Funding is available, on competitive basis, for UK/EU PhD studentships (information is here)
Current areas of research (click here for more details).
1. Bayesian modelling in wavelet nonparametric regression (a priori Besov regularity properties; optimality).
2. Bayesian inverse problems
3. Inference in nonregular problems
4. Concentration of the posterior distribution (Bernstein-von Mises theorem)
5. Inference under model misspecification
6. Sparse modelling of high dimensional data
7. Modelling of functional genomics data (microarrays, metabolic NMR spectra)
Brief research statement
My current main research direction 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 (2017) Joint Estimation of Sparse Networks with application to Paired Gene Expression data. On ArXiv: arXiv: 1608.05533.
2. Adria Caballe, Natalia Bochkina, Claus Mayer (2016) Selection of the Regularization Parameter in Graphical Models using Network Characteristics. On ArXiv: arXiv:1509.05326.
3. Natalia Bochkina and Judith Rousseau (2016) "Adaptive density estimation based on a mixture of Gammas", arXiv:1605.08467.
4. Carolina Costa Mota Paraiba, Natalia Bochkina and Carlos Alberto Ribeiro Diniz (2017) "Bayesian truncated beta nonlinear mixed-effects models", Journal of Applied Statistics DOI:10.1080/02664763.2016.1276891.
5. 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.
6. 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.
7. 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
8. 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.
9. N. Bochkina (2013) Consistency of posterior distribution in generalized linear inverse problems, Inverse problems, 29, 095010
10. Natalia Bochkina and Ya'acov Ritov (2011) Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA). (in â€śInverse
11. Natalia Bochkina and Alex Lewin (2010) Classification for Differential Gene Expression using Bayesian Hierarchical modelling, in â€śBayesian Modelling for Bioinformaticsâ€ť (eds D.Dey, S.Ghosh and B.Mallick, p. 37-71)
12. P.McNabb, N.Bochkina, D.Wilson and J.Bialek. (2010) Oscillation source location using wavelet transforms and generalized linear modelsâ€ť, Transmission and Distribution Conference and Exposition, IEEE PES (Conference Proceedings)
13. 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)
14. 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. (Referred (online) Supplement: Statistica Sinica, Vol. 19, S21-S37 (2009). )
15. 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.