Bayesian uses the concept of prior belief about the parameter
Then the uncertainty of
changes according to the data
Here Bayesian interprets
as a random variable,
and the prior belief is given in the form of probability density
In a Bayesian model we will investigates the postrior density
Let and be two events where
Then the conditional probability of given
can be defined as
The idea of ``conditioning''
is that ``if we have known that
has occurred, the sample space
should have become
It is often the case that one can use
Law of total probability.
Let and be two events.
Then we can write the probability as
In general, suppose that we have a sequence
of mutually disjoint events
where ``mutual disjointness'' means that
are called ``a partition of
Then for any event
be events such that the 's are
for all .
is called Bayes rule
Concept of Independence.
Intuitively we would like to say that and are independent if
knowing about one event give us no information about another.
We say and are independent if
This definition is symmetric in
to be 0.
Furthermore, a collection of events
is said to be
for any subcollection
© TTU Mathematics