• 1994
• 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)
• ontology
• 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)
• expresses
• The prior probability density function that expresses total ignorance of p except for the certain knowledge that it is neither 1 nor 0 (i.e., that we know that the experiment can in fact succeed or fail) is equal to 1 for 0 (wikipedia.org)
• It expresses the total probability of an outcome which can be realized via several distinct events-hence the name. (wikipedia.org)
• calculate
• 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)
• finite
• but, alternatives exist, such as the adoption of finite rather than countable additivity by Bruno de Finetti. (wikipedia.org)
• You do a few experiments and see how the finite distribution of results compares to the probabilities, and then assign a confidence level to the conclusion that a particular theory of the data is correct. (discovermagazine.com)
• likelihood
• It has also been referred to as modeling fields, modeling fields theory (MFT), Maximum likelihood artificial neural networks (MLANS). (wikipedia.org)
• mathematics
• Probability theory is the branch of mathematics concerned with probability. (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)
• 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)
• stochastic
• 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)
• Because queuing theory is highly complex, only the (stochastic) arrival process will be discussed in detail. (egms.de)
• 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)
• distribution
• 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)
• One may define a uniform probability distribution on the linear extensions in which each possible linear extension is equally likely to be chosen. (wikipedia.org)
• The 1/3-2/3 conjecture states that, under this probability distribution, there exists a pair of elements x and y such that the probability that x is earlier than y in a random linear extension is between 1/3 and 2/3. (wikipedia.org)
• Physical theories are often couched in the form of equations for the time evolution of the probability distribution, even in classical physics. (discovermagazine.com)
• In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. (wikipedia.org)
• In probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. (wikipedia.org)
• Bernoulli
• 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)
• If the probablity a particular even side comes up is 1/9 and the probability a particular odd side comes up is 2/9, can you consider this a Bernoulli trial in determining the probability of rolling five 4's in 10 rolls? (brainmass.com)
• 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)
• Algebra
• Some of the terminology in von Neumann algebra theory can be confusing, and the terms often have different meanings outside the subject. (wikipedia.org)
• The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: Perpendicularity of lines in geometry Orthogonality in linear algebra Independence of random variables in probability theory Comparability in order theory Coprimality in number theory Tee (symbol) (⊤) Table of mathematical symbols Alternative plus sign List of mathematical symbols "Mathematical Operators - Unicode" (PDF). (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)
• measure
• Glenn Shafer is also well known for his co-development of Dempster-Shafer theory, which is a brewing alternative to standard measure-theoretic probability theory which is quite useful in sensor fusion, and I think some machine learning frameworks. (wordpress.com)
• The more mathematically advanced measure theory-based treatment of probability covers the discrete, continuous, a mix of the two, and more. (wikipedia.org)
• Learning is an essential part of perception and cognition, and in NMF theory it is driven by the dynamics that increase a similarity measure between the sets of models and signals, L({X},{M}). The similarity measure is a function of model parameters and associations between the input bottom-up signals and top-down, concept-model signals. (wikipedia.org)
• Proportion
• The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. (brainmass.com)