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DoctorJohn Holmes

Lecturer

Mathematics and Statistics

Orcid identifier0009-0001-6687-7505 (opens in a new tab)⁠
  • Lecturer
    Mathematics and Statistics
  • +6433691060 (Work)

RESEARCH INTERESTS

  • Investigating properties of linear mixed models, particularly around random effect prediction in very large datasets.
      • This includes both random effect prediction, and approximate methods for finding standard errors of random effect levels. 
      • Most applications I study are related to animal breeding, where random effects are used to account for complicated correlation structures, rather than repeated measures which are more common in the health sciences.

 

  • Probabilistic approaches to determining latent structure, inspired by classical dimension reduction techniques such as principal components/factor  analysis, for a variety of categorical data types (binary, constrained count and unconstrained counts) found in the social and health sciences, with examples ranging from arrest and prosecution data, and to simultaneous modelling of cause of death and age of death time series.

 

  • Approximate Bayesian inference, mainly Variational Bayesian methods, with a focus on logistic regression (but can cover negative binomial) type models for a range of priors. 
        • This covers both fixed form and mean field Variational Bayes and mix between the two, focusing on developing methods that minimise error in approximation
          • The research into approximate Bayesian approaches to logistic models means a sub-research areas exist covering
                  • Properties of logistic transformations of  normal random variables
                  • development of more accurate confidence/credible intervals for proportions and odds ratios.