Notes on unknown uniform distributions in hierarchical probabilistic models

Iain Murray, 2009.

A common situation within a probabilistic model is that some variables x={x₁,...,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_n} 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.

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