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• ##### 1995
• Brightwell, Felsner & Trotter (1995) call it "one of the most intriguing problems in the combinatorial theory of posets. (wikipedia.org)
• ##### calculate the probability
• By assuming some probability distribution for the value (women's average lifespan-men's average lifespan), one could calculate the probability of obtaining just by chance the difference in average age found, with the variation that is found within each group, and, for the number of people in each group. (answersingenesis.org)
• Laplace used the rule of succession to calculate the probability that the sun will rise tomorrow, given that it has risen every day for the past 5000 years. (wikipedia.org)
• ##### mathematics
• This article is concerned with the mathematics of manipulating probabilities. (wikipedia.org)
• The theory of non-well-founded sets shows that this kind of circularity is perfectly consistent in terms of logic and mathematics. (goertzel.org)
• Probability theory is the branch of mathematics concerned with probability. (wikipedia.org)
• In order theory, a branch of mathematics, the 1/3-2/3 conjecture states that, if one is comparison sorting a set of items then, no matter what comparisons may have already been performed, it is always possible to choose the next comparison in such a way that it will reduce the number of possible sorted orders by a factor of 2/3 or better. (wikipedia.org)
• Roussas, George G. (2001) [1994], "Contiguity of probability measures", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4 van der Vaart, A. W. (1998). (wikipedia.org)
• ##### assigns
• Their consequences and utility values for a particular individual are: Beautiful and eventful trip by car: 16 utils Staying home: 9 utils Death by car accident: 4 utils If the person had to choose the best of two scenarios A and B, each of which assigns probabilities to the states of nature, how would they do it? (wikipedia.org)
• ##### 2000
• Chapter 8 of Donald Gillies' Philosophical Theories of Probability (2000) deals with intersubjective and pluralist views of probability. (blogspot.com)
• Furthermore, Gillies makes the case for a "pluralist" view of probability, a development of the two-concept view of probability by Ramsey and Carnap (Gillies 2000: 180-181). (blogspot.com)
• Between artefactual and intersubjective probabilities, Gillies sees some borderline cases such as in medicine or population studies (Gillies 2000: 180, 194). (blogspot.com)
• An intersubjective probability is a measure of the degree of belief of a social group where a consensus has formed (Gillies 2000: 179). (blogspot.com)
• If a group of people, though shared beliefs, can agree on a common betting quotient about some probability, then this can be seen as an intersubjective or consensus probability (Gillies 2000: 171). (blogspot.com)
• Contiguity Asymptopia: 17 October 2000, David Pollard Asymptotic normality under contiguity in a dependence case A Central Limit Theorem under Contiguous Alternatives Superefficiency, Contiguity, LAN, Regularity, Convolution Theorems Testing statistical hypotheses Necessary and sufficient conditions for contiguity and entire asymptotic separation of probability measures R Sh Liptser et al 1982 Russ. (wikipedia.org)
• Law of total expectation Law of total variance Law of total cumulance Marginal distribution Zwillinger, D., Kokoska, S. (2000) CRC Standard Probability and Statistics Tables and Formulae, CRC Press. (wikipedia.org)
• ##### thus
• Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. (wikipedia.org)
• ##### inference
• The purpose of this chapter is to provide a background on the results from probability and inference theory required for the study of several of the topics of contemporary econometrics. (springer.com)
• A Review of The Design Inference: Eliminating Chance Through Small Probabilities by William A. Dembski Cambridge University Press, 1998. (answersingenesis.org)
• Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for frequentist inference. (wikipedia.org)
• In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning-a kind of Prolog for probability instead of logic. (wikipedia.org)
• ##### Empirical
• Empirical applications of this rich theory are usually done with the help of statistical and econometric methods, especially via the so-called choice models, such as probit and logit models. (like2do.com)
• From almost one and a half centuries, scientific research mostly relies on empirical findings to provide support to their hypotheses, models, or theories. (intechopen.com)
• For a set empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed to minimize the difference between the area under the empirical probability distribution and the area under the theoretical probability distribution. (wikipedia.org)
• Therefore, the validity of expected utility theory depends on the empirical validity of the independence axiom. (wikipedia.org)
• ##### continuous
• Eventually, analytical considerations compelled the incorporation of continuous variables into the theory. (wikipedia.org)
• citation needed] One author even uses the terminology "continuous law of alternatives" in the continuous case. (wikipedia.org)
• ##### Exposition
• In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk , in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. (like2do.com)
• Barwise and Etchemendy's book " The Liar " gives a very nice exposition of this kind of set theory for the semi-technical reader. (goertzel.org)
• ##### fuzzy logic
• Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. (wikipedia.org)
