so on and so forth.
However, it's quite rare that one's probabilities would work out to exact powers of 2 like that. It's even rarer that all one's probabilities would work out to the exact powers of 2 that correspond to the specific powers of 2 that are optimal for a particular universal code. To say, therefore, that using a symbol of a particular bit length "implies" a particular probability is ... just grossly wrong.
If the above doesn't make any sense to you, try this analogy: You are given the task of sorting a large number of colored beads, utilizing four clay jars and the services of a large number of assistants. You know that the most effective method will be to go through a series of sorting stages, dividing the beads as evenly as you can in each stage. To get an idea of the specifics of doing that, you scoop up a handful of beads and count how many of each color you get in that (hopefully-representative) handful. "Okay," you say. "We're going to devote the first jar just to black beads." "Oh," pipes up one of your assistants, "that must mean that the probability of a black bead is 1/4, because you're devoting 1/4 of our jars to storing them!" However, your assistant is wrong. Your sampling actually indicated the probability of a black bead as 1/3, but with only four jars, the closest you could get to 1/3 is 1/4. Your choice would be optimal if the probability was 1/4, but your choice does not "imply" that the probability is 1/4. -- 65.78.13.238 ( talk) 16:40, 30 November 2008 (UTC)
This article has not yet been rated on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||
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Who is Elias and why isn't that question addressed on this page? Michael Hardy 03:40, 23 Jan 2005 (UTC)
Classicalecon ( talk · contribs) added "Implied probability" values to some of the entries of the table. I removed them because the article did not explain what "implied probability" was supposed to mean, and also because "implied probability" is not really accurate.
Ideally one picks a universal code to use so that a symbol which takes n bits to encode has a probability as close to 1/(n^2) as possible. This is not limited to this particular code; it's a basic fact of compression. If a symbol occurs 1/2 of the time, its optimal encoding is in 1 bit. If a symbol occurs 1/4 of the time, its optimal encoding is in 2 bits; if 1/8 of the time, in 3 bits; so on and so forth.
However, it's quite rare that one's probabilities would work out to exact powers of 2 like that. It's even rarer that all one's probabilities would work out to the exact powers of 2 that correspond to the specific powers of 2 that are optimal for a particular universal code. To say, therefore, that using a symbol of a particular bit length "implies" a particular probability is ... just grossly wrong.
If the above doesn't make any sense to you, try this analogy: You are given the task of sorting a large number of colored beads, utilizing four clay jars and the services of a large number of assistants. You know that the most effective method will be to go through a series of sorting stages, dividing the beads as evenly as you can in each stage. To get an idea of the specifics of doing that, you scoop up a handful of beads and count how many of each color you get in that (hopefully-representative) handful. "Okay," you say. "We're going to devote the first jar just to black beads." "Oh," pipes up one of your assistants, "that must mean that the probability of a black bead is 1/4, because you're devoting 1/4 of our jars to storing them!" However, your assistant is wrong. Your sampling actually indicated the probability of a black bead as 1/3, but with only four jars, the closest you could get to 1/3 is 1/4. Your choice would be optimal if the probability was 1/4, but your choice does not "imply" that the probability is 1/4. -- 65.78.13.238 ( talk) 16:40, 30 November 2008 (UTC)