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indicator of model selection and best data interval for real-time
flood forecasting.
Another related work mentioned in this topic is [
3
] which made an attempt to
compare different data selection approaches in solar radiation modeling along with
the information theory-based entropy concept.
3.3 Implementation of AIC and BIC
Identi
cation of a true model in hydrological time series-based nonlinear modeling
is nearly impossible in practice. In the early days, hydrological modelers adopted
some subjective judgments in model identi
cation. Fisher
'
s likelihood approach
was widely used to make a measure of the goodness-of-
t of the data; but this
approach is not appropriate if we wish to consider model complexity. The likeli-
hood ratio test is the basis of Fisher
is likelihood framework, which assumes that the
simpler models are a subset of the more complicated model. Because of this,
comparison of any two models was practically impossible in Fisher
'
'
s framework.
Moreover, other tests such as the chi-square and the Smirnov
Kolmogorov tests
adopt a subjective approach from which the conclusions drawn are based on the
level of con
-
dence
often lead to contradictory results. Another serious disadvantage in the use of
traditional goodness-of-fit tests in flood modeling is that they can pass more than
one peak-
dence adopted for that particular study. Different levels of con
ow model from the class of competing models. These disadvantages
generally account for the reduced usefulness of the conventional goodness-of-
t
tests in the optimum model identi
cation in
flood frequency analysis [
54
].
culty was effectively addressed by Hirotsugu Akaike through his
novel concept of the Akaike information criterion (AIC) [
4
]. This attempt encouraged
many researchers in related
This practical dif
fields to bring up new ideas in model selection. These
attempts led to the development of new concepts such as the Schwarz Information
Criterion (SIC), Bayesian Information Criterion (BIC), Hannan
Quinn Criterion
-
(HQ), and Amemiya
s Prediction Criterion (PC) [
5
,
44
,
63
]. Very solid theoretical
foundations exist in the development of both AIC and BIC. AIC is based on
Kullback
'
Leibler distance in information theory whereas BIC is based on integrated
likelihood in Bayesian theory. Research by Burnham and Anderson [
13
] suggests that
BIC is a much preferred criterion compared to AIC if the complexity of the true model
does not increase with the size of the data set. Using too many variables in time-series
analysis based on antecedent information can
-
fit the data perfectly with a high level of
accuracy, but it can lead to over
tting. Use of very few input variables may not
t the
data set at all, and thus lead to under
tting. AIC and BICwere used effectively to solve
these issues in the
fields of epidemiology, microarray data analysis, and DNA
sequence analysis [
48
,
49
].
AIC is grounded in the concept of entropy, in effect offering a relative measure
of the information lost when a given model is used to describe the reality and can be
said to describe the trade-off between bias and variance in model construction, or,
loosely speaking, that of precision and complexity of the model. The AIC can be
