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Howard Raiffa
Howard Raiffa (; January 24, 1924 – July 8, 2016) was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis. Early life After service in the Army Air Forces during World War II, Raiffa received a bachelor's degree in mathematics in 1946, a master's degree in statistics in 1947 and a PhD in mathematics in 1951, all from the University of Michigan. Career *His book ''Applied Statistical Decision Theory'' with Robert Schlaifer introduced the idea of conjugate prior distributions. *A lecture of his in the 1960s concerning the use o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Americans
Americans are the Citizenship of the United States, citizens and United States nationality law, nationals of the United States, United States of America.; ; Although direct citizens and nationals make up the majority of Americans, many Multiple citizenship, dual citizens, expatriates, and green card, permanent residents could also legally claim American nationality. The United States is home to race and ethnicity in the United States, people of many racial and ethnic origins; consequently, culture of the United States, American culture and Law of the United States, law do not equate nationality with Race (human categorization), race or Ethnic group, ethnicity, but with citizenship and an Oath of Allegiance (United States), oath of permanent allegiance. Overview The majority of Americans or their ancestors Immigration to the United States, immigrated to the United States or are descended from people who were Trans Atlantic Slave Trade, brought as Slavery in the United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Schlaifer
Robert Osher Schlaifer (13 September 1914 – 24 July 1994) was a pioneer of Bayesian decision theory. At the time of his death he was William Ziegler Professor of Business Administration Emeritus of the Harvard Business School. In 1961 he was elected as a Fellow of the American Statistical Association. Biography The son of Osher Schlaifer (who was later the superintendent of schools in Dundee, Illinois), a native of Vermillion, S.D., and a graduate of Amherst College, Schlaifer had a unique background for a statistical decision theorist. He was trained as a classical historian and classical Greek scholar: he attended the American School of Classical Studies in Athens and earned a Ph.D. in ancient history at Harvard in 1940. He taught history, economics and physics at the Faculty of Arts and Sciences at Harvard. During the Second World War he started writing technical reports and produced a major volume on the development of aircraft engines. He got an appointment at the Harva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom Of Transitivity
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. On the other hand, "is the birth parent of" is not a transitive relation, because if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then this does not imply that Alice is the birth parent of Claire. What is more, it is antitransitive: Alice can ''never'' be the birth parent of Claire. "Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions. Utility function Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive. Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. On the other hand, "is the birth parent of" is not a transitive relation, because if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then this does not imply that Alice is the birth parent of Claire. What is more, it is antitransitive: Alice can ''never'' be the birth parent of Claire. "Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitutability
The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1988 conference keynote address titled ''Data abstraction and hierarchy''. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. It is a semantic rather than merely syntactic relation, because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. Barbara Liskov and Jeannette Wing described the principle succinctly in a 1994 paper as follows: ''Subtype Requirement'': Let be a property provable about objects of type . Then should be true for objects of type where is a subtype of . Symbolically: :S <: T \to (\forall xT) \phi(x) \to (\forall yS) \phi(y) That ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axioms
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning. As used in mathematics, the term ''axiom'' is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms (e.g., ) are actually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov Axioms
The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. Axioms The assumptions as to setting up the axioms can be summarised as follows: Let (\Omega, F, P) be a measure space with P(E) being the probability of some event E'','' and P(\Omega) = 1. Then (\Omega, F, P) is a probability space, with sample space \Omega, event space F and probability measure P. First axiom The probability of an event is a non-negative real number: :P(E)\in\mathbb, P(E)\geq 0 \qquad \forall E \in F where F is the event space. It follows that P(E) is always finite, in contrast with more general measure theory. Theories which assign negative probability relax the first axiom. Second axiom This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjective Probability
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedures and formula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USS Scorpion (SS-278)
USS ''Scorpion'' (SS-278) – a ''Gato''-class submarine – was the fifth ship of the United States Navy to be named for the scorpion. Construction and commissioning ''Scorpion''′s keel was laid down at the Portsmouth Navy Yard at Kittery, Maine, on 20 March 1942. She was launched on 20 July 1942, sponsored by Ms. Elizabeth T. Monagle, and commissioned on 1 October 1942. Service history Following further yard work and fitting out, ''Scorpion'' conducted shakedown operations off the southern New England coast in January 1943 and sailed for Panama in late February. In mid-March she transited the Panama Canal and headed toward Pearl Harbor, Hawaii. On an unrecorded date while she was on the surface at about the midpoint of her voyage from the Panama Canal Zone to Pearl Harbor, she encountered an Allied merchant ship which mistook her for a Japanese submarine and opened gunfire on her despite her efforts to identify herself.Hinman & Campbell, p. 232. The merchant ship's she ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1966 Palomares B-52 Crash
The 1966 Palomares B-52 crash, also called the Palomares incident, occurred on 17 January 1966, when a B-52G bomber of the United States Air Force's Strategic Air Command collided with a KC-135 tanker during mid-air refueling at over the Mediterranean Sea, off the coast of Spain. The KC-135 was destroyed when its fuel load ignited, killing all four crew members. The B-52G broke apart, killing three of the seven crew members aboard. At the time of the accident, the B-52G was carrying four B28FI Mod 2 Y1 thermonuclear (hydrogen) bombs, all of which fell to the surface. Three were found on land near the small fishing village of Palomares in the municipality of Cuevas del Almanzora, Almería, Spain. The non-nuclear explosives in two of the weapons detonated upon impact with the ground, resulting in the contamination of a area with radioactive plutonium. The fourth, which fell into the Mediterranean Sea, was recovered intact after a search lasting two and a half months. Acci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palomares, Almería
Palomares is an agricultural, fishing, and tourist town along the Mediterranean Sea in the Almería province of Andalusia, Spain. It is about above sea level. The village falls within the municipality of Cuevas del Almanzora. The ruins of ''El Artial'' lie just outside the village. Crashes of a B-52 and a KC-135 in 1966 The town is noted for a fatal accident in 1966 in which a B-52 Stratofortress of the Strategic Air Command crashed after a midair collision with a KC-135 Stratotanker plane, causing radioactive contamination after its payload of four hydrogen bombs (H-bombs) was dispersed and crashed. There were four thermonuclear weapons in the bomber. The high-explosive igniters in two of these bombs detonated on impact, spreading radioactive material, including deadly plutonium-239, over a wide area of the Spanish countryside, but safety mechanisms and electronics prevented nuclear explosions. The third H-bomb landed via parachute into a stream, where it was relatively intact a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
