
170 Decision Based Design
Here
X
is the prior distribution and
X
is the posterior distribution of the
variable X, while
(|)fdx
D
is the likelihood of getting the data D (e.g., n successes
out of m trials) given the prior distribution of X. Many times we try to assess the
probability distribution of the relative frequency (probability) of an event, for
example, the probability of a tornado hitting a town given its path a few days
prior. The Bayesian method can help make a decision when data are scarce. On
the other hand, if the prior knowledge is incorrect, it can corrupt even good
information coming in the form of data. Priors therefo ...