Normalized Mahalanobis distance for comparing process-based stochastic models

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4 Citations (Scopus)

Abstract

We investigate a method based on normalized Mahalanobis distance, D, for comparing the performance of alternate stochastic models of a given environmental system. The approach is appropriate in cases where data are too limited to calculate either likelihood ratios or Bayes factors. Computational experiments based on simulated data are used to evaluate D's ability to identify a true model and to single out good models. Data are simulated for two populations with different signal-noise ratios (S/N) The expected value of D is decomposed to evaluate the effects of normalization, model bias, and model correlation structure on D's discriminatory power. Normalization compensates for the advantage one model may have over another due to technical features of its hypothesized correlation structure. The relative effects of bias and correlation structure vary with S/N, model bias being most important when S/N is relatively high and correlation structure increasing in importance as S/N decreases.

Original languageEnglish (US)
Pages (from-to)917-923
Number of pages7
JournalStochastic Environmental Research and Risk Assessment
Volume24
Issue number6
DOIs
StatePublished - 2010

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Stochastic models
Experiments
experiment

Keywords

  • Mahalanobis distance
  • Model comparison
  • Model uncertainty

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality

Cite this

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title = "Normalized Mahalanobis distance for comparing process-based stochastic models",
abstract = "We investigate a method based on normalized Mahalanobis distance, D, for comparing the performance of alternate stochastic models of a given environmental system. The approach is appropriate in cases where data are too limited to calculate either likelihood ratios or Bayes factors. Computational experiments based on simulated data are used to evaluate D's ability to identify a true model and to single out good models. Data are simulated for two populations with different signal-noise ratios (S/N) The expected value of D is decomposed to evaluate the effects of normalization, model bias, and model correlation structure on D's discriminatory power. Normalization compensates for the advantage one model may have over another due to technical features of its hypothesized correlation structure. The relative effects of bias and correlation structure vary with S/N, model bias being most important when S/N is relatively high and correlation structure increasing in importance as S/N decreases.",
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AB - We investigate a method based on normalized Mahalanobis distance, D, for comparing the performance of alternate stochastic models of a given environmental system. The approach is appropriate in cases where data are too limited to calculate either likelihood ratios or Bayes factors. Computational experiments based on simulated data are used to evaluate D's ability to identify a true model and to single out good models. Data are simulated for two populations with different signal-noise ratios (S/N) The expected value of D is decomposed to evaluate the effects of normalization, model bias, and model correlation structure on D's discriminatory power. Normalization compensates for the advantage one model may have over another due to technical features of its hypothesized correlation structure. The relative effects of bias and correlation structure vary with S/N, model bias being most important when S/N is relatively high and correlation structure increasing in importance as S/N decreases.

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