
132 Modeling and Inverse Problems in the Presence of Uncertainty
• Null hypothesis testing should not be mixed with the information crite-
rion in reporting the results.
– The information criterion is not a “test,” so one s hould avoid use of
“significant” and “not significant,” or “rejected” and “not rejected”
in rep orting results.
– One should not use the AIC to rank models in the set and then test
whether the best model is “significantly b etter” than the second-
best model.
• All the comp onents in each log-likelihood function should be retained
when comparing models with different probability distr ibutio n forms.
For example, if we want to use the