Natalia Bochkina's home page

I am a Reader in Statistics at the School of Mathematics, University of Edinburgh, and Director of the Centre for Statistics.

School of Mathematics offers a range of Master of Science programmes, including MSc in Statistics and Operational Research

Funding is available, on competitive basis, for PhD studentships (information is here)

Current areas of research (click here for more details).

1.      Theory of Bayesian inference (rate of contraction for adaptive Bayesian nonparametrics, Bernstein-von Mises theorem, inverse problems, nonregular models, Bayesian machine learning)

2.      Inference under model misspecification, including robust statistical inference (approximate models, machine learning, testing for mild model misspecifications)

3.      Sparse modelling of high dimensional data, with application to genomics data (single cell and bulk mRNA microarrays, proteomics, metabolic NMR spectra)

Current professional and editorial activities

Member of the Research Section of the Royal Statistical Society (2019-)

Member of the Program Committee of CMStatistics 2021, 2022, 2023.

Member of the Program Committee of Bayesian Nonparametric Conference (BNP) 2022

Associate editor of Bernoulli (2019-2021)

Member of Board of Directors of International Society for Bayesian Analysis (2017-2019)

Member of the Institute of Mathematical Statistics

Brief research statement

One of my research directions is Bayesian inference for nonregular statistical models, particularly where the unknown parameter is on the boundary of the parameter space. For such models, the MLE can be a sharp maximum point of the loglikelihood which changes the rate of concentration of the posterior distribution and the local concentration of the posterior distribution. This phenomenon can also occur for misspecified models. (Bochkina and Green, 2014)
My other area of interest is Bayesian inverse problems where the error distribution is not necessarily Gaussian and where the likelihood may not be regular. Such problems arise, for instance, in computerised tomography.
I am also working on wavelet nonparametric regression, including optimality of Bayesian wavelet estimators and the regularity properties of the prior model.
My other interest is Bayesian analysis of genomics data. My past work in this area included modelling differential expression for genomic, proteomic and metabolic data including mixture modelling and model checks, and currently I am working on recovering sparse gene, protein and metabolic networks from such data.

Brief CV.




1.     Jinlu Liu, Sara Wade, Natalia Bochkina (2022) Shared Differential Clustering across Single-cell RNA Sequencing Datasets with the Hierarchical Dirichlet Process (in submission).

2.     N.Bochkina and Jenovah Rodrigues (2022). Bayesian inverse problems with heterogeneous variance. Scandinavian Journal of Statistics (paper:

3.     N.Bochkina (2021) Bernstein - von Mises theorem and misspecified models: a review. In Foundations of Modern Statistics, Editors Belomestny et al . Springer (

4.     A. Hayes, L. Neyton, T. Murray, X. Zheng, N. Bochkina, J. Iredale, D. Mole and the KMO Team (2021) Kynurenine monooxygenase regulates inflammation during critical illness and recovery in experimental acute pancreatitis. HPB, Volume 23, SUPPLEMENT 1, S218

5.     Adria Caballe, Natalia Bochkina, Claus Mayer, Ioannis Papastathopoulos (2018) Testing for equal correlation matrices with application to paired gene expression data. arXiv: 1803.06669.

6.     Adria Caballe, Natalia Bochkina, Claus Mayer (2018) Joint Estimation of Sparse Networks with application to Paired Gene Expression data. arXiv: 1608.05533.

7.     A. Caballe, N.Bochkina and Claus Mayer (2018) Selection of the regularisation parameter in graphical models given complex network structures Journal of Computational and Graphical Statistics, 27:2, 323-333

8.     Carolina Costa Mota Paraiba, Natalia Bochkina, Carlos Alberto Ribeiro Diniz (2018) Bayesian truncated beta nonlinear models. Applied Statistics, 45:2, 320-346

9.     Nina V. Bordovskaia, Charles Anderson, Natalia Bochkina, Elena I. Petanova (2018) The Adaptive Capabilities of Chinese Students Studying In Chinese, British and Russian Universities. International Journal of Higher Education, Vol 7, No 4

