Back to home

# 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

Click on the chapter titles to see more.