Statistical Modelling and Inference
10 ECTS-credits
Learning Outcomes
On completion of this course, students will be able to:
- analyze data with the R software using models for non-normal outcomes, repeated measurement,
survival analysis and missing data
- analyze data with the R software using Bayesian sampling methods
- critically evaluate the output from these analyses
The students will be able to demonstrate knowledge of:
- statistical inference for a broad range of statistical models
- the assumptions behind the models
- the philosophical differences between statistical and machine-learning methods
- the philosophical differences between schools in statistics: frequentist, likelihoodist and
Bayesian
Course Content
Elements of likelihood inference, aspects of frequentist properties, profile likelihood, evidence and
the likelihood principle, Bayesian methods, extended likelihood principle, model selection, dealing
with nuisance parameters, survival analysis, classification of missing data mechanisms, dealing
with missing data using the EM algorithm and multiple imputation, mixed linear models.
Assessment
Written examination and home exercises.
Forms of Study
Lectures and computer exercises.
Prerequisites

Probability Theory and Markov Processes

Statistical Computing with R

Linear and Generalized Linear Models
Literature

Pawitan, Y.. (2001) In all likelihood : statistical modelling and inference using likelihood. Oxford :
Clarendon. (528 pp).

Gelman A., Carlin J.B., Stern H.S. and Rubin, D.B. (2004) Bayesian Data Analysis. Second Edition.
Chapman & Hall (689 pp).
Reference Literature

Hastie, T., Tibshirani, R. and Friedman, J. (2009) The elements of statistical learning:
data mining, inference and prediction. Second Edition. Springer.

Efron, B. 1987. Better bootstrap confidence intervals (with discussion). Journal of the
American Statistical Association 82, 171-200.
Efron, B. 1998. R.A. Fisher in the 21st century (with discussion). Statistical Science,
13, 95-122.
Schweder, T. 2003. Abundance estimation from photo-identification data: confidence
distributions and reduced likelihood for bowhead whales off Alaska. Biometrics, 59,
976-985.
Schweder, T. and Hjort, N.L. 2002. Confidence and likelihood. Scandinavian Journal
of Statistics, 29, 309-332.
Bjornstad, J., Predictive likelihood: A Review (with discussion), Statistical Science
vol 5, 1990, 242- 265
Bjornstad, J., On the generalization of the likelihood function and the likelihood
principle, JASA vol 91, 791 – 806
Ytterstad, E. (1991). Predictive likelihood predictors for the AR(1) model: a small
sample simulation, Scand. J. Statist vol 18, 97-110
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