I am interested primarily in foundational aspects of statistical theory and their bearing on scientific applications, and vice versa. Themes arising with commonality are:

Slides summarising of some of my work in this vein are below.

Occasionally I collaborate on topics in other disciplines requiring a statistical or an applied probability component.


Department of Mathematics, Imperial College London. h.battey@imperial.ac.uk


Editorial and other affiliations

Biometrika: Deputy Editor (screening), 2024--
Biometrika: Associate Editor, 2020--
Information and Inference: Associate Editor, 2022--2024.
J. Amer. Statist. Assoc.: Associate Editor, 2023--2025
J. R. Statist. Soc. Ser. B: Associate Editor, 2019--2024.

Honorary Secretary of the Research Section Committee
(editorial board for Series B discussion papers): 2022--2024.
Member of the Research Section Committee: 2018--2024

Institute for Digital Molecular Design and Fabrication.

Fisher Memorial Trust.


Research funding

EPSRC Early Career Research Fellowship, Oct 2020 - Apr 2026.
Theoretical foundations of inference in the presence of a large number of nuisance parameters.
EPSRC Postdoctoral Research Fellowship, Jan 2017 - Jan 2020.
Inference for functions of large covariance matrices.


PhD supervision

Charlotte Edgar (2024-- )
Statistical and causal models.

Jakub Rybak (2021--25)
Implicit models and sparsity.

Rebecca Lewis (2019--23)
High-dimensional inference and confidence sets of models.

Henrique Helfer Hoeltgebaum (informal supervision, 2018--19)
HCmodelSets: An R package for specifying sets of well-fitting models in high dimensions.


Pre-doctoral research supervision

Ervin Wee (MSc research dissertation 2025/26)
Meave Ma (MMath research disseration 2025/26)
Yorick Libiot (Visiting research scholar, ENS-Saclay, 2025)
Kian Shayeghi (MMath research disseration 2024/25)
Leah Nguyen (MMath research disseration 2024/25)
Meave Ma (Undergraduate Research Opportunities Programme 2024)
Moe Okawara (MMath research disseration 2023/24)
Tung Pham (Undergraduate Research Opportunities Programme 2023)
Daniel Vegara Balsa (MMath research dissertation 2021/22)
Su Hyeong Lee (Undergraduate Research Opportunities Programme 2020)
Seyeon Kim (MMath research disseration 2019/20)
Joanna Lada (Mary Lister McCammon scholar 2019)
Rebecca Lewis (Undergraduate Research Opportunities Programme 2018)
Jakub Rybak (MSc research dissertation 2017/18)
Edoardo Lisi (BSc research dissertation 2016/17)
Aarti Jhoke (MMath research dissertation 2015/16)
Richard Fu (Undergraduate Research Opportunities Programme 2015)


A few research talks

- Non-standard boundary behaviour.
- Regression graphs and sparsity-inducing reparametrisations.
- On the role of parametrisation ... misspecified nuisance component.
- Inducement of population-level sparsity.
- Confidence sets of models.


A few expository talks

- Some perspectives on models and their parametrisations.
  (RSS International Conference, Edinburgh, Sept 2025)
  (Nordic-Baltic Biometrics Conference, Oslo, June 2025)
- O. E. Barndorff Nielsen's approximate conditional inference.
  (Ole Barndorff-Nielsen Memorial Conference, Aarhus, May 2024)
- D. R. Cox: aspects of scientific inference.
  (A celebration of 50 years of the Cox model, LSHTM, Nov 2022)


Biographical outline

2025-present: Professor, Imperial College London.
2016-2025: Lecturer then Reader, Imperial College London.
2014-2016: Postdoctoral Fellow, Princeton University, USA.
2011-2014: Brunel Fellow in Statistics, University of Bristol, UK.
2008-2011: PhD, University of Cambridge, UK.


Peer-reviewed publications and arXiv preprints

Battey, H. S. and Reid, N. (2026)
Induced replication and the assessment of models.
arXiv:2603.27718.

Battey, H. S., Rasines, D. G. and Tang, Y. (2026)
Post-reduction inference for confidence sets of models.
arXiv:2507.10373. [code]

Battey, H. S., McCullagh, P. and Xiang, D. (2026)
Non-standard boundary behaviour in two-component mixture models.
arXiv:2407.20162. [code for reproducing figures]

Battey, H. S. and Edgar, C. (2026)
Treatment effect: a critique.
arXiv:2601.15467.

Rybak, J., Battey, H. S. and Bharath, K. (2026)
Regression graphs and sparsity-inducing reparametrisations.
Biometrika, 113, 1-23.

Reid, N. and Battey, H. S. (2026)
O. E. Barndorff-Nielsen's approximate conditional inference.
Bernoulli (invited issue), 32, 81-95.

Lewis, R. and Battey, H. S. (2025)
Cox reduction and confidence sets of models: a theoretical elucidation.
Statistical Science, 40, 313-328.

Rybak, J., Battey, H. S. and Zhou, W-X. (2025)
On inference in the implicit probability models of the support vector machine.
J. Machine Learning Research, 26 (85), 1-54.

Beale, N. and four others including Battey, H. S. (2025).
Dynamics of value tracking.
Journal of Dynamics and Games, 12, 24-47.

Battey, H. S. (2024)
Maximal co-ancillarity and maximal co-sufficiency.
Information Geometry, 7, 355-369.

Battey, H. S. and Reid, N. (2024)
On the role of parametrisation in models with a misspecified nuisance component.
Proc. Nat. Acad. Sci., 121 (36), e2402736121.

Lewis, R. and Battey, H. S. (2024)
On inference in high-dimensional logistic regression models with separated data.
Biometrika, 111, 989-1011.

