The relationship between maximum entropy and maximum likelihood spectra

Geophysics ◽  
1979 ◽  
Vol 44 (10) ◽  
pp. 1738-1739 ◽  
Author(s):  
J. V. Pendrel ◽  
D. E. Smylie
Keyword(s):  
Maximum Likelihood ◽  
Spectral Density ◽  
Maximum Entropy ◽  
Analytical Relationship ◽  
Density Estimates ◽  
Sample Interval ◽  
Successive Maximum ◽  
Entropy Estimates ◽  
The Relationship ◽  
Spectral Density Estimate

Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If [Formula: see text], j = 0, 1,… M − 1 and M successive maximum entropy spectral density estimates at frequency f, then the M‐length maximum likelihood spectral density estimate [Formula: see text] is given by [Formula: see text]. (1) The maximum entropy estimates are made via Burg's well‐known formula,[Formula: see text], (2) where [Formula: see text], k = 0, 1,…,N are the coefficients of the N‐length prediction‐error filter, [Formula: see text] is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).

THE RELATIONSHIP BETWEEN MAXIMUM ENTROPY SPECTRA AND MAXIMUM LIKELIHOOD SPECTRA

Geophysics ◽  
1972 ◽  
Vol 37 (2) ◽  
pp. 375-376 ◽  
Author(s):  
John Parker Burg
Keyword(s):  
Spectral Analysis ◽  
Maximum Likelihood ◽  
Maximum Entropy ◽  
Short Note ◽  
Entropy Method ◽  
Likelihood Method ◽  
Almost All ◽  
The Relationship ◽  
Exact Relationship ◽  
Special Case

In a long needed paper, R. T. Lacoss (1971) has presented many examples of spectra obtained by the maximum likelihood method and by the maximum entropy method and has shown that these newer techniques are in general superior to the more conventional spectral analysis methods. This short note shows that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag. The data are of this form in almost all practical cases of time series analysis as well as in the special case of wavenumber spectral analysis of wave propagation as seen by a linear array of equally spaced sensors. The wavenumber case will be explicitly considered in this note since it requires the complex variable form of the theory.

Metric for Disassembly and Reuse Decisions: Formulation and Validation

2008 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Deborah Thurston
Keyword(s):  
Maximum Likelihood ◽  
Value Function ◽  
Choice Theory ◽  
Decision Makers ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Maximum Value ◽  
Long Range Planning ◽  
The Relationship ◽  
The Value Function

Design for disassembly and reuse focuses on developing methods to minimize difficulty in disassembly for maintenance or reuse. These methods can gain substantially if the relationship between component attributes (material mix, ease of disassembly etc.) and their likelihood of reuse or disposal is understood. For products already in the marketplace, a feedback approach that evaluates willingness of manufacturers or customers (decision makers) to reuse a component can reveal how attributes of a component affect reuse decisions. This paper introduces some metrics and combines them with ones proposed in literature into a measure that captures the overall value of a decision made by the decision makers. The premise is that the decision makers would choose a decision that has the maximum value. Four decisions are considered regarding a component’s fate after recovery ranging from direct reuse to disposal. A method on the lines of discrete choice theory is utilized that uses maximum likelihood estimates to determine the parameters that define the value function. The maximum likelihood method can take inputs from actual decisions made by the decision makers to assess the value function. This function can be used to determine the likelihood that the component takes a certain path (one of the four decisions), taking as input its attributes, which can facilitate long range planning and also help determine ways reuse decisions can be influenced.

Computers and infrared spectroscopy: evolution and revolution

1991 ◽  
Vol 69 (11) ◽  
pp. 1781-1785 ◽  
Author(s):  
D. J. Moffatt ◽  
J. K. Kauppinen ◽  
H. H. Mantsch
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Key Words ◽  
Maximum Entropy ◽  
Input Data ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
History Of ◽  
The Fourier Transform ◽  
The Relationship

A brief history of the relationship between computer and infrared spectroscopist is given with emphasis on the use of the Fourier transform. Subsequently, an algorithm is developed that may be used to devise an objective Fourier self-deconvolution procedure which depends only on the input data and is not subject to the biases that are often introduced in such subjective techniques. Key words: deconvolution, Fourier transform, maximum entropy method.

scholarly journals Scrapie-resistant sheep show certain coat colour characteristics

2009 ◽  
Vol 91 (1) ◽  
pp. 39-46 ◽  
Author(s):  
R. M. SAWALHA ◽  
L. BELL ◽  
S. BROTHERSTONE ◽  
I. WHITE ◽  
A. J. WILSON ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Linear Model ◽  
Morphological Diversity ◽  
Coat Colour ◽  
Unintended Consequences ◽  
Colour Pattern ◽  
Reverse Pattern ◽  
Colour Patterns ◽  
Log Linear ◽  
The Relationship

SummarySusceptibility to scrapie is known to be associated with polymorphisms at the prion protein (PrP) gene, and this association is the basis of current selective programmes implemented to control scrapie in many countries. However, these programmes might have unintended consequences for other traits that might be associated withPrPgenotype. The objective of this study was to investigate the relationship betweenPrPgenotype and coat colour characteristics in two UK native sheep breeds valued for their distinctive coat colour patterns. Coat colour pattern, darkness and spotting andPrPgenotype records were available for 11 674 Badgerfaced Welsh Mountain and 2338 Shetland sheep. The data were analysed with a log–linear model using maximum likelihood. Results showed a strong significant association ofPrPgenotype with coat colour pattern in Badgerfaced Welsh Mountain and Shetland sheep and with the presence of white spotting in Shetland sheep. Animals with the ARR/ARR genotype (the most scrapie resistant) had higher odds of having a light dorsum and a dark abdomen than the reverse pattern. The implication of these associations is that selection to increase resistance to scrapie based only onPrPgenotype could result in change in morphological diversity and affect other associated traits such as fitness.

scholarly journals A Maximum Entropy Procedure to Solve Likelihood Equations

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 596
Author(s):  
Antonio Calcagnì ◽  
Livio Finos ◽  
Gianmarco Altoé ◽  
Massimiliano Pastore
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Score Function ◽  
Likelihood Estimation ◽  
Likelihood Equation ◽  
Equation Problem ◽  
Standard Procedures ◽  
Data Separation

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon’s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth’s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation.

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