• ##### Bayesian
• His dissertation and his paper Stochastic Independence, Causal Independence, and Shieldability are precursors of the theory of Bayesian networks and their causal interpretation. (wikipedia.org)
• Therefore, the aim of this chapter is to introduce a Bayesian approach to hypothesis testing that may represent a useful complement, or even an alternative, to the current NHST. (intechopen.com)
• The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. (biomedsearch.com)
• ##### probabilistic
• He is known especially for his contributions to the defense and development of alternatives to the classical calculus for probabilistic modeling and decision-making. (wikipedia.org)
• Probability and Probabilistic Reasoning for Electrical Engineering, Pearson/Prentice-Hall, 2006. (wikipedia.org)
• Probability and Probabilistic Causality. (wikipedia.org)
• ##### Laplace's
• In the 1940s, Rudolf Carnap investigated a probability-based theory of inductive reasoning , and developed measures of degree of confirmation, which he considered as alternatives to Laplace's rule of succession. (wikipedia.org)
• Despite Laplace's explicit and immediate disclaimer in the source, based on expertise in astronomy as well as probability, two centuries of criticism have followed. (wikipedia.org)
• ##### quantum
• Of the application of such theories to quantum mechanics, Bill Jefferys has said: "Such approaches are also not necessary and in my opinion they confuse more than they illuminate. (wikipedia.org)
• The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular. (wikipedia.org)
• Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics. (wikipedia.org)
• ##### consists
• The central notion is that of a causal probability space whose sample space consists of causal alternatives. (pitt.edu)
• So, in many cases the unique alternative consists of working with interpolated, outdated, or even absolutely unknown values. (hindawi.com)
• ##### statistical
• In the 20th century, interest was reignited by Abraham Wald's 1939 paper pointing out that the two central procedures of sampling-distribution-based statistical-theory, namely hypothesis testing and parameter estimation , are special cases of the general decision problem. (like2do.com)
• Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. (wikipedia.org)
• ##### density function
• If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. (wikipedia.org)
• Note however that the characteristic function of a distribution always exists, even when the probability density function or moment-generating function do not. (wikipedia.org)
• If random variable X has a probability density function fX, then the characteristic function is its Fourier transform with sign reversal in the complex exponential, and the last formula in parentheses is valid. (wikipedia.org)
• ##### asymptotic
• Alternative asymptotic tests of significance and related aspects of 2SLS and 3SLS estimated parameters. (springer.com)
• The concept was originally introduced by Le Cam (1960) as part of his contribution to the development of abstract general asymptotic theory in mathematical statistics. (wikipedia.org)
• Le Cam was instrumental during the period in the development of abstract general asymptotic theory in mathematical statistics. (wikipedia.org)
• Econometrics Asymptotic theory (statistics) Contiguity Probability space Wolfowitz J.(1974) Review of the book: "Contiguity of Probability Measures: Some Applications in Statistics. (wikipedia.org)
• ##### causation
• Spohn's research extends to philosophy of science, the theory of causation, metaphysics and ontology, philosophy of language and mind, two-dimensional semantics, philosophical logic, and decision and game theory (see the collection of papers). (wikipedia.org)
• Probability theory and causation. (pitt.edu)
• Why is the transference theory of causation insuffcient? (pitt.edu)
• ##### approaches
• Overall this is a well-written text that provides an interesting alternative to more classical approaches. (springer.com)
• ##### hypothesis
• The solution gives answers to multiple choice questions on probability and hypothesis testing. (brainmass.com)
• ##### causal
• PDF version : http://www.uni-konstanz.de/FuF/Philo/Philosophie/files/grundlagen_der_entscheidungstheorie.pdf „Stochastic Independence, Causal Independence, and Shieldability", Journal of Philosophical Logic 9 (1980) 73-99 „How to Make Sense of Game Theory", in: W. Stegmüller, W. Balzer, W. Spohn (Hg. (wikipedia.org)
• ##### whereas
• Closely related to the field of game theory , decision theory is concerned with the choices of individual agents whereas game theory is concerned with interactions of agents whose decisions affect each other. (like2do.com)
• ##### uncertain
• Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. (wikipedia.org)
• ##### successes
• If we repeat an experiment that we know can result in a success or failure, n times independently, and get s successes, then what is the probability that the next repetition will succeed? (wikipedia.org)
• ##### possible
• Probability is a way of assigning every "event" a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) be assigned a value of one. (wikipedia.org)
• According to Youssef, the valid possible alternatives for probability values are the real numbers, the complex numbers and the quaternions. (wikipedia.org)
• ##### exercises
• epub Exercises in Probability: A Guided Tour ': ' This description made totally have. (roadhaus.com)
• The epub Exercises in Probability: can look denied for the PLD Journal, approach cognitive system, ERO links and not also more! (roadhaus.com)
