Department of Mathematics, Imperial College London.

I am interested in statistical theory and applied probability motivated by scientific applications. Themes arising with commonality are:

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

h.battey@imperial.ac.uk

Research funding

EPSRC Early Career Research Fellowship, Oct 2020 - Jan 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.


Editorial affiliations

Biometrika: Screening Editor, 2024--
Biometrika: Associate Editor, 2020--2024.
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.
Member and Honorary Secretary of the Research Section Committee (editorial board for Series B discussion papers): 2018--2024
(Honorary Secretary 2022--2024).


PhD students

Charlotte Edgar (2024-- )
Jakub Rybak (2021-- )
Rebecca Lewis (2019--23)
Henrique Helfer Hoeltgebaum (informal supervision, 2018--19)


Pre-doctoral research supervision

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

- 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

- O. E. Barndorff Nielsen's approximate conditional inference.
- D. R. Cox: aspects of scientific inference.


Biographical outline

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

Fellow of the Institute of Mathematical Statistics (conferred 2023).

Peer-reviewed publications and arXiv preprints

Battey, H. S., McCullagh, P. and Xiang, D. (2025+)
Non-standard boundary behaviour in binary mixture models.
arXiv:2407.20162.

Rybak, J., Battey, H. S. and Bharath, K. (2025+)
Regression graphs and sparsity-inducing reparametrisations.
arXiv:2402.09112.

Lewis, R., Battey, H. S. and Zhou, W-X. (2025)
Inference in models with omitted covariates: Cramér-type moderate deviations and applications to high-dimensional regression.
Ann. Inst. Statist. Math., to appear.

Lewis, R. and Battey, H. S. (2025)
Cox reduction and confidence sets of models: a theoretical elucidation.
Statistical Science, to appear.

Rybak, J., Battey, H. S. and Zhou, W-X. (2025)
On inference for the support vector machine.
J. Machine Learning Research, 26, 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.

Tan, K. M., Battey, H. S. and Zhou, W-X. (2022)
Communication-constrained quantile regression with optimal guarantees.
J. Machine Learning Research, 23, 12456-12516.

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.

Nieto-Reyes, A. and Battey, H. S. (2021)
A topologically valid construction of depth for functional data.
J. Multivariate Analysis, 184, 104738.

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

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. [matlab implementation]

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. 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. (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.