| Description |
xviii, 521 pages : illustrations, maps ; 24 cm |
| Series |
Oxford statistical science series ; no. 36 |
|
Oxford statistical science series ; no. 36
|
| Contents |
Contents note continued: 2.2.2.Univariate non-Gaussian observation models -- Penalized likelihood estimation -- Bayesian inference -- Latent variable representations -- 2.2.3.Categorical observation models -- Nominal response models -- Cumulative models for ordinal responses -- Sequential models for ordinal responses -- Penalised likelihood inference -- Bayesian inference -- 2.2.4.Related smoothing approaches -- Integral penalties -- Smoothing splines -- Bayesian interpretation of smoothing splines -- Reproducing kernel Hilbert spaces -- Other types of basis functions -- 2.3.Generalized additive models -- 2.3.1.Gaussian additive models -- Simultaneous penalized least-squares (PLS) smoothing -- Backfitting -- Bayesian backfitting: the Gibbs sampler -- 2.3.2.Non-Gaussian additive models -- 2.4.Notes and further reading -- 3.Generalized Linear Mixed Models -- 3.1.Linear mixed models with Gaussian random effects -- 3.1.1.Linear mixed models for longitudinal data -- |
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Contents note continued: 4.3.Smoothing and correlation -- Correlations induced by penalized smoothing approaches -- Identifiability problems -- Radial basis functions and correlated errors -- Summary -- 4.4.Extensions based on non-Gaussian priors -- 4.4.1.SPMMs with DP-based random effects priors -- 4.4.2.Shrinkage priors for high-dimensional regression parameters -- Ridge prior -- Lasso prior -- Lq priors -- Further examples -- 4.4.3.Locally adaptive priors for functions -- Locally adaptive penalties -- Knot selection strategies -- 4.5.Model choice and model checking -- 4.5.1.Bayes factors and model selection criteria -- Bayes factors and marginal likelihoods -- Methods for estimating Bayes factors and marginal likelihoods -- Information criteria: AIC, BIC and DIC -- BIC -- AIC -- DIC -- 4.5.2.Predictive methods for model assessment -- Alternative predictive distributions -- Assessing calibration: PIT and BOT -- Proper scoring rules -- Custom summary statistics -- |
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Contents note continued: 4.Semiparametric Mixed Models for Longitudinal Data -- 4.1.Semiparametric mixed models based on Gaussian priors -- 4.1.1.Observation models for univariate responses from exponential families -- Generalized additive mixed models -- Varying coefficient mixed models -- ANOVA type interactions -- Generic representation -- 4.1.2.Observation models for categorical responses -- 4.1.3.Gaussian priors for regression parameters and functions -- 4.2.Estimation -- 4.2.1.Empirical Bayes inference -- Intuitive example -- Mixed model representation for P-splines -- Mixed model representation for general penalized smoothers -- Mixed model-based estimation of SPMMs -- Identifiability -- Constrained smoothness priors -- Credible intervals and bands -- Tests on the functional form -- 4.2.2.Full Bayes estimation with Gaussian priors for regression parameters -- Gaussian SPMMs -- Exponential family SPMMs -- Categorical SPMMs -- Credible intervals and bands -- |
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Contents note continued: 5.2.Discrete spatial data: Markov random fields -- 5.2.1.A heuristic spatial smoothness prior -- 5.2.2.Markov random fields -- Definition of Markov random fields -- Brook's lemma -- Negpotential function and Hammersley-Clifford theorem -- Auto-models -- 5.2.3.Gaussian Markov random fields/auto-normal models -- Basis function representation of GMRFs -- Direct vs. latent autoregressive models -- 5.2.4.Extended Markov random field models -- 5.3.Spatial smoothing approaches and interactions -- 5.3.1.Tensor product penalized splines -- Tensor product bases -- Kronecker product penalties for tensor product bases -- Generalized penalty concepts -- Null spaces of bivariate penalties -- Higher-order Markov random fields on regular grids -- Higher-order interactions -- 5.3.2.Radial bases -- Space filling algorithm -- Penalties for radial bases -- 5.3.3.Tensor products vs. radial bases -- 5.4.Continuous spatial data: Stationary Gaussian random fields -- |
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Contents note continued: Advantages of mixed models -- Marginal and conditional formulation -- Multilevel models -- 3.1.2.General linear mixed models -- 3.1.3.Bayesian linear mixed models -- 3.1.4.Likelihood-based inference -- Estimation and prediction -- Estimation of regression coefficients for given variance components -- Maximum likelihood (ML) estimation of variance components -- REML estimation for the variance parameters -- Details on REML estimation for variance parameters -- Bayesian interpretation of ML and REML estimation -- Testing hypotheses -- 3.1.5.Bayesian inference -- Empirical Bayes inference -- Full Bayes inference -- Full Bayes inference for longitudinal data -- 3.2.Linear mixed models with flexible random effects priors -- 3.2.1.Finite mixture models -- Finite mixture of normals prior: the heterogeneity model -- MCMC inference for finite mixture models -- Penalized mixture of normals priors -- 3.2.2.Dirichlet processes -- |
