Upper and lower envelopes can be represented by a set $\cM$ of (finitely additive) measures indexed by an unknown parameter $\theta$; this also specifies the classical frequentist concept of a compound hypothesis. Envelope models have hitherto been used almost exclusively in subjective settings to model the uncertainty or strength of belief of individuals or groups. Our interest in these imprecise probability representations is as mathematical models for those objective frequentist phenomena of engineering and scientific significance where what is known may be substantial, but relative frequencies, nonetheless, lack (statistical) stability. A full probabilistic methodology needs not only an appropriate mathematical probability concept, enriched by such notions as expectation and conditioning, but also an interpretive component to identify data that is typical of the model and an estimation component to enable inference to the model from data and background knowledge. Our starting point is this first task of determining typicality. Kolmogorov complexity is used as the key non-probabilistic idea to enable us to create simulation data from an envelope model in an attempt to identify ``typical'' sequences. First steps in frequentist modeling will also be taken towards inference of the set $\cM$ from frequentist data and applied to data on vowel production from an internet message source.
Keywords. lower envelopes, frequentist interpretation,simulation
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Authors addresses:
Pablo Fierens
391 Rhodes Hall
Cornell University
ITHACA, NY 14850
USA
Terrence Fine
Professor Terrence L. Fine
Center for Applied Mathematics
Rhodes Hall 612
Cornell University
Ithaca, NY 14853, USA
E-mail addresses:
| Pablo Fierens | pifierens@ee.cornell.edu |
| Terrence Fine | tlfine@ee.cornell.edu |