Statistical Inference Theory for Measures of Complexity in Chaos Theory and Nonlinear Science

NATO ASI Series - Measures of Complexity and Chaos ◽

10.1007/978-1-4757-0623-9_7 ◽

1989 ◽

pp. 79-97 ◽

Cited By ~ 4

Author(s):

W. A. Brock ◽

W. D. Dechert

Keyword(s):

Statistical Inference ◽

Chaos Theory ◽

Nonlinear Science ◽

Inference Theory

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Statistical Inference: Theory and Practice.

Biometrics ◽

10.2307/2532589 ◽

1993 ◽

Vol 49 (2) ◽

pp. 673

Author(s):

T. Bromek ◽

E. Pleszczynska

Keyword(s):

Statistical Inference ◽

Theory And Practice ◽

Inference Theory

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Models for probability and statistical inference: theory and applications

Choice Reviews Online ◽

10.5860/choice.45-5045 ◽

2008 ◽

Vol 45 (09) ◽

pp. 45-5045-45-5045

Keyword(s):

Statistical Inference ◽

Inference Theory

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Detecting Dependence in the Sensitive Parameter Space of a Model Using Statistical Inference and Large Forecast Ensembles

Monthly Weather Review ◽

10.1175/mwr-d-13-00340.1 ◽

2014 ◽

Vol 142 (10) ◽

pp. 3734-3755 ◽

Cited By ~ 2

Author(s):

J. G. McLay ◽

M. Liu

Keyword(s):

Statistical Inference ◽

Parameter Space ◽

Forecast Error ◽

Random Parameter ◽

Parameter Variation ◽

Physical Parameters ◽

Sensitive Parameter ◽

Multiple Parameter ◽

Considerable Range ◽

Inference Theory

Abstract This study looks for evidence of correlation among model physical parameters in the sensitive parameter space defined by those randomly sampled physical parameter vectors that induce the most notable response in some forecast metric. These “sensitive parameter vectors” are identified through an ensemble methodology. The correlation analysis is facilitated by two established techniques from statistical inference theory. The random parameter vectors are found to induce a considerable range of forecast responses in terms of five metrics, such as bias and variance. The metrics enable measurement not only of the biggest forecast response but also of the most beneficial forecast response (e.g., in terms of reduction of forecast error). For most metrics, multiple parameter pairs exhibit significantly more correlation than would be expected from random sampling processes. The correlations frequently involve parameters from two different physical routines. These inference results are independently supported by a Monte Carlo simulation. The results suggest that correlations among parameters must be taken into account in order to gain the most response from a model when carrying out parameter variation experiments. Also, they reinforce the idea that parameter estimation efforts need to be expanded so that they simultaneously estimate the joint distribution of parameters across multiple physical routines.

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