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

• Understand the Marginal likelihood for random effect models
• Apply and understand the Laplace approximation
• Formulate models in the framework of Generalized Linear Mixed effect models (GLMM)
• Formulate and apply random effect model 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
• Formulate and estimate parameters in non-homogeneous Hidden Markov Models, and interpret local and global decoding
• Estimation in non-linear SDE models using the Laplace approximation
• Transformation of the state space in state dependent diffusion models (e.g. the Lamperti transform)

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.

02418/02417/02427/02417/02429

Lectures and group exercises