Plausibility Inference

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Abstract
A scheme for inference—plausibility theory—is proposed. It parallels likelihood theory, the analogue of the likelihood function L(ω) = p(t; ω) being the plausibility function π(ω) = p(t; ω)/supt p(t; ω), but likelihood and plausibility throw light on different aspects of the evidence in the data t. The ordinate test for significance (which rejects for small values of the probability (density) function, of a simple hypothesis), the maximum ordinate estimate (which equals the set of ω's such that p(·; ω) has mode at t), and M‐ancillarity are, to some extent in modified form, integrated in plausibility theory. Among the subthemes, particular attention is given to relevant properties of universality (in its origin a preconcept for M‐ancillarity), to exponential models, and, naturally, to similarities and contrasts between plausibility inference and likelihood inference. The logic connected with the ordinate test is also attended to.

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