Author | Tanner, Martin A. author |
---|---|
Title | Tools for Statistical Inference [electronic resource] : Methods for the Exploration of Posterior Distributions and Likelihood Functions / by Martin A. Tanner |
Imprint | New York, NY : Springer New York, 1996 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4024-2 |
Descript | VIII, 208 p. online resource |
1. Introduction -- Exercises -- 2. Normal Approximations to Likelihoods and to Posteriors -- 2.1. Likelihood/Posterior Density -- 2.2. Specification of the Prior -- 2.3. Maximum Likelihood -- 2.4. Normal-Based Inference -- 2.5. The ?-Method (Propagation of Errors) -- 2.6. Highest Posterior Density Regions -- Exercises -- 3. Nonnormal Approximations to Likelihoods and Posteriors -- 3.1. Numerical Integration -- 3.2. Posterior Moments and Marginalization Based on Laplaceโs Method -- 3.3. Monte Carlo Methods -- Exercises -- 4. The EM Algorithm -- 4.1. Introduction -- 4.2. Theory -- 4.3. EM in the Exponential Family -- 4.4. Standard Errors in the Context of EM -- 4.5. Monte Carlo Implementation of the E-Step -- 4.6. Acceleration of EM (Louisโ Turbo EM) -- 4.7. Facilitating the M-Step -- Exercises -- 5. The Data Augmentation Algorithm -- 5.1. Introduction and Motivation -- 5.2. Computing and Sampling from the Predictive Distribution -- 5.3. Calculating the Content and Boundary of the HPD Region -- 5.4. Remarks on the General Implementation of the Data Augmentation Algorithm -- 5.5. Overview of the Convergence Theory of Data Augmentation -- 5.6. Poor Manโs Data Augmentation Algorithms -- 5.7. Sampling/Importance Resampling (SIR) -- 5.8. General Imputation Methods -- 5.9. Further Importance Sampling Ideas -- 5.10. Sampling in the Context of Multinomial Data -- Exercises -- 6. Markov Chain Monte Carlo: The Gibbs Sampler and the Metropolis Algorithm -- 6.1. Introduction to the Gibbs Sampler -- 6.2. Examples -- 6.3. Assessing Convergence of the Chain -- 6.4. The Griddy Gibbs Sampler -- 6.5. The Metropolis Algorithm -- 6.6. Conditional Inference via the Gibbs Sampler -- Exercises -- References