Title | Discretization and MCMC Convergence Assessment [electronic resource] / edited by Christian P. Robert |
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Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1716-9 |
Descript | XI, 192 p. 20 illus. online resource |
1 Markov Chain Monte Carlo Methods -- 1.1 Motivations -- 1.2 Metropolis-Hastings algorithms -- 1.3 The Gibbs sampler -- 1.4 Perfect sampling -- 1.5 Convergence results from a Duality Principle -- 2 Convergence Control of MCMC Algorithms -- 2.1 Introduction -- 2.2 Convergence assessments for single chains -- 2.3 Convergence assessments based on parallel chains -- 2.4 Coupling techniques -- 3 Linking Discrete and Continuous Chains -- 3.1 Introduction -- 3.2 Rao-Blackwellization -- 3.3 Riemann sum control variates -- 3.4 A mixture example -- 4 Valid Discretization via Renewal Theory -- 4.1 Introduction -- 4.2 Renewal theory and small sets -- 4.3 Discretization of a continuous Markov chain -- 4.4 Convergence assessment through the divergence criterion -- 4.5 Illustration for the benchmark examples -- 4.6 Renewal theory for variance estimation -- 5 Control by the Central Limit Theorem -- 5.1 Introduction -- 5.2 CLT and Renewal Theory -- 5.3 Two control methods with parallel chains -- 5.4 Extension to continuous state chains -- 5.5 Illustration for the benchmark examples -- 5.6 Testing normality on the latent variables -- 6 Convergence Assessment in Latent Variable Models: DNA Applications -- 6.1 Introduction -- 6.2 Hidden Markov model and associated Gibbs sampler -- 6.3 Analysis of thebIL67bacteriophage genome: first convergence diagnostics -- 6.4 Coupling from the past for theM1-M0model -- 6.5 Control by the Central Limit Theorem -- 7 Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression -- 7.1 Introduction -- 7.2 Hierarchical Model -- 7.3 Analysis of the San Francisco Menโs Health Study -- 7.4 Convergence assessment -- 8 Estimation of Exponential Mixtures -- 8.1 Exponential mixtures -- 8.2 Convergence evaluation -- References -- Author Index