• ##### 1995
• Brightwell, Felsner & Trotter (1995) call it "one of the most intriguing problems in the combinatorial theory of posets. (wikipedia.org)
• ##### calculate the probability
• By assuming some probability distribution for the value (women's average lifespan-men's average lifespan), one could calculate the probability of obtaining just by chance the difference in average age found, with the variation that is found within each group, and, for the number of people in each group. (answersingenesis.org)
• Laplace used the rule of succession to calculate the probability that the sun will rise tomorrow, given that it has risen every day for the past 5000 years. (wikipedia.org)
• ##### mathematics
• This article is concerned with the mathematics of manipulating probabilities. (wikipedia.org)
• The theory of non-well-founded sets shows that this kind of circularity is perfectly consistent in terms of logic and mathematics. (goertzel.org)
• Probability theory is the branch of mathematics concerned with probability. (wikipedia.org)
• In order theory, a branch of mathematics, the 1/3-2/3 conjecture states that, if one is comparison sorting a set of items then, no matter what comparisons may have already been performed, it is always possible to choose the next comparison in such a way that it will reduce the number of possible sorted orders by a factor of 2/3 or better. (wikipedia.org)
• Roussas, George G. (2001) [1994], "Contiguity of probability measures", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4 van der Vaart, A. W. (1998). (wikipedia.org)
• ##### assigns
• Their consequences and utility values for a particular individual are: Beautiful and eventful trip by car: 16 utils Staying home: 9 utils Death by car accident: 4 utils If the person had to choose the best of two scenarios A and B, each of which assigns probabilities to the states of nature, how would they do it? (wikipedia.org)
• ##### 2000
• Chapter 8 of Donald Gillies' Philosophical Theories of Probability (2000) deals with intersubjective and pluralist views of probability. (blogspot.com)
• Furthermore, Gillies makes the case for a "pluralist" view of probability, a development of the two-concept view of probability by Ramsey and Carnap (Gillies 2000: 180-181). (blogspot.com)
• Between artefactual and intersubjective probabilities, Gillies sees some borderline cases such as in medicine or population studies (Gillies 2000: 180, 194). (blogspot.com)
• An intersubjective probability is a measure of the degree of belief of a social group where a consensus has formed (Gillies 2000: 179). (blogspot.com)
• If a group of people, though shared beliefs, can agree on a common betting quotient about some probability, then this can be seen as an intersubjective or consensus probability (Gillies 2000: 171). (blogspot.com)
• Contiguity Asymptopia: 17 October 2000, David Pollard Asymptotic normality under contiguity in a dependence case A Central Limit Theorem under Contiguous Alternatives Superefficiency, Contiguity, LAN, Regularity, Convolution Theorems Testing statistical hypotheses Necessary and sufficient conditions for contiguity and entire asymptotic separation of probability measures R Sh Liptser et al 1982 Russ. (wikipedia.org)
• Law of total expectation Law of total variance Law of total cumulance Marginal distribution Zwillinger, D., Kokoska, S. (2000) CRC Standard Probability and Statistics Tables and Formulae, CRC Press. (wikipedia.org)
• ##### thus
• Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. (wikipedia.org)
• ##### inference
• The purpose of this chapter is to provide a background on the results from probability and inference theory required for the study of several of the topics of contemporary econometrics. (springer.com)
• A Review of The Design Inference: Eliminating Chance Through Small Probabilities by William A. Dembski Cambridge University Press, 1998. (answersingenesis.org)
• Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for frequentist inference. (wikipedia.org)
• In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning-a kind of Prolog for probability instead of logic. (wikipedia.org)
• ##### Empirical
• Empirical applications of this rich theory are usually done with the help of statistical and econometric methods, especially via the so-called choice models, such as probit and logit models. (like2do.com)
• From almost one and a half centuries, scientific research mostly relies on empirical findings to provide support to their hypotheses, models, or theories. (intechopen.com)
• For a set empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed to minimize the difference between the area under the empirical probability distribution and the area under the theoretical probability distribution. (wikipedia.org)
• Therefore, the validity of expected utility theory depends on the empirical validity of the independence axiom. (wikipedia.org)
• ##### continuous
• Eventually, analytical considerations compelled the incorporation of continuous variables into the theory. (wikipedia.org)
• citation needed] One author even uses the terminology "continuous law of alternatives" in the continuous case. (wikipedia.org)
• ##### Exposition
• In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk , in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. (like2do.com)
• Barwise and Etchemendy's book " The Liar " gives a very nice exposition of this kind of set theory for the semi-technical reader. (goertzel.org)
• ##### fuzzy logic
• Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. (wikipedia.org)
• ##### Bayesian
