# Observational equivalence

observationally equivalent observationally equivalentexperimentally indistinguishableobservably distinct
Observational equivalence is the property of two or more underlying entities being indistinguishable on the basis of their observable implications.wikipedia
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### Parameter identification problem

identificationidentification problemidentified
This term often arises in relation to the identification problem.
More generally, the term can be used to refer to any situation where a statistical model will invariably have more than one set of parameters that generate the same distribution of observations, meaning that multiple parametrizations are observationally equivalent.

### Underdetermination

underdeterminedindeterminacydifferent people can interpret the same evidence differently
*Underdetermination
Then, if the evidence available at a particular time can be equally well explained by at least one other hypothesis, there is no reason to believe it rather than the equally supported rival, which can be considered observationally equivalent (although many other hypotheses may still be eliminated).

### Scientific theory

theoryscientific theoriestheories
Thus, for example, two scientific theories are observationally equivalent if all of their empirically testable 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.

### Econometrics

econometriceconometricianeconometric analysis
In econometrics, 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.

### Semantics (computer science)

semanticsformal semantics of programming languagesformal semantics
In the formal semantics of programming languages, 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.

### Term (logic)

termstermfirst-order terms
In the formal semantics of programming languages, 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.

### Theory

theoreticaltheoriestheorist
A pair of such theories is called indistinguishable or observationally equivalent, and the choice between them reduces to convenience or philosophical preference.

### Quantum reference frame

Indeed, Newton was fully aware of this stated that all inertial frames are observationally equivalent to each other.

### Indeterminacy of translation

gavagaigavagai problemGavagai' example
The last of these, not discussed here, refers to Quine's assessment that evidence alone does not dictate the choice of a scientific theory, as different theories - observationally equivalent - may be able to explain the same facts.

### Identifiability

identifiableModel identificationnonidentifiable
A model that fails to be identifiable is said to be non-identifiable or unidentifiable: two or more parametrizations are observationally equivalent.

### Galileo affair

trial of GalileoGalileomedia
Simplicio's arguments are systematically refuted and ridiculed by the other two characters with what Youngson calls "unassailable proof" for the Copernican theory (at least versus the theory of Ptolemy – as Finocchiaro points out, "the Copernican and Tychonic systems were observationally equivalent and the available evidence could be explained equally well by either" ), which reduces Simplicio to baffled rage, and makes the author's position unambiguous.

### ProVerif

The tool is capable of evaluating reachability properties, correspondence assertions and observational equivalence.

### List of statistics articles

List of statistical topicsList of statistics topicsIndex of statistics articles

### Walter Kaufmann (physicist)

Walter KaufmannKaufmannWalter Kaufman
He was the first to discuss Albert Einstein's theory of special relativity and argued that, although Einstein's theory is based on quite different conditions and is logically more satisfying, it is observationally equivalent to Lorentz's theory.

### Denotational semantics

denotationalfully abstractHistory of denotational semantics

### One-way speed of light

Einstein convention or by slow clock synchronizationone-way speed
Even though this theory is experimentally indistinguishable from special relativity, Lorentz's theory is no longer used for reasons of philosophical preference and because of the development of general relativity.