# Notes on unknown uniform distributions in hierarchical probabilistic models

Iain Murray, 2009.

A common situation within a probabilistic model is that some variables
**x**={*x*_{1},...,*x _{N}*} 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 {

*x*} came from a uniform distribution, Uniform[

_{n}*a*,

*b*], with

*a*and

*b*unknown. This note contains the marginal likelihood of this model for quick reference.

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