Author | Tanner, Martin A. author |
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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 US, 1993 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0192-9 |
Descript | online resource |
1 Introduction -- 2 Normal Approximations to Likelihoods and to Posteriors -- 2.1 Likelihood/Posterior Density -- 2.2 Maximum Likelihood -- 2.3 Normal-Based Inference -- 2.4 The ?-Method (Propagation of Errors) -- 2.5 Highest Posterior Density Regions -- 3 Nonnormal Approximations to Likelihoods and to Posteriors -- 3.1 Conjugate Priors and Numerical Integration -- 3.2 Posterior Moments and Marginalization Based on Laplaceโs Method -- 3.3 Monte Carlo Methods -- 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 -- 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 -- 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 -- References