Professor Murray Aitkin

Professorial Fellow (Associate)  

Department of Mathematics and Statistics
The University of Melbourne


Room: G59

Ext. Number: 48820

Email: Murray.Aitkin AT unimelb.edu.au


Murray and Irit Aitkin Statistical Modeling of the National Assessment of Educational Progress Springer 2011.

This book describes our joint contract work for the US National Center for Educational Statistics, on an integrated psychometric and statistical model for the large-scale NAEP surveys of the US Department of Education. The model incorporates the clustered survey design through multiple model levels, and allows for stratification and oversampling of minority ethnic groups. We allow for guessing through a two-class latent class model with different item parameters in the classes. We are extending this work with a current Institute of Education Sciences grant to examine Bayesian model comparisons for the competing possible models for the survey data, and to obtain the full information from records with incomplete convariate information.


Statistical Inference: an Integrated Bayesian/Likelihood Approach , Chapman and Hall/CRC Press 2010

This book sets out an integrated Bayesian and likelihood approach to statistical inference, using the likelihood as the primary measure of evidence for statistical model parameters, and for the statistical models themselves.

To assess the strength of evidence from the data for competing parameter values or competing models, it uses likelihood ratios between the parameter values or the models. To interpret the likelihood ratios it uses a Bayesian approach which requires in general only the non-informative priors that are widely used in posterior inference about model parameters, though it can accommodate informative priors.

Comparison of different statistical models requires a treatment of the unknown model parameters. This problem is usually treated by Bayes factors; the book gives a different approach which uses the full posterior distribution of the likelihood for each model. This quite small change to standard Bayesian analysis allows a very general and unified approach to a wide range of apparently different inference problems.

A further contribution of the book is to develop a general Bayesian approach to finite population inference. This approach, using the multinomial distribution and a non-informative Dirichlet prior, can also be adapted to provide a general Bayesian "non-parametric" analysis.

The book is intended to provide both an exposition of an alternative to standard Bayesian inference, and the foundation for a course sequence in modern Bayesian theory at the graduate or advanced undergraduate level.

Book reviews


Bayesian Course


Paradigm paper


Professional Associations, Memberships & Awards:

  • 1971-2 Fulbright Senior Fellow, Educational Testing Service, Princeton
  • 1976-9 Social Science Research Council Professorial Fellow, University of Lancaster
  • 1982 Elected Member, International Statistical Institute
  • 1984 Fellow, American Statistical Association
  • 1992-6 Australian Research Council Senior Research Fellow, Australian National University and University of Western Australia
  • DSc Sydney University 1997
  • Member, Biometric Society, Royal Statistical Society

Editorial Consultation

  • Consulting Editor, Multivariate Behavioral Research
  • Editorial Advisory Board, Statistical Modelling: An International Journal
  • Former Associate Editor of:
    • Journal of the Royal Statistical Society Series B
    • Psychometrika
    • British Journal of Mathematical and Statistical Psychology
    • Journal of Educational Statistics
    • Biometrics

National and International Activities

  • Editorial Board of Statistical Modelling: An International Journal.
  • Advisor to the National Center for Education Statistics, US Department of Education.


Current and Recent Funded Research

Australian Research Council (ARC) 2012-2015

The ARC supported a Discovery project on latent class modelling approaches to sub-group structure in social networks, which supported Duy Vu as Research Associate and visits from Brian Francis. Analyses in this project (Social Networks 2014 - hotkey) recovered the known group structure in a well-known social network of women in Natchez Mississippi in the 1930s (a classic sociological data set) and the known leadership structure in the Noordin Top terrorist network (Journal of the Royal Statistical Society - hotkey), which other extensive social network analyses had failed to identify. A simulation study (Metron - hotkey) supported the integrated Bayesian/likelihood approach to model comparison, as applied to finite mixture models.

US Department of Education 2003-2011

I have been working since 2003 with Irit Aitkin, in a series of research contracts with the US National Center for Education Statistics and several research grants from the Institute of Education Sciences, on the development and implementation of fully model-based approaches to the analysis of the large-scale US National Assessment of Educational Progress (NAEP) surveys of primary and high-school students' achievement. We have developed multi-level model-based approaches for the clustered and stratified survey designs, examined alternative distributions for the latent ability, and formulated alternative latent class models for guessing, or "engagement" on the test items. For each of these developments, we have compared the results of the model-based approach with the current methods of analysis using both simulated and actual NAEP data.

A detailed description of this approach, its principles and a summary of each project can be found here.

Australian Research Council (ARC) 2005-2008

The ARC supported a Discovery project 2005-8 on Bayesian and likelihood approaches to finite mixture, random effect and multinomial models, on which Irit Aitkin worked part-time with me. The project also supported Charles Liu briefly. This project led to the development of the integrated Bayesian/likelihood approach to statistical inference set out in the book and in research papers Journal of Mathematical Psychology 2008 and Annals of Applied Statistics 2009 with Charles Liu.



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