Notes on unknown uniform distributions in hierarchical probabilistic models
Iain Murray · 2009
A common situationwithin a probabilistic model is that some variables x={x1, . . . , xN} are assumed to have come from an unknown distribution. For large datasets it may be necessary to introduce a flexible or non-parametric prior over possible distributions. A simple assumption, often good enough for small N , is to assume that the {xn} came from a uniform distribution, Uniform[a, b], with a and b unknown. This note contains the marginal likelihood of this model for quick reference.