The Resource Bayesian smoothing and regression for longitudinal, spatial and event history data, Ludwig Fahrmeir, Thomas Kneib

Bayesian smoothing and regression for longitudinal, spatial and event history data, Ludwig Fahrmeir, Thomas Kneib

Label
Bayesian smoothing and regression for longitudinal, spatial and event history data
Title
Bayesian smoothing and regression for longitudinal, spatial and event history data
Statement of responsibility
Ludwig Fahrmeir, Thomas Kneib
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
YDXCP
http://library.link/vocab/creatorName
Fahrmeir, L
Dewey number
519.5/36
Illustrations
illustrations
Index
index present
LC call number
QA278.2
LC item number
.F34 2011
Literary form
non fiction
Nature of contents
  • bibliography
  • statistics
http://library.link/vocab/relatedWorkOrContributorName
Kneib, Thomas
Series statement
Oxford statistical science series
Series volume
36
http://library.link/vocab/subjectName
  • Regression analysis
  • Bayesian statistical decision theory
  • Smoothing (Statistics)
Label
Bayesian smoothing and regression for longitudinal, spatial and event history data, Ludwig Fahrmeir, Thomas Kneib
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [495]-518) and index
Contents
  • Basic Concepts for Smoothing and Semiparametric Regression
  • Finite mixture of normals prior: the heterogeneity model
  • MCMC inference for finite mixture models
  • Penalized mixture of normals priors
  • 3.2.2.
  • Dirichlet processes
  • Dirichlet process: descriptive definition
  • Stick breaking representation
  • Posterior Dirichlet process
  • Predictive distribution and clustering property
  • Dirichlet process mixtures
  • 2.1.
  • 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
  • Time series smoothing
  • 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
  • 2.1.1.
  • GLMMs with DP random effects priors
  • GLMMs with DPM random effects priors
  • 3.4.
  • Notes and further reading
  • 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
  • Gaussian observation models
  • 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
  • Penalized least-squares smoothing
  • 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
  • Bayesian smoothing
  • 4.2.2.
  • Full Bayes estimation with Gaussian priors for regression parameters
  • Gaussian SPMMs
  • Exponential family SPMMs
  • Categorical SPMMs
  • Credible intervals and bands
  • 4.3.
  • Smoothing and correlation
  • Correlations induced by penalized smoothing approaches
  • Identifiability problems
  • 2.1.2.
  • 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
  • Some modifications and extensions
  • 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
  • Estimation of smoothing parameters and variances
  • 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
  • Machine generated contents note:
  • Other model components
  • Proper scoring rules
  • Custom summary statistics
  • 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
  • Correlated errors
  • 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.
  • Locally adaptive smoothing
  • 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.
  • Unequally spaced time-series observations
  • 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
  • 5.2.
  • Discrete spatial data: Markov random fields
  • 5.2.1.
  • 2.1.3.
  • 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
  • Non-Gaussian observation models
  • 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
  • 2.2.
  • 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.
  • Semiparametric regression based on penalized splines
  • Continuous spatial data: Stationary Gaussian random fields
  • 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
  • 2.2.1.
  • 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
  • Gaussian observation models
  • 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
  • 1.
  • Polynomial splines
  • 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
  • Piecewise exponential model
  • Truncated power series and B-splines
  • 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.
  • Nonparametric regression based on polynomial splines
  • 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.
  • Characteristics of a spline fit
  • 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 --
  • P-splines
  • Customized penalties
  • Bayesian P-splines
  • Bayesian inference
  • Degrees of freedom of a P-spline
  • 2.2.2.
  • Introduction: Scope of the Book and Applications
  • 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
  • 1.1.
  • 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
  • Semiparametric regression
  • 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.
  • 1.2.
  • Generalized Linear Mixed Models
  • 3.1.
  • Linear mixed models with Gaussian random effects
  • 3.1.1.
  • Linear mixed models for longitudinal data
  • Advantages of mixed models
  • Marginal and conditional formulation
  • Multilevel models
  • 3.1.2.
  • General linear mixed models
  • Applications
  • 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
