Geology Reference
In-Depth Information
Fig. 5.10 Variation of gamma static (
ʓ
) with unique data points corresponding to 6-hourly
records [
6
]
The quantity of the available input data to predict the desirable output was
analysed using the M-test (a repeat execution of the Gamma Test with different
number of input data lengths). The M-test results help to determine whether there
were suf
cient data to provide an asymptotic Gamma estimate and subsequently a
reliable model. The M-test analysis results for the best scenario (with 3 inputs:
horizon extraterrestrial radiation, air dry bulb temperature, wet bulb temperature)
are shown in Fig.
5.10
. The test produced an asymptotic convergence of the
Gamma statistic to a value of 0.022 at around 550 data points. The SE corre-
sponding to M = 550 is very small at 0.0027, which shows the precision and
accuracy of the Gamma statistic.
5.3.3 Data Selection Results from the AIC and BIC
In order to compare the result of the Gamma Test with two popular information
criterion (AIC and BIC), a LLR model and an ANN model are developed for each
scenario using the training results. AIC concept 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. AIC and BIC values are used here for model input selection since the
more inputs, the more parameters of the model would have. Their results are pre-
sented in Fig.
5.11
. It has been found that the rank of scenarios is similar to the entropy
results. The AIC penalizes free parameters less strongly than does the Schwarz
criterion. The performance of AIC and BIC were similar in most of the scenarios. In
both cases, the scenario 15 has exhibited the least information criterion numerical
values (BIC value is
−
6299.3 whereas the least AIC value is
−
2177.88).
