Non-linear random effect models: time-independent and dynamic models

• Understand the Marginal likelihood for random effect models
• Indentify reasonable correlation structure in linear mixed effect models, based on relevant assumptions
• Apply and understand the Laplace approximation
• Formulate models in the framework of Generalized Linear Mixed effect models (GLMM)
• Formulate and apply random effect models using conjugate priors
• Formulate and implement General mixed effect models, i.e. non-linear/non-Gaussian first and second stage models
• Formulate and estimate parameters in generalized state space models.
• Apply automatic diffferention for parameter and state estimation in Hierarchical models
• Formulate and estimate parameters in non-homogeneous Hidden Markov Models, and interpret local and global decoding
• Estimate state variables and parameters in SDE models using the Laplace approximation
• Compare and discuss different statistical models and methods

Formulation and calculation/approximation, using e.g. the Laplace approximation, of the marginal likelihood for nonlinear random effect models is the core of the course. This include models with explicit solutions for the marginal likelihood and more general models where the Laplace approximation is needed, for example Generalized Linear Mixed Effect model, non-linear and non-Gaussian models. In addition non-linear/non-Gaussian stochastic state space models (e.g generalized state space models) is also presented. The course include both mathematical derivations and practical implementation using TMB (Template Model Builder), and other model specific R-packages.

• 6 – 20 (Fri 8-12)

02418/02417/02429, Students are assumed to have a good understanding of likelihood theory, standard statistical models (e.g. the generalized linear model), time series analysis, linear state estimation (the Kalman filter), and some knowledge of linear mixed effect models.

Lectures and group exercises