Efterår eller Forår The course is only offered after agreement with the teacher - not each year.
Undervisningsform:
12 two-hour sessions. Before each 2-hour session, read and work with examples/exercises from the relevant chapter. At the session one student is presenting and the remaining are discussants.
Kursets varighed:
[Kurset følger ikke DTUs normale skemastruktur]
Evalueringsform:
Hjælpemidler:
Bedømmelsesform:
Faglige forudsætninger:
Ønskelige forudsætninger:
Overordnede kursusmål:
To obtain a fundamental insight in the possibilities and limitations of using likelihood based modelling and inference together with likelihood based estimation methods.
Læringsmål:
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
Identify and apply elements of likelihood inference
Understand basic properties of likelihood such as sufficiency and invariance
Identify and apply profile likelihood methods
Recognize and apply likelihood methods in wellknown modelclasse such as normal, binomial and poisson models
Identify and understand frequentist, bayesian and Fisherian reasoning.
Identify and apply likelihood methods for regression models - normal and Generalized.
Understand and handle nuissance parameters
Identify and apply large sample properties of likelihood methods
Analyze and apply likelihood methods in a number of more advanced model settings
Kursusindhold:
General concepts, Bayesian, frequentist and Fisherian. Likelihood definition, inference and test. Invariance principle. Sufficiency, profile likelihood and calibration. Fundamental model families and applications – Exponential, Box-Cox transformation and Location-scale families. Frequentist properties – bias, p-value, confidence intervals and coverage probabilities, bootstrap confidence intervals. Regression models in the exponential family, Generalized Lineær Model, IWLS estimation, regression with Box-Cox and Location-scale families. Likelihood principle, sufficiency and conditionality. Properties of the score function and the Fisher information. Results for large samples, distribution of the maximum likelihood estimate, p*-formula. Nuisance parameters, marginal and conditional likelihood. EM-algorithm, general properties and applications of mixture models. Robustness of likelihood estimation, model misspecification and Kullback-Leibler distance, results for large samples, Akaike information criterion.
Litteratur:
“In All Likelihood: Statistical Modelling and Inference Using Likelihood by Yudi Pawitan, Oxford Science Publications, 2001
