Fourier-analysis-based Form of Normalized Maximum Likelihood: Exact Formula and Relation to Complex Bayesian Prior

2021 ◽  
pp. 1-1
Author(s):  
Atsushi Suzuki ◽  
Kenji Yamanishi
Keyword(s):  
Maximum Likelihood ◽  
Fourier Analysis ◽  
Exact Formula ◽  
Normalized Maximum Likelihood ◽  
Bayesian Prior

scholarly journals A Note on the Applied Use of MDL Approximations

2004 ◽  
Vol 16 (9) ◽  
pp. 1763-1768 ◽  
Author(s):  
Daniel J. Navarro
Keyword(s):  
Maximum Likelihood ◽  
Fisher Information ◽  
Minimum Description Length ◽  
Geometric Interpretation ◽  
Applied Problem ◽  
Full Model ◽  
Large Samples ◽  
Psychological Models ◽  
Normalized Maximum Likelihood ◽  
Practical Implications

An applied problem is discussed in which two nested psychological models of retention are compared using minimum description length (MDL). The standard Fisher information approximation to the normalized maximum likelihood is calculated for these two models, with the result that the full model is assigned a smaller complexity, even for moderately large samples. A geometric interpretation for this behavior is considered, along with its practical implications.

scholarly journals A note on the applied use of MDL approximations

2019 ◽  
Author(s):  
Danielle Navarro
Keyword(s):  
Maximum Likelihood ◽  
Fisher Information ◽  
Minimum Description Length ◽  
Geometric Interpretation ◽  
Applied Problem ◽  
Full Model ◽  
Large Samples ◽  
Psychological Models ◽  
Normalized Maximum Likelihood ◽  
Practical Implications

An applied problem is discussed in which two nested psychological models of retention are compared using minimum description length (MDL). The standard Fisher information approximation to the normalized maximum likelihood is calculated for these two models, with the result that the full model is assigned a smaller complexity, even for moderately large samples. A geometric interpretation for this behavior is considered, along with its practical implications.

scholarly journals Selecting Amongst Multinomial Models: An Apologia for Normalized Maximum Likelihood

2019 ◽  
Author(s):  
David Kellen ◽  
Karl Christoph Klauer
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Minimum Description Length ◽  
Seminal Paper ◽  
Multinomial Data ◽  
Functional Flexibility ◽  
Multinomial Models ◽  
Tremendous Progress ◽  
Normalized Maximum Likelihood ◽  
Important Addition

The modeling of multinomial data has seen tremendous progress since Riefer and Batchelder’s (1988) seminal paper. One recurring challenge, however, concerns theavailability of relative performance measures that strike an ideal balance between goodness of fit and functional flexibility. One approach to the problem of model selection is Normalized Maximum Likelihood (NML), a solution derived from the Minimum Description Length principle. In the present work we provide an R implementation of a Gibbs sampler that can be used to compute NML for models of joint multinomial data. We discuss the application of NML in different examples, compare NML with Bayes Factors, and show how it constitutes an important addition to researchers’ toolboxes.

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