Battey, H. S. and McCullagh, P. (2024)
An anomaly arising in the analysis of processes with more than one source of variability.
Biometrika, 111, 677-689.

Battey, H. S., Cox, D. R. and Lee, S. (2024)
On partial likelihood and the construction of factorisable transformations.
Information Geometry, 7, 9-28.

Battey, H. S. (2024)
D. R. Cox: aspects of scientific inference.
J. R. Statist. Soc. Ser. A, 187, 594-605 (invited issue).

Ward, S., Battey, H. S. and Cohen, E.A.K. (2023)
Estimation of the intensity function of a spatial point process on a Riemannian manifold.
Biometrika, 110, 1009-1021.

Battey, H. S. and Reid, N. (2023)
On inference in high-dimensional regression.
J. R. Statist. Soc. Ser. B, 85, 149-175. [matlab implementation]

Battey, H. S. and Cox, D. R. (2023)
Missing observations in regression: a conditional approach.
Royal Society Open Science, 10, 220267. [matlab implementation]

Battey, H. S. (2023)
Inducement of population-level sparsity.
Canadian J. Statist. (invited issue), 51, 760-768.
(Festschrift for Nancy Reid)

Battey, H. S. and Cox, D. R. (2022)
Some perspectives on inference in high dimensions.
Statistical Science, 37, 110-122.

Battey, H. S. and Cox, D. R. (2022)
Aspects of non-standard multivariate analysis.
J. Multivar. Analysis (invited issue), 188, 104810.

Rybak, J. and Battey, H. S. (2021)
Sparsity induced by covariance transformation: some deterministic and probabilistic results.
Proc. Roy. Soc. Lond. A: Math. Phys. Sci., 477, 20200756.

Castagno, S. and five others including Battey, H. S. (2021)
Seizure outcomes of temporoparietooccipital and frontal disconnection in children with drug-resistant epilepsy.
Epilepsy Research, 177, 106769.

Battey, H. S. (2021)
A note on the analytic approximation of exceedance probabilities in heterogeneous populations.
Statist. Probab. Lett., 179, 109215.

Battey, H. S. and Cox, D. R. (2020)
High-dimensional nuisance parameters: an example from parametric survival analysis.
Information Geometry, 3, 119-148.

Beale, N., Battey, H. S., Davison, A. C. and MacKay, R. S. (2020)
An unethical optimization principle.
Royal Society Open Science, 7, 200462.

Battey, H. S., Cox, D. R. and Jackson, M. V. (2019)
On the linear in probability model for binary data.
Royal Society Open Science, 6, 190067. [code] [accepted version]

Hoeltgebaum, H. H. and Battey, H. S. (2019)
HCmodelSets: An R package for specifying sets of well-fitting models in high dimensions.
The R Journal, 11, 370-379.

Battey, H. S. (2019)
On sparsity scales and covariance matrix transformations.
Biometrika, 106, 605-617.

Battey, H. S. and Cox, D. R. (2018)
Large numbers of explanatory variables: a probabilistic assessment.
Proc. Roy. Soc. Lond. A: Math. Phys. Sci., 474, 20170631. [software]

Avella, M., Battey, H. S., Fan, J. and Li, Q. (2018)
Robust estimation of high-dimensional covariance and precision matrices.
Biometrika, 105, 271-284.

Battey, H. S., Fan, J., Liu, Lu and Zhu, Z. (2018)
Distributed testing and estimation in sparse high dimensional models.
Ann. Statist., 46, 1352-1382.

Cox, D. R. and Battey, H. S. (2017)
Large numbers of explanatory variables, a semi-descriptive analysis.
Proc. Nat. Acad. Sci., 114 (32), 8592-8595. [software].

Battey, H. S. (2017)
Eigen structure of a new class of structured covariance and inverse covariance matrices.
Bernoulli, 23, 3166-3177.

Nieto-Reyes, A. and Battey, H. S. (2016)
A topologically valid definition of depth for functional data.
Statistical Science, 31 61-79.

Battey, H. S., Feng, Q. and Smith, R. J. (2016)
Improving confidence set estimation when parameters are weakly identified.
Statist. Probab. Lett., 118 117-123.

Battey, H. S. and Linton, O. B. (2014)
Nonparametric estimation of multivariate elliptic densities via finite mixture sieves.
J. Multivar. Analysis, 123 43-67.

Battey, H. S. and Sancetta, A. (2013)
Conditional estimation for dependent functional data.
J. Multivar. Analysis, 120 1-17.

Beale, N., Rand, D., Battey, H., Croxson, May, R. M., Nowak, M. A. (2011)
Individual versus systemic risk and the Regulator's Dilemma.
Proc. Nat. Acad. Sci., 108 (31) 12647-12652



Discussion contributions

Battey, H. S. (2026)
Discussion of `Regression by composition' by Farewell et al.
J. R. Statist. Soc. Ser. B, to appear.

Battey, H. S. (2024)
Discussion of `Parameterizing and simulating from causal models' by Evans and Didelez.
J. R. Statist. Soc. Ser. B, 86, 575-576.

Battey, H. S. (2022)
Discussion of `Assumption-lean inference for generalised linear model parameters' by Vansteelandt and Dukes.
J. R. Statist. Soc. Ser. B, 84, 696-698.



Non-refereed commissioned material

Battey, H. S. (2023)
D. R. Cox: extracts from a memorial lecture.
Harvard Data Science Review, 5 (2).

Battey, H. S. (2022)
D. R. Cox Memorial Lecture.
JSM Proceedings, Washington DC, 635-639.

Battey, H. S. and Reid, N. (2022)
Obituary: David Cox
IMS Bulletin, 51 (3), 14-16.

Battey, H. S. (2022)
Significance, 19 (2), 37.