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Free Parameter
A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model and must be estimated experimentally or theoretically. A mathematical model, theory, or conjecture is more likely to be right and less likely to be the product of wishful thinking if it relies on few free parameters and is consistent with large amounts of data. See also * Decision variables * Exogenous variables * Overfitting * Random variables * State variable A state variable is one of the set of Variable (mathematics), variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behavi ...s References Philosophy of science Scientific method Ignorance {{science-philo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Estimation
In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate. Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference. More generally, a point estimator can be contrasted with a set estimator. Examples are given by confidence sets or credible sets. A point estimator can also be contrasted with a distribution estimator. Examples are given by confidence distributions, randomized estimators, and Bayesian posteriors. Properties of point estimates Biasedness “Bias” is defined as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wishful Thinking
Wishful thinking is the formation of beliefs based on what might be pleasing to imagine, rather than on evidence, rationality, or reality. It is a product of resolving conflicts between belief and desire. Methodologies to examine wishful thinking are diverse. Various disciplines and schools of thought examine related mechanisms such as neural circuitry, human cognition and emotion, types of bias, procrastination, motivation, optimism, attention and environment. This concept has been examined as a fallacy. It is related to the concept of wishful seeing. Some psychologists believe that positive thinking is able to positively influence behavior and so bring about better results. This is called the " Pygmalion effect". Christopher Booker discussed wishful thinking in terms of "the fantasy cycle", which he described as "a pattern that recurs in personal lives, in politics, in history – and in storytelling." He added: "When we embark on a course of action which is unconscious ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, rationally under uncertainty. It differs from the Cognitive science, cognitive and Behavioural sciences, behavioral sciences in that it is mainly Prescriptive economics, prescriptive and concerned with identifying optimal decision, optimal decisions for a rational agent, rather than Descriptive economics, describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by Social science, social scientists, as it lays the foundations to Mathematical model, mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science. History The roots of decision theory lie in probability theory, developed by Blai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exogeny
In a variety of contexts, exogeny or exogeneity () is the fact of an action or object originating externally. It is the opposite of endogeneity or endogeny, the fact of being influenced from within a system. Economics In an economic model, an exogenous change is one that comes from outside the model and is unexplained by the model. Such changes of an economic model from outside factors can include the influence of technology, in which this had previously been noted as an exogenous factor, but has rather been noted as a factor that can depict economic forces as a whole. In economic sociology, Project IDEA (Interdisciplinary Dimensions of Economic Analysis) gave notion to understanding the exogenous factors that play a role within economic theory. Developed from the International Social Science Council (ISSC) in the year of 1982, Project IDEA was founded to gather ideas from economists and sociologists in order to conceptualize what economic sociology incorporates, as they hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overfitting
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be justified by the data. In the special case where the model consists of a polynomial function, these parameters represent the degree of a polynomial. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the Statistical noise, noise) as if that variation represented underlying model structure. Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. Underfitting would occur, for example, when fitting a linear model to nonlinear data. Such a model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Variable
A state variable is one of the set of Variable (mathematics), variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable form. Examples *In mechanics, mechanical systems, the position coordinates and Velocity, velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system. *In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy, enthalpy, thermodynamic temperature, temperature, pressure, volume and entropy. Heat and Work (Thermodynamics), work are not state functions, but process functions. *In electronics, electronic/electrical circuits, the voltages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Science
Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, and the ultimate purpose and meaning of science as a human endeavour. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of scientific practice, and overlaps with metaphysics, ontology, logic, and epistemology, for example, when it explores the relationship between science and the concept of truth. Philosophy of science is both a theoretical and empirical discipline, relying on philosophical theorising as well as meta-studies of scientific practice. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science. Many of the central problems concerned with the philosophy of science lack contemporary consensus, including whether ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Method
The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and medieval world. The scientific method involves careful observation coupled with rigorous skepticism, because Philosophy of science#Observation inseparable from theory, cognitive assumptions can distort the interpretation of the Perception#Process and terminology, observation. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results. Although procedures vary across Branches of science, fields, the underlying #Process, process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
