Editing Bayesian inference (section)

===Multiple observations===

For a sequence of [[independent and identically distributed]] observations <math>\mathbf{E} = (e_1, \dots, e_n)</math>, it can be shown by induction that repeated application of the above is equivalent to
<math display="block">P(M \mid \mathbf{E}) = \frac{P(\mathbf{E} \mid M)}{\sum_m {P(\mathbf{E} \mid M_m) P(M_m)}} \cdot P(M),</math>
where
<math display="block">P(\mathbf{E} \mid M) = \prod_k{P(e_k \mid M)}.</math>
<!-- It may be more informative if an actual example is given: e1/M, e2/M, ... might be shown as .05/4, .061/4, .033/4.  Then showing the actual calculations using these three terms in the summation. -->