Author | Pfeiffer, Paul E. author |
---|---|
Title | Conditional Independence in Applied Probability [electronic resource] / by Paul E. Pfeiffer |
Imprint | Boston, MA : Birkhรคuser Boston, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6335-7 |
Descript | IX, 158 p. online resource |
A. Preliminaries -- 1. Probability Spaces and Random Vectors -- 2. Mathematical Expectation -- 3. Problems -- B. Conditional Independence of Events -- 1. The Concept -- 2. Some Patterns of Probable Inference -- 3. A Classification Problem -- 4. Problems -- C. Conditional Expectation -- 1. Conditioning by an Event -- 2. Conditioning by a Random Vector-Special Cases -- 3. Conditioning by a Random Vector-General Case -- 4. Properties of Conditional Expectation -- 5. Conditional Distributions -- 6. Conditional Distributions and Bayesโ Theorem -- 7. Proofs of Properties of Conditional Expectation -- 8. Problems -- D. Conditional Independence, Given a Random Vector -- 1. The Concept and Some Basic Properties -- 2. Some Elements of Bayesian Analysis -- 3. A One-Stage Bayesian Decision Model -- 4. A Dynamic-Programming Example -- 5. Proofs of the Basic Properties -- 6. Problems -- E. Markov Processes and Conditional Independence -- 1. Discrete-Parameter Markov Processes -- 2. Markov Chains with Costs and Rewards -- 3. Continuous-Parameter Markov Processes -- 4. The Chapman-Kolmogorov Equation -- 5. Proof of a Basic Theorem on Markov Processes -- 6. Problems -- Appendices -- Appendix I. Properties of Mathematical Expectation -- Appendix II. Properties of Conditional Expectation, Given a Random Vector -- Appendix III. Properties of Conditional Independence, Given a Random Vector -- References -- Selected Answers, Hints, and Key Steps