PhD Courses in Denmark

This advanced statistics course aims to enable the students to draw inference from models which are not covered by linear model routines in standard statistical software packages. Such non-standard models are very common in natural resource modelling an dcould e.g. contain: non-trival non-linearities, complex covariance structures, complicated couplings between fixed and random effects, or different sources of observations needing different likelihood types. in additionthey could contain large amounts of data. By the end of the course the students should be able to formulate (on paper and in code) non-standard models, estimate model parameters from these, quantify uncertainties, and test model hypothesis.

A student who has met the objectives of the course will be able to:

• Identify observational situations that cannot be analyzed via standard statistical software packages.
• Carry out analysis for non-standard statistical models with non-trivial non-linearities and multiple data sources.
• Describe non-standard models precisely in text and formulas.
• Carry out inference efficiently in models including random and fixed effects.
• Utilize efficient representations of the multivariate Gaussian to implement spatio-temporal (and similar high-dimensional) models .
• Propagate uncertainties from observations to estimates and derived quantities of interest.
• Conduct proper statistical model validation of statistical models with non-normal and non-independent observations.
• Formulate the result of a statistical analysis (estimates, uncertainties, and hypothesis testing) in a style suitable for a scientific publication.

This advanced statistics course deals with non-standard models, which are models that are not possible to analyze via pre-written code in standard statistical software packages. The analysis of non-standard require the analysts to explicity write efficient code for the likelihood, which function of the problem and optimize the likelihood, which require use of modern techniques for automatic calculation of derivatives. These tools will be taught and studied. In addition to the technical side of things a lot of emphasis will be put on model-formulation, on drawing correct conclusions from the models and on validating that appropriate models are being applied. Among the types of models that wll be studied are: Non-linear regression models, general random-effects models (including state-space models), multivariate models, and models informed by multiple different data sources.