Agriculture Reference
In-Depth Information
assumed P
prior
of 0.9 is illustrated in Fig. 12.3. To obtain the value of LR
-req
we begin
by projecting vertically upwards from horizontal axis at 0.9, until the projected line
intersects with the LR
-req
curves. Reading across from the point of intersection to the
vertical axis provides the desired value. In the example it can be seen that the ln(LR
-
req
) values for P
post_req
of 0.1 and 0.2 are, respectively,
-
3.5. The actual
values LR
-req
obtained from the mathematical relationship are, respectively, 0.012
and 0.028 to 3 decimal places (0.012 = e
-4.39
and 0.028 = e
-3.58
).
≅
-
4.5 and
≅
Figure 12.3. Likelihood ratios for the prediction of no disease (LR
-
) required to achieve fixed
posterior probabilities of disease occurrence as a function of the prior probability of disease.
The curves for posterior probabilities of 0.2 and 0.1 are shown.
Recalling the definition of LR
-
given above, (i.e
.
the false negative proportion
divided by the true negative proportion) we can translate these values of LR
-req
into
an indication of what we are expecting from our IT-based forecaster in terms of
correct and incorrect predictions. For P
post_req
= 0.2 (LR
-
= 0.028), for example, the
frequency of false negative decisions is (approximately) 3% of the frequency of true
negative decisions; i.e., for every 100 correct predictions not to take action, only
three incorrect decisions not to take action can be tolerated. The more stringent
criterion of having the P
post_req
= 0.1 (LR
−
= 0.012) requires the forecaster to make
only one false negative prediction for every 100 true negative predictions. How do
these standards compare with forecasters that are actually in use? Yuen and Hughes
(2002) reported three alternative LR
-
values for a
Sclerotinia
stem rot forecaster for
use in oilseed rape in Sweden: 0.130, 0.274, 0.684, depending on the choice of risk
point threshold for action. De Wolf
et al
. (2003) (see also Madden, 2006) estimated
a LR
-
of 0.200 for their risk prediction system for
Fusarium
head blight of wheat in
the north-east USA. A web-based prediction system (Burnett and Hughes, 2004) for
