Maximum entropy in data analysis with error-carrying constraints

Lieu, Richard; Hicks, R. B.; Bland, C. J.

doi:10.1088/0305-4470/20/9/025

Cited by 6 publications

(5 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hybrid character shares some affinities with the work of Lieu et al [40] and Lieu and Hicks [41], who combine entropy maximization and least-squares minimization to address conflicting constraints.…”

Section: Least-squares Methodsmentioning

confidence: 94%

A Bayesian Approach to the Balancing of Statistical Economic Data

Rodrigues

2014

Entropy

View full text Add to dashboard Cite

Abstract:This paper addresses the problem of balancing statistical economic data, when data structure is arbitrary and both uncertainty estimates and a ranking of data quality are available. Using a Bayesian approach, the prior configuration is described as a multivariate random vector and the balanced posterior is obtained by application of relative entropy minimization. The paper shows that conventional data balancing methods, such as generalized least squares, weighted least squares and biproportional methods are particular cases of the general method described here. As a consequence, it is possible to determine the underlying assumptions and range of application of each traditional method. In particular, the popular biproportional method is found to assume that all source data has the same relative uncertainty. Finally, this paper proposes a simple linear iterative method that generalizes the biproportional method to the data balancing problem with arbitrary data structure, uncertainty estimates and multiple data quality levels.

show abstract

Section: Least-squares Methodsmentioning

confidence: 94%

A Bayesian Approach to the Balancing of Statistical Economic Data

Rodrigues

2014

Entropy

View full text Add to dashboard Cite

show abstract

“…In conclusion, the method presented here separates chemical shift and line shape information (i.e., J coupling information), which can simplify “everyday” spectral analysis. This N -channel MaxEnt approach is implemented in the Gifa software, a complete NMR data processing software and available upon request. − Gifa is written in Fortran and C, and it is available for most UNIX platforms. Calculation times depend on the data sizes and the number of channels.…”

Section: Discussionmentioning

confidence: 99%

“…This N-channel MaxEnt approach is implemented in the Gifa software, a complete NMR data processing software and available upon request. [14][15][16][17][18][19][20][21][22] Gifa is written in Fortran and C, and it is available for most UNIX platforms. Calculation times depend on the data sizes and the number of channels.…”

Section: Discussionmentioning

confidence: 99%

“…In the simplest case (no deconvolution), T equals the inverse FT Unfortunately, because the FID signal is finite and noisy, many S‘ (ω) spectra fulfill the condition that D is optimum. However, we know from the information theory that, among all the trial spectra that satisfy eq 6, one must choose the spectrum the entropy of which is maximum. , This spectrum equivalently contains the minimum information. The entropy of S‘ (ω) is defined as where A is a normalization constant: Hence, the MaxEnt spectrum should simultaneously satisfy two criteria: (i) D is minimum (χ 2 = M) and (ii) E is maximum.…”

Section: A Brief Account On Classical Deconvolution By Maximum Entropymentioning

confidence: 99%

“…However, we know from the information theory that, among all the trial spectra that satisfy eq 6, one must choose the spectrum the entropy of which is maximum. 15,16 This spectrum equivalently contains the minimum information. The entropy of S′(ω) is defined as where A is a normalization constant: Hence, the MaxEnt spectrum should simultaneously satisfy two criteria: (i) D is minimum (χ 2…”

Section: A Brief Account On Classical Deconvolution By Maximum Entropymentioning

confidence: 99%

See 2 more Smart Citations

A New N-Channel Maximum Entropy Method in NMR for Automatic Reconstruction of “Decoupled Spectra” and J-Coupling Determination

Stoven

Annereau

Delsuc

et al. 1997

J. Chem. Inf. Comput. Sci.

View full text Add to dashboard Cite

A new N-channel (or multichannel) deconvolution method of 1D and 2D NMR spectra is presented based on the Maximum Entropy method. In the general case of spectra exhibiting several lines of various fine structures, the method allows simultaneous deconvolution of all lines. While deconvolution is performed, determination of the values of the coupling constants is possible. Reconstruction of “decoupled” 1D and 2D spectra is also performed in a fully automated approach. The efficiency of the method is illustrated on experimental 1D and 2D spectra. The method has been developed in the GIFA software, a complete package for processing of NMR data available from the authors.

show abstract