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A note on weighted combination methods for probability estimation
Sečkárová, Vladimíra
To successfully learn from the information provided by avail- able information sources, the choice of automatic method combining them into one aggregate result plays an important role. To respect the reliability in the source’s performance each of them is assigned a weight, often subjectively influenced. To overcome this issue, we briefly describe the method based on Bayesian decision theory and elements of infor- mation theory. In particular we consider discrete-type information, rep- resented by probability mass functions (pmfs) and obtain an aggregate result, which has also form of pmf. This result of decision making pro- cess is found to be a weighted linear combination of available information. Besides the brief description of the novel method, the paper focuses on its comparison with other combination methods. Since we consider the available information and unknown aggregate as pmfs, we mainly focus on the case when the parameter of binomial distribution is of interest and the sources provide appropriate pmfs.
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Planck's Law and the Rise of Information Physics
Gottvald, Aleš
A centennial history of celebrated Planck's radiation formula is briefly discussed from an information-theoretic perspective. A new rationale, based on Maximum Entropy Principle (MaxEnt), is suggested for the Planck formula. The MaxEnt-approach is intrinsically silent about famous quantum hypothesis, which is neiter required nor forbidden in this formalism. Some common historical myths and conceptual inconsistencies behind the Planck law are indicated, too.
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Beyond the MaxEnt Principle: Bayes, Fourier, Zipf and Spirals in Metamorphoses
Gottvald, Aleš
A radical solution is offered to clarify an obscure relationship between the Maximum Entropy Principle (MaxEnt) and Bayesian Probability Theory (BPT). The logical consistency of MaxEnt and BPT is guaranteed by definition in our theory. Close links between the MaxEnt and Fourier Transform are emphasized. Reproducibility is being recognized as the fundamental precondition of the MaxEnt-formalism. Consequently, it is proposed that the MaxEnt principle manifests itself in terms of Spiral Geometries, Zipf's law, Power laws, Fractals, and many other ubiquitous reproducible phenomena.
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