[Fis] definitions of information by Theil (1972) derived from Shnnon (1948); back to the basics?

[Roy Morrison]

I guess that's why black swan events magically and consistently lead to financial calamity when events supposedly more than two or three standard deviations from normal are considered to offer zero information.
Roy

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  On Mon, Jan 23, 2023 at 10:30 AM, Loet Leydesdorff<loet at leydesdorff.net> wrote:   Theil (1972) pp. 1 and 2: 
1.1. Information
 
Consider an event E with probability p; the nature of the event is irrele­vant. At some point in time wereceive a reliable message stating that Ein fact occurred. The question is: How should one measure the amount ofinformation conveyed by this message?
 
Information
 
Since the question is vague, we shall try to answer it inan intuitive manner. Suppose that p isclose to 1 (e.g., p = .95). Then, onemay argue, the message conveys very little information, because it wasvirtually certain that E would takeplace. But suppose that p = .01, sothat it is almost certain E will notoccur. If E nevertheless does occur,the message stating this will be unexpected and hence contains a great deal ofinformation.
 
 These intuitive ideassuggest that, if we want to measure the information derived from a message interms of the probability p thatprevailed before or to the arrival of the message, we should select a decreasing function. The function proposedby SHANNON (1948) is when the probability prior to the message is zero) to 0 (zero information when the probability is one).
The unit of information is determined by the base of the logarithm. Frequently 2 is used as a base, which implies that any message concerning a 50-50 event has unit information: h() = log  2   2 = 1, and information is then said to be measured in binary digits or, for short,   bits.   When natural logarithms are used, the information unit is a   nit. 
best, loet
 
_______________

Loet Leydesdorff




"The Evolutionary Dynamics of Discusive Knowledge"(Open Access)

Professor emeritus, University of Amsterdam 

Amsterdam School of Communication Research (ASCoR)
 
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