Natalia Bochkina
Niharika Peddinenikalva has written the following article as part of our series of Academic Interviews; featuring Natalia Bochkina!
Early life
Natalia Bochkina is a Reader in Statistics at the School of Mathematics who received a PhD in Statistics from University of Bristol.
Considering both her parents were involved in maths, it’s no wonder that she always wanted to pursue mathematics. As a young girl, she discovered that if you take a number and multiply together the numbers above and below, then the result will be one less than the square of the first number. When she showed her mother this fascinating discovery, her mother wrote out the formula:
(x+1)(x-1)=(x^2)-1
Of course, this was a popular equation but that was her introduction to the world of research.
At the age of 10, Natalia had decided that she would study probability. She recalls reading a Russian book called “Mathematical labyrinth” which described a boy who had to navigate a labyrinth by solving mathematical problems. ‘It was while I was reading this book, that I first ever came across probability’, she said.
Current research
Her main research is on Bayesian inference which studies the behaviour of a parameter’s distribution for given data with large sample size. In the frequentist approach, this would lead to the Central Limit Theorem which says that the Maximum Likelihood Estimator of the parameter has an asymptotically normal distribution. In Bayesian approach, the conditional distribution of the parameter given data has the same asymptotic distribution.
Natalia also works on models with mis-specified distributions. For example, assuming a model is normally distributed when it does not follow the behaviour of a normal distribution. In this case, the asymptotic distribution is also normal but with different parameters from the asymptotic distribution of the MLE, and the frequentist approach works better here than the Bayesian one. She also works on non-regular models, like a Uniform (0,q) distribution where the conditional distribution of the parameter given data follows Exponential distribution rather than normal. Here, the Bayesian approach works better than the frequentist approach. These results are referred to as the Bernstein-von Mises theorem.
Machine learning
When asked for her views on the growing popularity of machine learning and statistics, she describes that with today’s technology we can have adventurous methods like deep neural networks which require substantial running memory and storage capacity. These developments have caused a paradigm shift in statistics over the last 10-15 years. She raises a relevant question – a machine learner might have an algorithm that works for a given data set, but does it work for every single data set and are there constraints involved?
Natalia works on other machine learning methods such as “ranking problems” with application to tennis ranking and solving these using the Bayesian approach. She confirmed that today we can look at a wider range of cases where we can vary the sample or parameter sizes to show that these methods work under different conditions.
Sharing her tips for statistics students, she says that there are many interesting problems in theory, so it’s promising, but so is working with machine learners directly. When working in theory without interactions with researchers who produced the data or the method, ‘you work separately and are not involved in data collection so you might make assumptions such that theory works but which are not verifiable or not applicable in practice’. However, working with researchers who produced the data or the method you are analysing motivates you to make the assumptions that are minimal and relevant to practitioners. For example, biologists or doctors who work with Natalia, in need a statistical model for a data sample, often use machine learning methods, but, as a statistician she confirmed, ‘it’s not just an interesting problem to solve. It’s also important to talk to the people who want the problem solved, so that your results are useful and relevant.’ This helps one understand what is required of them.
An early interest in chemistry
Natalia recalls from her schooldays that her teachers designed Olympiad questions for every subject and that she herself came second in the Soviet Union for the Chemistry Olympiad. As her performance in the Maths Olympiad was not as good, she considered pursuing chemistry instead of maths. However, in her penultimate year, her teacher told her that ‘the Olympiads are like sprints while research is more like a marathon and different people are suited to different things’. She believes going into research is like going into a marathon with patience and perseverance.
Teaching
While Natalia enjoys teaching and research equally, she started off university teaching at the tutorial level as a PhD student. Lecturing was a skill she developed with time she confirmed, ‘It’s a challenge to explain something well and make it reasonably interesting.’ As a PhD student, she was comfortable teaching maths and physics students at tutorials but she recalls a time when she replaced a biology tutor. It was the same material to teach but when she hinted that they should try to differentiate a function to find its maximum, they looked confused.
Changes in the University experience
Regarding differences in her university experience from that of students’ today, she believes that there are more opportunities to connect to companies through things like internships. Also, in her university days, she had oral exams which were a great experience. With the usual tension before an exam, in 90% of cases, she would memorise a big list of all the theorems and definitions. However, at the exam, owing to the examiner’s skills, she felt capable of linking all those things together.