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Contents note continued: Dirichlet process: descriptive definition -- Stick breaking representation -- Posterior Dirichlet process -- Predictive distribution and clustering property -- Dirichlet process mixtures -- 3.2.3.LMM with DP-based random effects priors -- Longitudinal data LMMs with DP random effects priors -- Longitudinal data LMMs with DPM priors -- 3.3.Generalized linear mixed models -- 3.3.1.Generalized linear mixed models for longitudinal data -- GLMMs for univariate responses -- Marginal and conditional models -- Interpretation of regression parameters -- GLMMs for categorical responses -- 3.3.2.General mixed models for non-Gaussian responses -- 3.3.3.Likelihood-based and empirical Bayes inference -- 3.3.4.Full Bayesian inference for longitudinal data -- 3.3.5.Longitudinal data GLMMs with flexible random effects priors -- GLMMs with DP random effects priors -- GLMMs with DPM random effects priors -- 3.4.Notes and further reading -- |
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Contents note continued: Model formulation -- Correlation functions -- Parametric classes of correlations functions -- Bochner's theorem -- Range anisotropic correlation functions -- Variogram -- Estimation of covariance and correlation parameters -- Nonparametric covariogram and variogram estimation -- Gaussian random fields as radial basis function smoothers -- Identifiability in geostatistical models -- Classical geostatistics -- 5.5.Geoadditive regression -- Full Bayes inference -- Empirical Bayes inference -- 5.6.Notes and further reading -- 6.Event History Data -- 6.1.Survival data -- 6.1.1.Basic notions for continuous survival times -- 6.1.2.Censoring and truncation -- 6.1.3.Likelihood contributions for different types of censoring -- 6.1.4.Discrete-time survival data -- 6.2.Continuous-time hazard regression -- 6.2.1.Observation models, priors and likelihoods -- Observation models -- Priors -- Likelihoods -- 6.2.2.Full Bayes inference for right-censored observations -- |
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Contents note continued: Monte Carlo estimation of predictive measures -- Posterior predictive goodness-of-fit assessment -- Exact cross validatory predictive assessment -- Approximate cross validatory predictive assessment -- 4.5.3.Predictor selection using spike and slab priors -- Variable selection -- Function selection -- Covariance matrix selection for random effects -- 4.6.Notes and further reading -- 4.6.1.Individual-specific curves and functional mixed models -- 4.6.2.Approximate Bayesian inference -- Variational Bayes approaches -- Integrated nested laplace approximation (INLA) -- 4.6.3.Further comments -- 5.Spatial Smoothing, Interactions and Geoadditive Regression -- 5.1.Spatial data structures -- 5.1.1.Point-referenced data: Continuous spatial information -- 5.1.2.Interaction surfaces -- 5.1.3.Areal data: Discrete spatial information -- 5.1.4.Continuous vs. discrete spatial information -- 5.1.5.Spatial regression models -- 5.1.6.Other types of spatial data -- |
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Contents note continued: Piecewise exponential model -- Models with general structured additive predictor -- 6.2.3.Empirical Bayes (EB) inference for right-censored observations -- 6.2.4.Inference for interval-censored observations -- 6.3.Discrete-time hazard regression -- 6.4.Accelerated failure time models -- 6.4.1.Observation models, likelihoods and priors -- Penalized Gaussian mixture (PGM) -- AFT models with DP(M) priors -- 6.5.Multi-state models -- 6.5.1.Continuous-time transition rate models -- 6.5.2.Counting process representation and likelihood contributions -- 6.5.3.Empirical and full Bayes inference -- 6.5.4.Model checking based on martingale residuals -- 6.5.5.Discrete-time multi-state models -- 6.6.Notes and further reading -- 6.6.1.Models for correlated survival data -- 6.6.2.Joint modelling of longitudinal and event history data |
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Machine generated contents note: 1.Introduction: Scope of the Book and Applications -- 1.1.Semiparametric regression -- 1.2.Applications -- 2.Basic Concepts for Smoothing and Semiparametric Regression -- 2.1.Time series smoothing -- 2.1.1.Gaussian observation models -- Penalized least-squares smoothing -- Bayesian smoothing -- 2.1.2.Some modifications and extensions -- Estimation of smoothing parameters and variances -- Other model components -- Correlated errors -- Locally adaptive smoothing -- Unequally spaced time-series observations -- 2.1.3.Non-Gaussian observation models -- 2.2.Semiparametric regression based on penalized splines -- 2.2.1.Gaussian observation models -- Polynomial splines -- Truncated power series and B-splines -- Nonparametric regression based on polynomial splines -- Characteristics of a spline fit -- P-splines -- Customized penalties -- Bayesian P-splines -- Bayesian inference -- Degrees of freedom of a P-spline -- |
| Notes |
Formerly CIP. Uk |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Bayesian statistical decision theory.
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Regression analysis.
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Smoothing (Statistics)
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| Author |
Kneib, Thomas.
|
| LC no. |
2010942421 |
| ISBN |
0199533024 (hbk.) |
|
9780199533022 (hbk.) |
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