  • 2.
  • 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
  • Contents note continued:
  • 6.6.1.
  • Models for correlated survival data
  • 6.6.2.
  • Joint modelling of longitudinal and event history data
Dimensions
25 cm.
Extent
xviii, 521 p.
Isbn
9780199533022
Other physical details
ill.
System control number
  • (CaMWU)u2219870-01umb_inst
  • 2402344
  • (Sirsi) i9780199533022
  • (OCoLC)676872585
Label
Bayesian smoothing and regression for longitudinal, spatial and event history data, Ludwig Fahrmeir, Thomas Kneib
Publication
Bibliography note
Includes bibliographical references (p. [495]-518) and index
Contents
  • Basic Concepts for Smoothing and Semiparametric Regression
  • Finite mixture of normals prior: the heterogeneity model
  • MCMC inference for finite mixture models
  • Penalized mixture of normals priors
  • 3.2.2.
  • Dirichlet processes
  • Dirichlet process: descriptive definition
  • Stick breaking representation
  • Posterior Dirichlet process
  • Predictive distribution and clustering property
  • Dirichlet process mixtures
  • 2.1.
  • 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
  • Time series smoothing
  • 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
  • 2.1.1.
  • GLMMs with DP random effects priors
  • GLMMs with DPM random effects priors
  • 3.4.
  • Notes and further reading
  • 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
  • Gaussian observation models
  • 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
  • Penalized least-squares smoothing
  • 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
  • Bayesian smoothing
  • 4.2.2.
  • Full Bayes estimation with Gaussian priors for regression parameters
  • Gaussian SPMMs
  • Exponential family SPMMs
  • Categorical SPMMs
  • Credible intervals and bands
  • 4.3.
  • Smoothing and correlation
  • Correlations induced by penalized smoothing approaches
  • Identifiability problems
  • 2.1.2.
  • 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
  • Some modifications and extensions
  • 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
  • Estimation of smoothing parameters and variances
  • 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
  • Machine generated contents note:
  • Other model components
  • Proper scoring rules
  • Custom summary statistics
  • 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
  • Correlated errors
  • 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.
  • Locally adaptive smoothing
  • 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.
  • Unequally spaced time-series observations
  • 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
  • 5.2.
  • Discrete spatial data: Markov random fields
  • 5.2.1.
  • 2.1.3.
  • 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
  • Non-Gaussian observation models
  • 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
  • 2.2.
  • 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.
  • Semiparametric regression based on penalized splines
  • Continuous spatial data: Stationary Gaussian random fields
  • 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
  • 2.2.1.
  • 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
  • Gaussian observation models
  • 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
  • 1.
  • Polynomial splines
  • 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
  • Piecewise exponential model
  • Truncated power series and B-splines
  • 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.
  • Nonparametric regression based on polynomial splines
  • 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.
  • Characteristics of a spline fit
  • 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 --
  • P-splines
  • Customized penalties
  • Bayesian P-splines
  • Bayesian inference
  • Degrees of freedom of a P-spline
  • 2.2.2.
  • Introduction: Scope of the Book and Applications
  • 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
  • 1.1.
  • 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
  • Semiparametric regression
  • 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.
  • 1.2.
  • Generalized Linear Mixed Models
  • 3.1.
  • Linear mixed models with Gaussian random effects
  • 3.1.1.
  • Linear mixed models for longitudinal data
  • Advantages of mixed models
  • Marginal and conditional formulation
  • Multilevel models
  • 3.1.2.
  • General linear mixed models
  • Applications
  • 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
  • 2.
  • 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
  • Contents note continued:
  • 6.6.1.
  • Models for correlated survival data
  • 6.6.2.
  • Joint modelling of longitudinal and event history data
Dimensions
25 cm.
Extent
xviii, 521 p.
Isbn
9780199533022
Other physical details
ill.
System control number
  • (CaMWU)u2219870-01umb_inst
  • 2402344
  • (Sirsi) i9780199533022
  • (OCoLC)676872585

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  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
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