Research
Bavarian Alps, Germany

Research Interests

• Analysis of non-Euclidean data on general metric spaces or manifolds

Classical statistical techniques can only be partially leveraged to deal with non-Euclidean data, such as data on the sphere. Developing new methodology and models in a way that accounts for the geometry of the space is an active area of research.

• Algebraic statistics and graphical models

Many statistical models, like graphical models which aim to describe conditional independencies, can be described in terms of polynomial constraints. By studying such constraints using the tools of nonlinear algebra, statistical insights can be gleaned. 

• Matrix and tensor decompositions and the analysis of tensor-valued data

Matrix and tensor decompositions provide techniques for obtaining low-dimensional representations of high-dimensional data. Finding representations that are interpretable, computationally tractable, and have appealing theoretical properties is a challenging pursuit. 

• Information geometry

At its core, information geometry studies statistical models as geometric objects, traditionally endowed with the Fisher-Rao metric. Ideas from optimal transport have more recently permeated into this field. Among other things, these geometric ideas can be used to devise new statistical procedures.     

• Statistical decision theory

The philosophical foundation that underlies almost all of my work is classical statistical decision theory à la Wald as well as the partially antithetical, Bayesian decision theory. Given a new method a statistician needs to know how to measure its performance. Decision theory provides various ways to do this. I am always interested in exploring the various optimality criteria that are satisfied by new and old decision procedures. 

Publications

• McCormack, A. & Hoff, P. (2024). Information Geometry and Asymptotics for Kronecker Covariances.
  (Accepted, Bernoulli)
  arXiv preprint arXiv:2308.02260
  arXiv

• Drton, M., Grosdos, A., & McCormack, A. (2024). Rational Maximum Likelihood Estimators of Kronecker Covariance Matrices.
  Algebraic Statistics, 15(1), 145-163
  arXiv AlgStat

• McCormack, A. & Hoff, P. (2023). Equivariant Estimation of Fréchet Means.
  Biometrika, 110(4), 1055-1076.
  arXiv  BKA

• McCormack, A. & Hoff, P. (2022). The Stein Effect for Fréchet Means.
  Annals of Statistics, 50(6), 3647-3676.
  arXiv  AOS  PDF

• McCormack, A. & Hoff, P. (2022). Tests of Linear Hypotheses using Indirect Information.
  Canadian Journal of Statistics, 51(3), 852-876. Special Issue in Honour of Nancy Reid.
  arXiv  CJS

• Hoff, P., McCormack, A., & Zhang, A. R. (2022). Core Shrinkage Covariance Estimation for Matrix-variate Data.
  Journal of the Royal Statistical Society Series B: Statistical Methodology, 85(5), 1659-1679.
  arXiv  JRSSB

• McCormack, A., Reid, N., Sartori, N., & Theivendran, S. A. (2019). A directional look at F tests.
  Canadian Journal of Statistics, 47(4), 619-627.
  arXiv  CJS