The last line is the kernel of the prior distribution, i.e.

In a Bayes change-detection problem, a prior distribution is available for the change time.

One should also keep the purpose of the analysis in mind when choosing the prior distribution.

Ideally, ensemble members would form a sample from the prior distribution.

An example is a prior distribution for the temperature at noon tomorrow.

Note that, in the above model (and also the one below), the prior distribution of the initial state is not specified.

Apart from the current available data, a prior distribution of unknown parameters should be assigned.

Use of an informative prior distribution on the variance, however, would allow such analysis.

Such problems related to the need to assign a prior distribution to the unknown values.

From a Bayesian point of view, we would regard it as a prior distribution.