|Ruby||v1.5.0Sep 24th 2020||(+226/-9)|
|Tyrrell_McAllister||v1.4.0Aug 14th 2013||(+199/-69) Added definition in terms of independence. Removed needless proliferation of variable letters.|
|komponisto||v1.3.0Jan 15th 2011||(+19/-15)|
|komponisto||v1.2.0Jun 4th 2010||(+7)|
|Vladimir_Nesov||v1.1.0May 26th 2010||(+37/-58) fixed formatting|
|komponisto||v1.0.0May 26th 2010||(+2486) created page|
If A is a hypothesis and B and C are two pieces of evidence relating to A, then B is said to screen off C from A if P(A|B&C) = P(A|B). That is,
if knowing C provides no additional information about A once B is known.
For example, suppose A is
"Proposition X is true", B is "the arguments for X say Y", and C is "experts believe X". Presumably, experts believe X because of what the arguments say; thus, while expert belief in X is evidence for X, it is not additional evidence for X over and above the arguments for X, once one has already ascertained what the latter are. We say that the authority of the experts is screened off by the arguments for X.
Failure to take into account the dependence relationships among various pieces of information can lead to serious errors, as P(A|B) may be
much lower than P(A|C). An example of this may be seen in the Meredith Kercher murder case, where A is "Amanda Knox killed Meredith Kercher", B is "Rudy Guede killed Meredith Kercher", and C is "Meredith Kercher was killed". Here, P(A|C) is arguably substantial, since Knox was Kercher's roommate. However, B, which is known to be true (to a high level of certainty), implies C, so that P(A|B&C) = P(A|B); the evidence against Guede thus (approximately) screens off Kercher's death as evidence against Knox. And, in fact, P(A|B) is close to the prior probability P(A) (since there is little connection between Knox and Guede); hence the rest of the evidence against Knox has far less Bayesian significance than the investigators and jurors in the case intuitively assigned to it.
If A is a hypothesis and B and C are two pieces of evidence relating to A, then B is said to screen off C if P(A|B&C) = P(A|B). That is, if knowing C provides no additional information about A once B is known.