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"In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy.The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes and high levels of precision in the measurement of their effects. The practical sciences--medicine, business, engineering, and artificial intelligence--must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both of these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making in the practical sciences.Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government, and science. The Art of Causal Conjecture shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated, and confronted by statistical evidence."

Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical logic --- Artificial intelligence. --- Causation. --- Prediction (Logic) --- Probabilities. --- 681.3*I24 --- 681.3*F41 --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Conjecture --- Judgment (Logic) --- Causality --- Cause and effect --- Effect and cause --- Final cause --- Beginning --- God --- Metaphysics --- Philosophy --- Necessity (Philosophy) --- Teleology --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*I24 Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- Prediction (Logic). --- Artificial intelligence --- Causation --- Probabilities --- COMPUTER SCIENCE/General

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Artificial intelligence --- Reasoning --- Uncertainty (Information theory) --- 681.3*I20 --- Measure of uncertainty (Information theory) --- Shannon's measure of uncertainty --- System uncertainty --- Information measurement --- Probabilities --- Questions and answers --- Argumentation --- Ratiocination --- Reason --- Thought and thinking --- Judgment (Logic) --- Logic --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Artificial intelligence (AI) in general; cognitive simulation; philosophical foundations --- 681.3*I20 Artificial intelligence (AI) in general; cognitive simulation; philosophical foundations --- Artificial intelligence.

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Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler's holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.

Mathematics --- History --- geschiedenis --- wiskunde

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