10.  Nina V. Bordovskaia, Elena Koshkina, Marina Tikhomirova, Natalia Bochkina (2018) Case Method as a Tool for Evaluation and Development of Terminological Competence of Future Teachers, Integration of Education 22(4):728-749. DOI:10.15507/1991-9468.093.022.201804.728-749

11.  Nina Bordovskaia, Elena Koshkina, Natalia Bochkina (2018) STRATEGIES OF PRACTICAL USE OF CASES WHEN FORMING TERMINOLOGICAL COMPETENCE OF FUTURE TEACHERS. Conference Paper: 10th International Conference on Education and New Learning Technologies. DsOI:10.21125/edulearn.2018.1219

12.  N.Bochkina and J.Rousseau (2017) Adaptive density estimation based on a mixture of Gammas. Electronic Journal of Statistics, Volume 11, Number 1, 916-962. arXiv:1605.08467

13.  Adria Caballe, Natalia Bochkina, Claus Mayer (2017) Selection of the Regularization Parameter in Graphical Models using Network Characteristics, Journal of Computational and Graphical Statistics (accepted), arXiv:1509.05326.

14.  Bordovskaia N., Koshkina E., Tikhomirova M., Bochkina N., (2017) Consistency between pedagogical assessment and self-assessment of educational results in the context of professional and personal development of students. EDULEARN17, Proceedings, pp. 7372-7380.

15.  Bordovskaia N., Koshkina E., Bochkina N., (2017) Method of studying the level of terminological competence of students. ICERI17, Proceedings, pp. 2521-2527

16.  Bordovskaia, Nina V.; Bochkina, Natalia A.; Koshkina, Elena A.(2016) Use of didactic terminology by teachers at various stages of professional communication 2016 INTERNATIONAL CONFERENCE EDUCATION ENVIRONMENT FOR THE INFORMATION AGE (EEIA-2016) Book Series: SHS Web of Conferences Volume: 29 Article Number: UNSP 01013

17.  Natalia Bochkina (2016) Selection of KL neighbourhood in robust Bayesian inference, Statistical Science, Vol. 31, No. 4, 499-502

18.  Elena Koshkina, Nina Bordovskaia, Natalia Bochkina (2016) Didactic Terminology Operated by Russian Future and Practising Teachers: Comparative Analysis Procedia - Social and Behavioral Sciences, V. 217, p. 42 - 48

19.  Bordovskaia, Nina V.; Bochkina, Natalia A.; Koshkina, Elena A.(2016) Use of didactic terminology by teachers at various stages of professional communication 2016 INTERNATIONAL CONFERENCE EDUCATION ENVIRONMENT FOR THE INFORMATION AGE (EEIA-2016) Book Series: SHS Web of Conferences Volume: 29 Article Number: UNSP 01013

20.  Natalia A. Bochkina and Peter J. Green (2014) The Bernstein-von Mises theorem and non-regular models. Annals of Statistics, V. 42, N. 5, 1850-1878. On ArXiv:

21.  N. Bochkina (2013) Consistency of posterior distribution in generalized linear inverse problems, Inverse problems, 29, 095010

22.   Natalia Bochkina and Ya'acov Ritov (2011) Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA). (in Inverse Problems and High-Dimensional estimation, Springer Lecture Notes in Statistics, eds P. Alquier, E. Gautier, G. Stolz, p171-189).

23.  Natalia Bochkina and Alex Lewin (2010) Classification for Differential Gene Expression using Bayesian Hierarchical modelling, in Bayesian Modelling for Bioinformatics (eds D.Dey, S.Ghosh and B.Mallick, p. 37-71)

24.  P.McNabb, N.Bochkina, D.Wilson and J.Bialek. (2010) Oscillation source location using wavelet transforms and generalized linear models, Transmission and Distribution Conference and Exposition, IEEE PES (Conference Proceedings)

25.  P.McNabb, N.Bochkina and J.Bialek. (2010) Oscillation source location in power systems using logic regression, Innovative Smart Grid Technologies Conference Europe (ISGT Europe), IEEE PES (Conference Proceedings)