• His dissertation and his paper Stochastic Independence, Causal Independence, and Shieldability are precursors of the theory of Bayesian networks and their causal interpretation. (wikipedia.org)
• Therefore, the aim of this chapter is to introduce a Bayesian approach to hypothesis testing that may represent a useful complement, or even an alternative, to the current NHST. (intechopen.com)
• The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. (biomedsearch.com)
• ##### probabilistic
• He is known especially for his contributions to the defense and development of alternatives to the classical calculus for probabilistic modeling and decision-making. (wikipedia.org)
• Probability and Probabilistic Reasoning for Electrical Engineering, Pearson/Prentice-Hall, 2006. (wikipedia.org)
• Probability and Probabilistic Causality. (wikipedia.org)
• ##### Laplace's
• In the 1940s, Rudolf Carnap investigated a probability-based theory of inductive reasoning , and developed measures of degree of confirmation, which he considered as alternatives to Laplace's rule of succession. (wikipedia.org)
• Despite Laplace's explicit and immediate disclaimer in the source, based on expertise in astronomy as well as probability, two centuries of criticism have followed. (wikipedia.org)
• ##### quantum
• Of the application of such theories to quantum mechanics, Bill Jefferys has said: "Such approaches are also not necessary and in my opinion they confuse more than they illuminate. (wikipedia.org)
• The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular. (wikipedia.org)
• Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics. (wikipedia.org)
• ##### consists
• The central notion is that of a causal probability space whose sample space consists of causal alternatives. (pitt.edu)
• So, in many cases the unique alternative consists of working with interpolated, outdated, or even absolutely unknown values. (hindawi.com)
• ##### statistical
• In the 20th century, interest was reignited by Abraham Wald's 1939 paper pointing out that the two central procedures of sampling-distribution-based statistical-theory, namely hypothesis testing and parameter estimation , are special cases of the general decision problem. (like2do.com)
• Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. (wikipedia.org)
• ##### density function
• If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. (wikipedia.org)
• Note however that the characteristic function of a distribution always exists, even when the probability density function or moment-generating function do not. (wikipedia.org)
• If random variable X has a probability density function fX, then the characteristic function is its Fourier transform with sign reversal in the complex exponential, and the last formula in parentheses is valid. (wikipedia.org)
• ##### asymptotic
• Alternative asymptotic tests of significance and related aspects of 2SLS and 3SLS estimated parameters. (springer.com)
• The concept was originally introduced by Le Cam (1960) as part of his contribution to the development of abstract general asymptotic theory in mathematical statistics. (wikipedia.org)
• Le Cam was instrumental during the period in the development of abstract general asymptotic theory in mathematical statistics. (wikipedia.org)
• Econometrics Asymptotic theory (statistics) Contiguity Probability space Wolfowitz J.(1974) Review of the book: "Contiguity of Probability Measures: Some Applications in Statistics. (wikipedia.org)
• ##### causation
• Spohn's research extends to philosophy of science, the theory of causation, metaphysics and ontology, philosophy of language and mind, two-dimensional semantics, philosophical logic, and decision and game theory (see the collection of papers). (wikipedia.org)
• Probability theory and causation. (pitt.edu)
• Why is the transference theory of causation insuffcient? (pitt.edu)
• ##### approaches
• Overall this is a well-written text that provides an interesting alternative to more classical approaches. (springer.com)
• ##### hypothesis
• The solution gives answers to multiple choice questions on probability and hypothesis testing. (brainmass.com)
• ##### causal
• PDF version : http://www.uni-konstanz.de/FuF/Philo/Philosophie/files/grundlagen_der_entscheidungstheorie.pdf „Stochastic Independence, Causal Independence, and Shieldability", Journal of Philosophical Logic 9 (1980) 73-99 „How to Make Sense of Game Theory", in: W. Stegmüller, W. Balzer, W. Spohn (Hg. (wikipedia.org)
• ##### whereas
• Closely related to the field of game theory , decision theory is concerned with the choices of individual agents whereas game theory is concerned with interactions of agents whose decisions affect each other. (like2do.com)
• ##### uncertain
• Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. (wikipedia.org)
• ##### successes
• If we repeat an experiment that we know can result in a success or failure, n times independently, and get s successes, then what is the probability that the next repetition will succeed? (wikipedia.org)
• ##### possible
• Probability is a way of assigning every "event" a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) be assigned a value of one. (wikipedia.org)
• According to Youssef, the valid possible alternatives for probability values are the real numbers, the complex numbers and the quaternions. (wikipedia.org)
• ##### exercises
• epub Exercises in Probability: A Guided Tour ': ' This description made totally have. (roadhaus.com)
• The epub Exercises in Probability: can look denied for the PLD Journal, approach cognitive system, ERO links and not also more! (roadhaus.com)