Principles of uncertainty
 Author/Creator
 Kadane, Joseph B.
 Language
 English.
 Imprint
 Boca Raton : CRC Press, c2011.
 Physical description
 xxvii, 475 p. : ill. ; 27 cm.
 Series
 Texts in statistical science.
Access
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 449464) and indexes.
 Contents

 Probability Avoiding being a sure loser Disjoint events Events not necessarily disjoint Random variables, also known as uncertain quantities Finite number of values Other properties of expectation Coherence implies not a sure loser Expectations and limits Conditional Probability and Bayes Theorem Conditional probability The Birthday Problem Simpson's Paradox Bayes Theorem Independence of events The Monty Hall problem Gambler's Ruin problem Iterated Expectations and Independence The binomial and multinomial distributions Sampling without replacement Variance and covariance A short introduction to multivariate thinking Tchebychev's inequality Discrete Random Variables Countably many possible values Finite additivity Countable Additivity Properties of countable additivity Dynamic sure loss Probability generating functions Geometric random variables The negative binomial random variable The Poisson random variable Cumulative distribution function Dominated and bounded convergence Continuous Random Variables Introduction Joint distributions Conditional distributions and independence Existence and properties of expectations Extensions An interesting relationship between cdf's and expectations of continuous random variables Chapter retrospective so far Bounded and dominated convergence The RiemannStieltjes integral The McShaneStieltjes Integral The road from here The strong law of large numbers Transformations Introduction Discrete Random Variables Univariate Continuous Distributions Linear spaces Permutations Number systems DeMoivre's formula Determinants Eigenvalues, eigenvectors and decompositions Nonlinear transformations The BorelKolmogorov paradox Normal Distribution Introduction Moment generating functions Characteristic functions Trigonometric Polynomials A Weierstrass approximation theorem Uniqueness of characteristic functions Characteristic function and moments Continuity Theorem The Normal distribution Multivariate normal distributions Limit theorems Making Decisions Introduction An example In greater generality The St. Petersburg Paradox Risk aversion Log (fortune) as utility Decisions after seeing data The expected value of sample information An example Randomized decisions Sequential decisions Conjugate Analysis A simple normalnormal case A multivariate normal case, known precision The normal linear model with known precision The gamma distribution Uncertain Mean and Precision The normal linear model, uncertain precision The Wishart distribution Both mean and precision matrix uncertain The beta and Dirichlet distributions The exponential family Large sample theory for Bayesians Some general perspective Hierarchical Structuring of a Model Introduction Missing data Metaanalysis Model uncertainty/model choice Graphical Hierarchical Models Causation Markov Chain Monte Carlo Introduction Simulation The Metropolis Hasting Algorithm Extensions and special cases Practical considerations Variable dimensions: Reversible jumps Multiparty Problems A simple threestage game Private information Design for another's analysis Optimal Bayesian Randomization Simultaneous moves The Allais and Ellsberg paradoxes Forming a Bayesian group Exploration of Old Ideas Introduction Testing Confidence intervals and sets Estimation Choosing among models Goodness of fit Sampling theory statistics Objective" Bayesian Methods Epilogue: Applications Computation A final thought.
 (source: Nielsen Book Data)
 Publisher's Summary
 An intuitive and mathematical introduction to subjective probability and Bayesian statistics. An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains: Introductory chapters examining each new concept or assumption Justintime mathematics  the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniques Problems involving more than one decisionmaker Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Joseph B. Kadane.
 Series
 Chapman & Hall/CRC texts in statistical science series
 ISBN
 9781439861615
 1439861617