Inverse Probability. 179 



On Inverse Probability and the Rules required for it. 



9. It has been already stated that the only funda 

 mental rules of inference in Probability are the two described 

 in 2, 3, but there are of course abundance of derivative 

 rules, the nature and use of which are best obtained from the 

 study of any manual upon the subject. One class of these 

 derivative rules, however, is sufficiently distinct in respect of 

 the questions to which it may give rise, to deserve special 

 examination. It involves the distinction commonly recog 

 nised as that between Direct and Inverse Probability. It is 

 thus introduced by De Morgan : 



&quot; In the preceding chapter we have calculated the chances 

 of an event, knowing the circumstances under which it is to 

 happen or fail. We are now to place ourselves in an inverted 

 position : we know the event, and ask what is the probability 

 which results from the event in favour of any set of circum 

 stances under which the same might have happened 1 .&quot; The 

 distinction might therefore be summarily described as that 

 between finding an effect when we are given the causes, and 

 finding a cause when we are given effects. 



On the principles of the science involved in the definition 

 which was discussed and adopted in the earlier chapters of 

 this work, the reader will easily infer that no such distinction 

 as this can be regarded as fundamental. One common feature 

 was traced in all the objects which were to be referred to 

 Probability, and from this feature the possible rules of 



1 Essay on Probabilities, p. 53. I peedia Metropolitana he has stated 

 have been reminded that in his arti- that such rules involve no new prin- 

 le on Probability in the Encyclo- ciple. 



122 



