Observational equivalence
Encyclopedia
In econometrics
, two parameter values (sometimes called 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
, two term
s 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.
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
, two parameter values (sometimes called 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
Parameter identification problem
The parameter identification problem is a problem which can occur in the estimation of multiple-equation econometric models where the equations have variables in common....
.
In the formal semantics of programming languages
Formal semantics of programming languages
In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation...
, two term
Term (mathematics)
A term is a mathematical expression which may form a separable part of an equation, a series, or another expression.-Definition:In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables separated from another term by a + or - sign in an...
s 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.