Revisiting the Welch Uniform Model: A case for Conditional Inference?∗

The Welch (1939) uniform distribution example,  v U(−2  +12) ∈R, ever since its introduction, continues to be used as one of few crucial examples in debates concerning the problems of initial vs. final precision and conditional vs. unconditional inference. The primary aim of this paper is, first, to argue that none of the proposed inference procedure gives rise to satisfactory results in the case of this particular example, and, second, to put forward an alternative, based on a (post-data) truncated sampling distribution, which deals effectively with the weaknesses of the other procedures and addresses the foundational issue of initial vs. final precision. Key terms: Welch uniform, non-regular statistical models, conditionality principle, conditional vs. unconditional inference, ancillarity, post-data support, truncation, relevance principle, initial vs. final precision. ∗Published in Advances and Applications in Statistical Science, 5: 33-52, 2011.