**FOA Home**
**UP:** Probabilisitic retrieval

In addition to evidence the features provides that a document
*is* \Rel, $Pr(\mathname{Rel} | {\bf x})$, they may also provide
evidence that they are not: $\Pr(\overline{\mathname{Rel}} | {\bf x})$
{One way to know that we are talking about a ``rational'' world is to
say that: \[\Pr(\mathname{Rel} | {\bf x}) = 1 -
\Pr(\overline{\mathname{Rel}} | {\bf x}) \] } An *odds*
calculation balances both probabilities as a ratio:
\mathname{Odds}(\mathname{Rel} | {\bf x}) &\equiv& {\Pr(\mathname{Rel} |
{\bf x})\over \Pr(\overline{\mathname{Rel}} | {\bf x})} Bayes Rule can
also be applied to this ratio: \mathname{Odds}(\mathname{Rel} | {\bf x})
&=& {\Pr(\mathname{Rel} | {\bf x})\over \Pr(\overline{\mathname{Rel}} |
{\bf x})} \\ &=&{\Pr(\mathname{Rel})\over
\Pr(\overline{\mathname{Rel}})}\cdot {\Pr({\bf x} | \mathname{Rel})\over
\Pr({\bf x} | \overline{\mathname{Rel}})} \\
&=&\mathname{Odds}(\mathname{Rel}) \cdot {\Pr({\bf x} |
\mathname{Rel})\over \Pr({\bf x} | \overline{\mathname{Rel}})} The first
term will be small; the odds of picking a relevant vs. irrelevant
document independent of any features of the document are not good.
Still, they can be expected to be a characteristic of the entire corpus
and insensitive to any analysis we might perform on aparticular
documents.

In order to calculate the second term, we need a more refined model of how documents are ``constructed'' from their features.

*Top of Page*
**UP:** Probabilisitic retrieval
**FOA Home**