Efterår
Forår
The course is only offered after agreement with the teacher - not
each year.
Undervisningens placering:
Campus Lyngby
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:
Anbefalede 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.
Litteraturhenvisninger:
“In All Likelihood: Statistical Modelling and Inference Using
Likelihood by Yudi Pawitan, Oxford Science Publications, 2001
