Difficulties have arisen with specifying a prior in the situation
where there is, in fact, no actual prior information. While it was
possible to specify a uniform prior for the example of
determination of the proportion of rusted vehicles (i.e.
) this is not possible where the possible range
for 
is infinite and the prior being a proper
distribution. A prior 
for the range 
is a
solution, as an improper prior, but even then issues arise as to
transformations of the parameters of interest. Clearly, if
then all values of in the range
[0,1] are equally likely. This is not prior ignorance as
maintained in [38] but is in fact a concrete and active
statement of prior belief that all values of are as
likely as each other, and that belief will quite properly
correspond with a non-uniform prior for transformations of
. For example, if we have N competitors each running
in a race, with 1 from country A and N-1 from country B, and
prior information tells us that each is equally likely to win the
race, then this does not correspond to prior information that
country A and country B are equally likely to have winners. It is
important, therefore to ensure that it is clear as to what prior
information is being elicited.
Prior elicitation is the process of specifying, in the form of a probability distribution, prior information about the parameters of interest. The practical issues detailing methods of obtaining an informative prior are dealt with in [37]. Examples in practice are mentioned in [46] and [55]. It is the assertion of this author that all priors are informative and that for this reason, due consideration should be given in every circumstance to the elicitation process.
In including an informative prior, the statistical analysis is not objective. It has been mentioned above that the Bayesian framework is unapologetically subjective, and this is emphasised once again here.
In the past there have been attempts to ``objectify'' Bayesian techniques. Notably we have work by Jeffreys [21], but this depends on the form of the data. Subjective scientific inquiry seems a contradiction in terms, but is quite acceptable, provided that we realise that we have subjective inputs, and are careful about such things. For this reason, Bayesian statisticians are interested in concepts of sensitivity and robustness [3].