
LTCC Advanced Course: Likelihood Inference
November/December, 2012
Course Outline
Also available as a pdf.
 Asymptotic theory for likelihood; likelihood root, maximum likelihood estimate, score function, pivotal quantities, exact and approximate ancillary.
Laplace approximations for Bayesian inference.
 Higher order approximations for nonBayesian inference. Marginal, conditional and adjusted loglikelihoods for inference in the presence of nuisance parameters. Examples: regression models with nonnormal error; logistic regression.
 Sample space differentiation and approximate ancillary; tangent exponential models;
Examples: contingency tables; risk difference and risk ratio; nonlinear regression
 Likelihood inference for complex data structure: time series, spatial models, spacetime models, extremes. Composite likelihood: definition, summary statistics, asymptotic theory. Examples: longitudinal binary data; Gaussian random fields; Markov chains
 Semiparametric likelihoods for point process data; empirical likelihood.
If you are taking the course for a mark
The homework has been graded, and the grades submitted to my contact at UCL, Nisha Jones. The papers may be picked up from Dr. Russell Evans, in Room 120 of the Statistical Science Department, until the end of term.
In each of weeks 14 some problems will be assigned, due the following week. Please bring hard copy to the class. These solutions will be the basis of your mark in the course. Problem solutions will be discussed in Week 5. The problems for Week 1, due November 12, are at the end of the Week 1 handout. The ``exercises'' embedded in the Week 1 slides are not required.
Hint for Week 1 Problems: The solution to 1(a) requires establishing properties about the constrained maximum likleihood estimator. The steps will be similar to those outlined in this moderately rigorous proof of the results in the scalar parameter case.
Running list of references and background reading
Review Papers
Likelihood Basics
 Davison, A.C. (2003) Statistical Models (SM) Cambridge University Press.  Ch 4
 BarndorffNielsen, O.E. and Cox, D.R. (1994) Inference and Asymptotics (BNC) Chapman and Hall.  Ch 2.2
 Cox, D.R. and Hinkley, D.V. (1974) Theoretical Statistics (CH) Chapman and Hall.  Ch 2.1 (i), (ii)
 Cox, D.R. (2006). Principles of Statistical Inference (Cox)  Ch.2.1
Likelihood and models
 Stochastic models: SM  Ch 6
 Transformation models: SM  Ch 5.3, BNC  Ch 2.8
 Pivots: Brazzale, A.R., Davison, A.C. and Reid, N. (2007). Applied Asymptotics. (BDR)  Ch. 2
Approximations
 Various: BarndorffNielsen, O.E. and Cox, D.R. (1989). Asymptotic Techniques for Use in Statistics. Good introduction to Laplace, Edgeworth, and saddlepoint expansions.
 Laplace approximation: SM  Ch 11.3
 Approximate posteriors:
Tierney, L.J. and Kadane, J.B. (1986). Accurate approximation to posterior moments and marginal densities. JASA 81, 8286
Johnson, R.A. (1970).
Asymptotic expansions associated with posterior
distributions.
Ann. Math. Statist. 41, 851864.
Datta, G.S. and Mukerjee, R. (2004). Probability
Matching Priors: Higher Order Asymptotics. Lecture
Notes in Statistics 178, New York: SpringerVerlag
 Saddlepoint approximation: SM  Ch 12.3
 Examples: BDR  Ch 3, 4, 5
 Adjusted profile likelihood: SM  Ch 12.4, BNC  Ch 8
 Tangent exponential model: BDR  CH 8.3
Composite Likelihood
Week 1
Week 2
Week 3
Week 4
Week 5
