Publisher:

Chapman & Hall/CRC

Number of Pages:

475

Price:

89.95

ISBN:

9781439861615

Date Received:

Monday, June 13, 2011

Reviewable:

No

Reviewer Email Address:

Series:

Texts in Statistical Science

Publication Date:

2011

Format:

Hardcover

Audience:

Category:

Monograph

**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

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

Finite additivity

Countable Additivity

Properties of countable additivity

Dynamic sure loss

The negative binomial random variable

The Poisson random variable

Cumulative distribution function

Dominated and bounded convergence

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 Riemann-Stieltjes integral

The McShane-Stieltjes Integral

The road from here

The strong law of large numbers

Discrete Random Variables

Univariate Continuous Distributions

Linear spaces

Permutations

Number systems; DeMoivre's formula

Determinants

Eigenvalues, eigenvectors and decompositions

Non-linear transformations

The Borel-Kolmogorov paradox

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

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

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

Missing data

Meta-analysis

Model uncertainty/model choice

Graphical Hierarchical Models

Causation

Simulation

The Metropolis Hasting Algorithm

Extensions and special cases

Practical considerations

Variable dimensions: Reversible jumps

Private information

Design for another's analysis

Optimal Bayesian Randomization

Simultaneous moves

The Allais and Ellsberg paradoxes

Forming a Bayesian group

Testing

Confidence intervals and sets

Estimation

Choosing among models

Goodness of fit

Sampling theory statistics

Objective" Bayesian Methods

A final thought

Publish Book:

Modify Date:

Friday, March 30, 2012

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