Title Markov processes and learning models / M. Frank Norman

Published New York : Academic Press, 1972

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Description 1 online resource (xiii, 274 pages) Series Mathematics in science and engineering ; v. 84 Mathematics in science and engineering ; v. 84. Contents Front Cover; Markov Processes and Learning Models; Copyright Page; Contents; Preface; Chapter 0. Introduction; 0.1 Experiments and Models; 0.2 A General Theoretical Framework; 0.3 Overview; PART I: DISTANCE DIMINISHING MODELS; Chapter 1. Markov Processes and Random Systems with Complete Connections; 1.1 Markov Processes; 1.2 Random Systems with Complete Connections; Chapter 2. Distance Diminishing Models and Doeblin-Fortet Processes; 2.1 Distance Diminishing Models; 2.2 Transition Operators for Metric State Spaces Chapter 3. The Theorem of Ionescu Tulcea and Marinescu, and Compact Markov Processes3.1 A Class of Operators; 3.2 The Theorem of Ionescu Tulcea and Marinescu; 3.3 Compact Markov Processes: Preliminaries; 3.4 Ergodic Decomposition; 3.5 Subergodic Decomposition; 3.6 Regular and Absorbing Processes; 3.7 Finite Markov Chains; Chapter 4. Distance Diminishing Models with Noncompact State Spaces; 4.1 A Condition on p; 4.2 Invariant Subsets; Chapter 5. Functions of Markov Processes; 5.1 Introduction; 5.2 Central Limit Theorem; 5.3 Estimation of pu; 5.4 Estimation of s2; 5.5 A Representation of s2 5.6 Asymptotic Stationarity5.7 Vector Valued Functions and Spectra; Chapter 6. Functions of Events; 6.1 Theprocess Xn' = (En, Xn+1); 6.2 Unbounded Functions of Several Events; PART II: SLOW LEARNING; Chapter 7. Introduction to Slow Learning; 7.1 Two Kinds of Slow Learning; 7.2 Small Probability; 7.3 Small Steps: Heuristics; Chapter 8. Transient Behavior in the Case of Large Drift; 8.1 A General Central Limit Theorem; 8.2 Properties of f(t); 8.3 Proofs of (A) and (B); 8.4 Proof of (C); 8.5 Near a Critical Point; Chapter 9. Transient Behavior in the Case of Small Drift 9.1 Diffusion Approximation in a Bounded Interval9.2 Invariance; 9.3 Semigroups; Chapter 10. Steady-State Behavior; 10.1 A Limit Theorem for Stationary Probabilities; 10.2 Proof of the Theorem; 10.3 A More Precise Approximation to E(Xn?); Chapter 11. Absorption Probabilities; 11.1 Bounded State Spaces; 11.2 Unbounded State Spaces; PART III: SPECIAL MODELS; Chapter 12. The Five-Operator Linear Model; 12.1 Criteria for Regularity and Absorption; 12.2 The Mean Learning Curve; 12.3 Interresponse Dependencies; 12.4 Slow Learning; Chapter 13. The Fixed Sample Size Model 13.1 Criteria for Regularity and Absorption13.2 Mean Learning Curve and Interresponse Dependencies; 13.3 Slow Learning; 13.4 Convergence to the Linear Model; Chapter 14. Additive Models; 14.1 Criteria for Recurrence and Absorption; 14.2 Asymptotic A1 Response Frequency; 14.3 Existence of Stationary Probabilities; 14.4 Uniqueness of the Stationary Probability; 14.5 Slow Learning; Chapter 15. Multiresponse Linear Models; 15.1 Criteria for Regularity; 15.2 The Distribution of Yn and Y8; Chapter 16. The Zeaman-House-Lovejoy Models; 16.1 A Criterion for Absorption; 16.2 Expected Total Errors Summary Markov processes and learning models Bibliography Includes bibliographical references (pages 263-267) and index Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL Print version record digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Subject Learning, Psychology of -- Mathematical models Markov processes. Learning models (Stochastic processes) Markov Chains SCIENCE -- Cognitive Science. PSYCHOLOGY -- Cognitive Psychology. Learning models (Stochastic processes) Learning, Psychology of -- Mathematical models Markov processes Lerntheorie Markov-Prozess Markov-processen. Leerprocessen. Form Electronic book ISBN 9780125214506 0125214502 9780080955933 0080955932 1282289748 9781282289741

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