The quantization of the attention function under a Bayes information theoretic model
UNSPECIFIED (2001) The quantization of the attention function under a Bayes information theoretic model. In: 20th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2000), GIF SUR YVETTE, FRANCE, JUL 08-13, 2000. Published in: BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING, PT 2, 568 pp. 159-168.Full text not available from this repository.
Bayes experimental design using entropy, or equivalently negative information, as a criterion is fairly well developed. The present work applies this model but at a primitive level in statistical sampling. It is assumed that the observer/experimentor is allowed to place a window over the support of a sampling distribution and only "pay for" observations that fall in this window. The window can be modeled with an "attention function", simply the indicator function of the window. The understanding is that the cost of the experiment is only the number of paid for observations: n. For fixed n and under the information model it turns out that for standard problems the optimal structure for the window, in the limit amongst all types of window including disjoint regions, is discrete. That is to say it is optimal to observe the world (in this sense) through discrete slits. It also shows that in this case Bayesians with different priors will receive different samples because typically the optimal attention windows will be disjoint. This property we refer to as the quantisation of the attention function.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QC Physics|
|Series Name:||AIP CONFERENCE PROCEEDINGS|
|Journal or Publication Title:||BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING, PT 2|
|Publisher:||AMER INST PHYSICS|
|Number of Pages:||10|
|Page Range:||pp. 159-168|
|Title of Event:||20th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2000)|
|Location of Event:||GIF SUR YVETTE, FRANCE|
|Date(s) of Event:||JUL 08-13, 2000|
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