### 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 language | English (US) |
---|---|

Pages (from-to) | 917-923 |

Number of pages | 7 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 24 |

Issue number | 6 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### 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

**Normalized Mahalanobis distance for comparing process-based stochastic models.** / Winter, C Larrabee.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Normalized Mahalanobis distance for comparing process-based stochastic models

AU - Winter, C Larrabee

PY - 2010

Y1 - 2010

N2 - 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.

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.

KW - Mahalanobis distance

KW - Model comparison

KW - Model uncertainty

UR - http://www.scopus.com/inward/record.url?scp=77954423028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954423028&partnerID=8YFLogxK

U2 - 10.1007/s00477-010-0386-z

DO - 10.1007/s00477-010-0386-z

M3 - Article

AN - SCOPUS:77954423028

VL - 24

SP - 917

EP - 923

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 6

ER -