Contents

• Preface
• Notation
• Chapter 1: Introduction
  • Examples of types of data
  • Motivating examples
  • A first view on the models
• Chapter 2: The likelihood principle
  • Introduction
  • Point estimation theory
  • The likelihood function
  • The Score Function
  • The information matrix
  • Alternative parameterizations of the likelihood
  • The Maximum Likelihood Estimate (MLE)
  • Distribution of the ML estimator
  • Generalized loss-function and deviance
  • Quadratic approximation of the log-likelihood
  • Likelihood ratio tests
  • Successive testing in hypothesis chains
  • Dealing with nuisance parameters
  • Problems
• Chapter 3: General Linear Models
  • Introduction
  • The multivariate normal distribution
  • General Linear Models
  • Estimation of parameters
  • Likelihood ratio tests
  • Tests for model reduction
  • Collinearity
  • Inference on individual parameters in parameterized models
  • Model diagnostics: residuals and influence
  • Residual analysis
  • Representation of linear models
  • General linear models in R
  • Problems
• Chapter 4: Generalized Linear Models
  • Types of response variables
  • Exponential families of distributions
  • Generalized Linear Models
  • Maximum likelihood estimation
  • Likelihood ratio tests
  • Test for model reduction
  • Inference on individual parameters
  • Examples
  • Generalized linear models in R
  • Problems
• Chapter 5: Mixed effects models
  • Gaussian mixed effects model
  • One-way random effects model
  • More examples of hierarchical variation
  • General linear mixed effects models
  • Bayesian Interpretations
  • Posterior distributions for multivariate normal distributions
  • Random effects for multivariate measurements
  • Hierarchical models in metrology
  • General mixed effects models
  • Laplace approximation
  • Mixed effects models in R
  • Problems
• Chapter 6: Hierarchical models
  • Introduction, approaches to modelling of overdispersion
  • Hierarchical Poisson Gamma model
  • Conjugate prior distributions
  • Examples of generalized one-way random effects models
  • Hierarchical generalized linear models
  • Problems
• Chapter 7: Real life inspired problems
  • Dioxin emission
  • Depreciation of used cars
  • Young fish in the North sea
  • Traffic accidents
  • Mortality of snails
• Chapter 8: Supplement on the law of error propagation
  • Function of one random variable
  • Function of several random variable
• Appendix A: Some probability distributions
  • The binomial distribution model
  • The Poisson distribution model
  • The negative binomial distribution model
  • The exponential distribution model
  • The gamma distribution model
  • The inverse Gaussian distribution model
  • Distributions derived from the normal distribution
  • The Gamma-function
• Appendix B: List of symbols
• Bibliography
• Index

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