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19-Sep-2000

�� , 16(5), ��-�� 1999, 511-515

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�� : �� , �� , ��, �� , ��.

1. ��

� �� , �� , �� .¹ � �� , �� , ��, �� . � ��, �� , �� (�� ) ��. � �� (��) �� : Pr (�� /�� ). � �� , �� . �� (��) �� -�� , �� . �� Kolmogorov. �� , �� (� �� ) �� , �� explanans �� (�� explanandum) ��. �� explanandum (�� ) �� , �� .²

� �� 1959 �� , �� .³ �� , �� , �� , �� , �� .

�� , �� , �� . �� (�traffic accident and taxi colour�).^4,5

2. ��

�� , �� , �� . �� . �� , � �� (�� 15% �� , �� p=0,15) �� (�� 85%, �� 1�p=0,85). �� : �� , �� , �� , �� . � �� 80% �� . �� , �� , �� , �� . �� , �� 0,50. �� , � �� 0,80. �� .

1� ��: ��

�� . �� 1 �� (12) �� (17) �� (�� ) �� , �� .

��, � a priori (� ��) �� p=0,15 �� (1�p)= 0,85, �� , �� , �� 12/29=0,41. � �� , ��, �� 0,15 �� 0,41, �� 0,50. �� , � �� 0,59. �� , �� , �� 0,85 �� 0,96, �� (0,04). � �� * (��), �� (0,80) �� (0,80), �� .^5,6

* �� , �� .
��: �� , �� .

2� ��: �� Bayes

�� : �� , �� ;�.

3� ��: � ��

�� 2 �� , �� , �� .^7,8

4� ��: �� *

� �� , �� , �� 0,80 (�� ) �� , �� , �� 0,20 (�� ). � �� , ��, �� L=0,80/0,20=4 �� =0,20/0,80=0,25. �� Bayes, � �� (��) �� :

�� , ��, �� , �� :

�� p₁ �� p₂, ��:

��, ��, � �� 0 �� 0,20, �� , � �� 0,50, �� (0,59).^4,9

* �� (��, positive and negative likelihood, ��, vraisemblance) �� . �� . � �� R.A. Fisher, � �� , �� . �� .

5� ��: �� (odds)

�� 0,15/0,85=�=0,176 �� ٴL=0,176�4=0,70 �� (�� ) �� (��) �� :

6� ��: ��

�� (odds) �� (logit).¹⁰ � �� (0,15) �� 0,15 �� :

ln (�� 0,15)=ln 0,176=100 ln �=�1,73

� �� (� �� ) �� , �� :

ln L=ln 4=1,386 �, ��, �� : 100 ln 4=138,6* �� (�� ) �� (��), �� , �� :

100 ln (�� )=100 ln �+100 ln L=(�173)+138,6=(�34)

�� =e^-0,34=0,71 ��, ��, � �� :

* �� , �� , �� 100 �� .¹¹

7� ��: ��

� �� (0,15) �� (0,80) �� 0,15 x0,80=0,12. � �� ߻ (0,85) �� (0,20) �� 0,85 x 0,20=0,17. �� 0,12+0,17=0,29 (�� 1).^8,9

�� , � �� , �� 0,12, �� (p) ��, �� 0,29x (p)=0,12 �� :

�� , �� .

� �� , �� 0,17, �� (p) �� 0,59. �� , �� .

�� (0,12)+(0,17)=(0,29) �� . ��, � �� 100 �� (15 �� 85 ��) �� 29 �� 71 ��.

� �� , �� (�� ) �� .

P (�� /�� ߻)=�� x �� =0,15 x 2,76=0,41.

�� , �� , � �� . �� , �� , �� . ��, �� , � �� 0,50. �� , �� , �� .

�� , �� 0,50. �� , � �� :

��: p>=0,85

��, ��, � �� 0,05 �� (0,80), �� .

�� (0,80) �� 0,85, �� (�) ��, �� :

�� (n)=250 �� .

� �� , �� , �� . � �� , ��, �� .

3. ��

�� , �� . �� ߻ �� (��) �� (�� ). � �� , �� , �� . ��, � �� , �� , �� .

�� :
�� .

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