Abstract
This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.
Highlights
In several already published articles, I defend the use of Bayesian Statistics in the epistemological framework of cognitive constructivism
In Statistics, specially in the design of statistical experiments, Randomization plays a role which is in the very core of objective-subjective complementarity, a concept of great significance in the epistemological framework of cognitive constructivism as well as in the theory of Bayesian statistics
Entropy is presented as a cornerstone concept for the precise analysis and a key idea for the correct understanding of several important topics in probability and statistics. This understanding should help to clear the way for establishing Bayesian statistics as a preferred tool for scientific inference in mainstream cognitive constructivism
Summary
In several already published articles, I defend the use of Bayesian Statistics in the epistemological framework of cognitive constructivism. Charles Saunders Peirce and his student Joseph Jastrow, who introduced the idea of randomization in statistical trials, struggled with some of the very same dilemmas faced by Spencer-Brown, namely, the eventual detection of distinct patterns or seemingly ordered (sub)strings in a long random sequence. 15 of [62]: For electronic digital computers it is most convenient to calculate a sequence of numbers one at a time as required, by a completely specified rule which is, so devised that no reasonable statistical test will detect any significant departure from randomness. Carlo methods is generally lost for problems of high dimension or problems in which the integrand is not smooth
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