4,378
edits
Model validation: Difference between revisions
m
→The logical trap
No edit summary |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 13: | Line 13: | ||
Anyone would agree that the logical inference 'if A is true, then B must be true' combined with the observation that 'B is true' does not imply that 'A is true'. | Anyone would agree that the logical inference 'if A is true, then B must be true' combined with the observation that 'B is true' does not imply that 'A is true'. | ||
And yet this mistake appears to be rather common: if a given plasma model (A) describes a given | And yet this mistake appears to be rather common: if a given plasma model (A) describes a given experimental result (B), it is inferred that the model must be 'OK' - erroneously, because the agreement may be fortuitous or due to constraints that are hard to identify, or the data interpretation problem may be ''badly posed'' (see below). | ||
There are several ways of avoiding this trap: | There are several ways of avoiding this trap: | ||
| Line 25: | Line 25: | ||
== Hidden assumptions == | == Hidden assumptions == | ||
The equations describing the behaviour of plasmas are mostly known (Maxwell's equations, etc.) but are untractable due to the large number | The equations describing the behaviour of plasmas are mostly known (Maxwell's equations, etc.) but are untractable due to the large number of particles involved. | ||
Hence, simplifying assumptions are always made, usually of the type 'assume ''X >> Y'' '. It is quite common that these assumptions are not made fully explicit, which entrains the risk that the assumptions are violated in some specific case without this circumstance being detected. Therefore, it is important to clarify as precisely as possible under what conditions the model is valid, and check that these conditions are met for all relevant applications of the model. | Hence, simplifying assumptions are always made, usually of the type 'assume ''X >> Y'' '. It is quite common that these assumptions are not made fully explicit, which entrains the risk that the assumptions are violated in some specific case without this circumstance being detected. Therefore, it is important to clarify as precisely as possible under what conditions the model is valid, and check that these conditions are met for all relevant applications of the model. | ||