I am a lecturer in Statistics at the School of Mathematics, University of Edinburgh.

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 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)

LMS/Turing workshop on inverse problems and Data Science, 8-10 May 2017

**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 (2016) Selection of the Regularization Parameter in Graphical Models using Network Characteristics. On ArXiv: arXiv:1509.05326.

2. Natalia Bochkina and Judith Rousseau (2016) "Adaptive density estimation based on a mixture of Gammas", arXiv:1605.08467.

3. Carolina Costa Mota Para?ba, Natalia Bochkina and Carlos Alberto Ribeiro Diniz (2017) "Bayesian truncated beta nonlinear mixed-effects models", DOI:10.1080/02664763.2016.1276891.

4. Natalia Bochkina (2016) "Selection of KL neighbourhood in robust Bayesian inference", Statistical Science (accepted) http://www.imstat.org/sts/future_papers.html.

5. 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.

6. 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.

7. N. Bochkina (2013) Consistency of posterior distribution in generalized linear inverse problems, Inverse problems, 29, 9, 095010

**
8.
**** **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).

**
9.
****
**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)

**
10.
****
**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)

**
10.
****
**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)

**11.**
**
**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). )

**12.**
**
****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.

**13.**
**
**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)

**14.**
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

**15.**
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

**16.**
Bochkina N., Sapatinas T. (2006) **On****
pointwise optimality of Bayes Factor wavelet regression
estimators**. *Sankhya,
***68**, 513-541. (pdf).