Database Reference
In-Depth Information
1 is also useful in respect of the delivery of competing initial
recommendations. For this we initially assume
s
C
¼
1. As long as
The selection
s
C
>
n
p
ss
0
^
is in the
initialization phase, i.e.,
n
<
n
min
, under the mostly valid (and not crucial) assump-
8s
0
tion
e
p
ss
0
¼ p
ss
0
,
6¼ s
a
(i.e., the other unconditional probabilities are stable),
(
5.25
) takes the form
ðÞ¼p
ss
a
r
ss
a
þ
1
X
s
0
6¼s
a
p
ss
0
r
ss
0
¼
X
s
0
q
π
s
p
ss
0
r
ss
0
¼ q
0
^
;
ð
,
s
;
q
π
and thus
ðÞ
is the same for all recommendations in the initial phase.
On the other hand, the introduction of the scaling factor
s
C
>
^
s
;
1 yields the desired
behavior:
q
π
s
ðÞ> q
π
s
;
ðÞ,p
ss
a
r
ss
a
>
;
p
ss
b
r
ss
b
:
Thus the method for the initial recommendations works similarly to that of the
P-Version. For methodological purposes we therefore introduce a simplified
version of (
5.25
):
q
s
π
s
p
ss
a
r
ss
a
:
^
ðÞ¼^
;
ð
5
:
26
Þ
This therefore combines the P-Version for unconditional and conditional prob-
abilities. As long as
n
n
min
, it corresponds largely to the P-Version for the
corresponding recommendation, i.e.,
<
q
s
π
s
ðÞ¼ s
C
p
ss
a
r
ss
a
,
;
and for
s
C
¼
1 it is actually identical:
q
s
π
s
ðÞ¼p
ss
a
r
ss
a
¼ q
P
^
;
ð :
s
;
As soon as the threshold value
n
min
is reached, it changes into a P-Version
operating on the basis of conditional probability:
q
s
π
s
ðÞ¼p
ss
a
r
ss
a
:
^
;
The transition from unconditional to conditional probabilities in (
5.25
)or(
5.26
)
makes sense in terms of content too: as long as the statistical mass is small, one
should not operate with the complex conditional probabilities. Therefore, the
unconditional probabilities are used, whose stability increases more quickly - and
without requiring the delivery of recommendations. If then the necessary statistical
mass is reached, we change over to the qualitatively more demanding conditional
probabilities. In this way we achieve a continuous transition from the P- to the
DP-Version.
