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By Geert Dhaene

The background of many sciences is characterised by way of a nearly non-stop emer­ gence of recent theories. From a normative standpoint, the survival of a brand new concept should still normally be decided via its skill to give an explanation for a brand new physique of proof which the present theories are not able to give an explanation for. If additionally the recent concept is ready to clarify all of the effects acquired by means of the present theories and if it may indicate why those theories fail to give an explanation for definite proof, it may turn into the dominant conception. differently, it may possibly coexist with different theories for it slow. for this reason, a brand new thought must be judged not just via confronting it with current proof, but in addition through confronting it with latest theories. the concept that a idea might be in a position to account for the consequences ob­ tained via different theories, even supposing implicitly adhered to by way of many scientists, has infrequently been formalized. The facts literature on parametric hypoth­ esis trying out, although, will be visible for example of the sort of formalization.

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Sample text

If (3D exists and F £]; Q, then G(3D = G(3O (VP: Q;: C Pc Q =? F £]; P). Proof. If F £]; Q and Q;: C P c Q, then P'YD = G(3D = G(3-YD = P'YO

D} £I; g. Proof. The result follows immediately from the definition of £I; . 1. 2. If DE F, then F £I; g. o Proof. If D E F, then D = Fo: D. 3. 3) £I; g ¢:::::> D E gfj. Proof. The result follows immediately from the definitions of £I; and gfj. , where one family is a subset of the other), we have the following properties. 4. 4) Vg: Fe Proof. Let D ¢ F g and DE g 9 F II; g. c g and DE g. Then, D = G{3D and FO:D = Gp"'D =I- D, wherefrom G pD =I- Gp"'D. 5. 6) Proof. If F c g, then FE}; 9 <===> FaD = G{3D' <===> Jp(D, F) c g, then FaD = Jp(D, g).

Hat these pu,railieter~ have an interesting interpretation outside the models, is more structural in nature. This chapter is organized as follows. In Section 2, we discuss at some length the basic framework and terminology from the point of view of an empirical model builder who wants to compare two different parametric empirical models. A formal definition of the encompassing relation is given in Section 3. We study the theoretical properties of this relation in Section 4, and draw some conclusions regarding modelling strategy in Section 5.

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