Why is the normal distribution a default choice for a prior over a set of real numbers? I found this question without any context while preparing for a job interview. 
The only reason I can think of is that the Normal distribution's support are the real numbers. 
Why wouldn't we use a uniform distribution? Because there is no uniform distribution over the real numbers from -infinity to infinity?
Thanks!
 A: There is no reason to use the Normal distribution as a default prior for a real parameter and there are many instances in the Bayesian literature where another prior is used. For instance, when testing for a zero mean in a Normal sample, Jeffreys (1939) uses a standard Cauchy distribution as a prior. The "uniform" prior does not exist as a probability distribution but it can be used as an "improper:" prior, provided the posterior is well defined. This is also a choice found in Jeffreys (1939). Note that using a Normal prior with a large variance is a poor idea, as large may not be large enough.
A: The first question you need to think about is why you consider that you need a totally uninformative prior. Do you really know absolutely nothing about the situation? Some allegedly uninformative priors place unrealistically high densities on regions in the sample space that a moment's reflection will tell you is unlikely. 
Moreover, you do not need to restrict yourself to a single choice of prior.
In short, beware of default choices of prior.
