Maximum entropy technique

Carvalho, C A M., Hashizume, H., Stevenson, A.W. and Robinson, I K. (1996) Electron-density maps for the Si( 111) 7x7 surface calculated with the maximum-entropy technique using X-ray and electron-diffraction data, Physica B, 221,469 186. 

The fundamental application of maximum entropy techniques requires an understanding of Bayes theorem. Various definitions are necessary ... 

The reader is referred to the articles by Berko [37] and West [38] for overviews of the analysis and interpretation of ACAR data and to Dugdale et al [39] on data reduction by the maximum entropy technique. 

Maximum likelihood method, similar to maximum entropy, works in reciprocal space and results in finding a raw model that has the best chance to be improved by applying small steps to achieve full agreement between the observed and calculated structure amplitudes, rather than the final structure. Maximum likelihood and maximum entropy techniques are often combined together. - ... 

The theory of maximum likelihood (ML) is the subject of a chapter in Janson s book on deconvolution. In another monograph on deconvolution, Frieden also discussed the theory of ML in the context of emission spectra, however the same principles also apply to NMR. The introduction section of the paper makes it clear that the use of prior knowledge makes experimental data more informative. Maximum entropy techniques and others are examples of such integration discussed in the paper. 

Use the maximum entropy technique to identify the most probable distribution of cluster sizes that is consistent with the observed scattering data. ° In this method, the experimental data are fitted by an algorithm which varies the volume fraction of each size class of precipitate. The advantage of this method is that no prior assumptions need be made regarding the form of the size distribution. Furthermore, the size distribution must be positive for all sizes. 

A spectrum is built up from at least a million lifetime measurements from individual positrons. Standard computer codes are available for the decomposition of the spectra including POSITRONFIT in which a least squares fit is used to fit a model spectrum with a given number of decay components to the observed spectrum. Maximum entropy techniques have also been used to determine the most probable underlying distribution of trap lifetimes. As the number of different traps increases, interpretation becomes increasingly difficult. Several research groups have published positron annihilation lifetime data on irradiated RPV steels (see Section 9.11.1). 

Although other techniques have been developed for smoothing, notably using Fourier or maximum entropy techniques, they do share one common feature— noise can only be reduced at the expense of resolution. Smoothing can easily result in loss of information by removing shoulders from bands or erasing small, narrow peaks situated near large ones. It can... 

Novel data processing The advent of more widespread application of the maximum-entropy technique, where any prior knowledge about the system can be used to advantage, is imminent as the method becomes more widely available. It will probably gain more credence when careful benchmarking and comparisons have been completed. Undoubtedly, it will find application in all areas of NMR spectroscopy. 

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