26.  Bochkina N., Sapatinas T. (2009). Minimax rates of convergence and optimality of Bayes factor wavelet regression estimators under pointwise risks. Statistica Sinica, Vol. 19, 1389-1406. (Refereed online Supplement: Statistica Sinica, Vol. 19, S21-S37 (2009). )

27.  Dirk Hadaschik, Ulrika Andersson, Mande Kumaran, Natalia Bochkina, Sylvia Richardson, Timothy J Aitman, James Scott, Stephen O’Rahilly & Kenneth Siddle (2008) Impact of metformin on gene expression, glucose uptake and lipolysis in adipocyte. Endocrine, 16 OC3.7

28.  Lewin A., Bochkina N., Richardson S (2007) Fully Bayesian Mixture Model for Differential Gene Expression: Simulations and Model Checks. Statistical Applications in Genetics and Molecular Biology: Vol. 6 : Iss. 1, Article 36.

29.  Bochkina N., Richardson S. (2007) Tail posterior probability for inference in pairwise and multiclass gene expression data. Biometrics, 63(4): 1117-25 (journal website and Supplementary material)

30.  Turro E, Bochkina N, Hein AM, Richardson S. (2007) BGX: a Bioconductor package for the Bayesian integrated analysis of Affymetrix GeneChips (application note). BMC Bioinformatics, 12; 8(1):439

31.  Bochkina N. (2007) Goodness-of-fit Test for Dependent Observations via Wavelets. Journal of Statistical Planning and Inference, Volume 137, Issue 8, 1 August 2007, Pages 2593-2612

32.  Bochkina N., Sapatinas T. (2006) On pointwise optimality of Bayes Factor wavelet regression estimators. Sankhya, 68, 513-541. (pdf).

33.  Bochkina N.A., Sapatinas T. (2005) On the Posterior Median Estimators of Possibly Sparse Sequences. Annals of Institute of Statistical Mathematics, Vol. 57, 315-351 (Abstract).

 S.Parry, D.Hadaschik, C.Blancher, K.Mande, N.Bochkina, H.Morris, S.Richardson, T.Aitman, D.Gauguier, K.Siddle, J.Scott and A.Dell. (2006) Glycomics investigation into insulin action. Biochimica et Biophysica Acta, 1760(4):652-68.

34.  A.Bart, N.Alekseyeff (Klochkova), N.Bochkina. Partial Inversion of Functions for Statistical Modelling of Regulatory Systems. In Advances in Stochastic Simulation Methods (Series: Statistics for Industry and Technology) p.355-371. Eds. Balakrishnan, V.B.Melas, S.Ermakov, Burkhaser, Boston-Basel-Berlin, 2000. A.G. Bart, V.M. Kozhanov, N.M. Chmykhova, N.A. Botchkina, L.A. Ternovaya, H.P. Clamann. Topological and statistical analysis of 3-D reconstructions of axon collaterals. Neurophysiol 32:249-259, 2000

35.  A.G.Bart, N.A.Bochkina. (1998) Fiducial Distributions in Statistical Simulation of Regulatory Systems, p.238-242, In Proceedings of St.Petersburg Workshop on Simulation, Eds. S.M.Ermakov, Y.N.Kashtanov, V.B.Melas, St.Petersburg University Press.

Book review

Bochkina N. (2006) Probabilistic Modeling in Bioinformatics and Medical Informatics by D. Husmeier, R. Dybowski and S. Roberts (eds) (book review). Journal of the Royal Statistical Society: Series A 169 (4), 1009-1010.


Bochkina N., Ritov Y. Sparse Empirical Bayes Analysis.

Bochkina N. Besov regularity of functions with sparse random wavelet coefficients. ( arxiv 0911.5482)


















Contact details.

Office: JCMB 4612


School of Mathematics,

Kings Buildings,

University of Edinburgh,
Mayfield Road,

Edinburgh, EH9 3FD.

Tel:   0131 650 8597

Fax:  0131 650 6553

Email: N.Bochkina at (