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Observational Equivalence
Observational equivalence is the property of two or more underlying entities being indistinguishable on the basis of their observable implications. 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. 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. This term often arises in relation to the identification problem. 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 ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question. Quantum mechanics In quantum physics, observables manifest as linear operators on a Hilbert space representing the state space of quantum states. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Theory
A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge. A scientific theory differs from a scientific fact or scientific law in that a theory explains "why" or "how": a fact is a simple, basic observation, whereas a law is a statement (often a mathematical equation) about a relationship between facts. For example, Newton’s Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain ''how'' gravity works. St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which ''Scientific method#Confirmation, confirms'' or ''disconfirms'' Hypothesis#Scientific hypothesis, scientific hypotheses and arbitrates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 logically possible. #The practical feasibility of observing a reproducible series of such counterexamples if they do exist. In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone. This allows anyone to decide whether a theory can be supported or refuted by data. However, the interpretation of experimental data may be also inconclusive or uncertain. Karl Popper introduced the concept that scientific knowledge had the property of Falsifiability.as published in ''The Logic of Scientific Discovery.Karl Popper "The Logic of Scientific Discovery", 1934 (as Logik der Forschung, English translation 1959)'', ISBN 0415278449 and 2002 ISBN 9780415278447, 0415278449 See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 [pp. 8–22]. Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1[pp. 1–34].Abstract (The New Palgrave Dictionary of Economics, 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic Phenomenon, phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used toda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter Identification Problem
In economics and econometrics, the parameter identification problem arises when the value of one or more parameters in an economic model cannot be determined from observable variables. It is closely related to non-identifiability in statistics and econometrics, which occurs when a statistical model has more than one set of parameters that generate the same distribution of observations, meaning that multiple parameterizations are observationally equivalent. For example, this problem can occur in the estimation of multiple-equation econometric models where the equations have variables in common. In simultaneous equations models Standard example, with two equations Consider a linear model for the supply and demand of some specific good. The quantity demanded varies negatively with the price: a higher price decreases the quantity demanded. The quantity supplied varies directly with the price: a higher price increases the quantity supplied. Assume that, say for several years, we ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation. History In 1967, Robert W. Floyd publishes the paper ''Assigning meanings to programs''; his chief aim is "a rigorous standard for proofs about computer programs, including proofs of correctness, equivalence, and termination". Floyd further writes: A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It must specify which of the phrases in a syntactically correct program represent commands, and what conditions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term (logic)
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation. For example, is a term built from the constant 1, the variable , and the binary function symbols and ; it is part of the atomic formula which evaluates to true for each real-numbered value of . Besides in logic, terms play important roles in universal algebra, and rewriting systems. Formal definition Given a set ''V'' of variable symbols, a set ''C'' of constant symbols and sets ''F''''n'' of ''n''-ary fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James H
James is a common English language surname and given name: *James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (other), various kings named James * Saint James (other) * James (musician) * James, brother of Jesus Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Arts, entertainment, and media * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * James the Red Engine, a character in ''Thomas the Tank En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 response to it. The ''underdetermination thesis'' says that all evidence necessarily underdetermines any scientific theory. Underdetermination exists when available evidence is insufficient to identify which belief one should hold about that evidence. For example, if all that was known was that exactly $10 was spent on apples and oranges, and that apples cost $1 and oranges $2, then one would know enough to eliminate some possibilities (e.g., 6 oranges could not have been purchased), but one would not have enough evidence to know which specific combination of apples and oranges was purchased. In this example, one would say that belief in what combination was purchased is underdetermined by the available evidence. In contrast, overdeterminat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures. Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization. Scope Statistical theory provides an underlying rationale and provides a consistent basis for the choice of methodology used in ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometric Modeling
Econometric models are statistical models used in econometrics. An econometric model specifies the statistical relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon. An econometric model can be derived from a deterministic economic model by allowing for uncertainty, or from an economic model which itself is stochastic. However, it is also possible to use econometric models that are not tied to any specific economic theory. A simple example of an econometric model is one that assumes that monthly spending by consumers is linearly dependent on consumers' income in the previous month. Then the model will consist of the equation :C_t = a + bY_ + e_t, where ''C''''t'' is consumer spending in month ''t'', ''Y''''t''-1 is income during the previous month, and ''et'' is an error term measuring the extent to which the model cannot fully explain consumption. Then one objective of the econometrician is to obtain estimates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
