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.
In: Stochastic Environmental Research and Risk Assessment, Vol. 24, No. 6, 2010, p. 917-923.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 -