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)
2. Inference under model misspecification, including robust statistical inference for
3. Sparse modelling of high dimensional data, with application to genomics data (microarrays, proteomics, metabolic NMR spectra)
Professional and editorial activities
Member of Board of Directors of International Society for Bayesian Analysis (2017-2019)
Associate editor of Bernoulli (2019-)
Member of Royal Statistical Society, 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.
1. Adria Caballe, Natalia Bochkina, Claus Mayer, Ioannis Papastathopoulos (2018) Testing for equal correlation matrices with application to paired gene expression data. arXiv: 1803.06669.
2. Adria Caballe, Natalia Bochkina, Claus Mayer (2017) Joint Estimation of Sparse Networks with application to Paired Gene Expression data. arXiv: 1608.05533.
3. 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
4. Carolina Costa Mota Paraiba, Natalia Bochkina, Carlos Alberto Ribeiro Diniz (2018) “Bayesian truncated beta nonlinear models.” Applied Statistics, 45:2, 320-346
5. 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
6. 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
7. 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.
8. 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.
9. Bordovskaia N., Koshkina E., Bochkina N., (2017) Method of studying the level of terminological competence of students. ICERI17, Proceedings, pp. 2521-2527
10. 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
11. Natalia Bochkina (2016) "Selection of KL neighbourhood in robust Bayesian inference", Statistical Science, Vol. 31, No. 4, 499-502 http://dx.doi.org/10.1214/16-STS562.
12. 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 http://www.sciencedirect.com/science/article/pii/S187704281600046X.
13. 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
14. 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. http://projecteuclid.org/euclid.aos/1410440627. On ArXiv: http://arxiv.org/abs/1211.3434.
15. N. Bochkina (2013) Consistency of posterior distribution in generalized linear inverse problems, Inverse problems, 29, 095010
Natalia Bochkina and Ya'acov Ritov (2011) Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA). (in “Inverse
17. 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)
18. 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)
19. 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)
20. 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). )
21. 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.
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.
Email: N.Bochkina at edinburgh