Observational equivalence is the property of two or more underlying entities being indistinguishable on the basis of their
observable
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum phys ...
implications. Thus, for example, two
scientific theories are observationally equivalent if all of their
empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
ly
testable
Testability is a primary aspect of Science and the Scientific Method and is a property applying to an empirical hypothesis, involves two components:
#Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logica ...
predictions are identical, in which case empirical evidence cannot be used to distinguish which is closer to being correct; indeed, it may be that they are actually two different perspectives on one underlying theory.
In
econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8� ...
, two parameter values (or two ''structures,'' from among a class of statistical models) are considered observationally equivalent if they both result in the same probability distribution of observable data.
This term often arises in relation to the
identification problem.
In the
formal semantics of programming languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax.
Semantics describes the processes ...
, two
terms ''M'' and ''N'' are observationally equivalent if and only if, in all contexts ''C''
..where ''C''
'M''is a valid term, it is the case that ''C''
'N''is also a valid term with the same value. Thus it is not possible, within the system, to distinguish between the two terms. This definition can be made precise only with respect to a particular calculus, one that comes with its own specific definitions of ''term'', ''context'', and the ''value of a term''. The notion is due to
James H. Morris, who called it "extensional equivalence."
See also
*
Underdetermination
In the philosophy of science, underdetermination or the underdetermination of theory by data (sometimes abbreviated UTD) is the idea that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in re ...
References
Statistical theory
Econometric modeling
Programming language semantics
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