Statistical inference and simulations in stochastic modelling

 

Simulation methods within statistical data analysis provide invaluable tools to advance knowledge in many areas, such as biomedicine. Umberto Picchini has recently been appointed Full Professor in Mathematical Statistics and will hold an inaugural lecture about his very personal journey through statistical inference and stochastic modelling.

Umberto’s main research interest is to construct statistical methods to quantify uncertainty in stochastic models, especially mathematical models aiming at describing natural – physical or biological – processes that are affected by randomness. Most of his current research is about Bayesian inference methodology. Examples of applied work concern the growth of tumours on the skin of mice, single-cell dynamics in systems biology, dynamics in the concentration of glucose and insulin in blood plasma, and neuropathy problems, where neurons in skin die due to diabetes.

Deliberately or not, all my applications so far have been biomedical. It really interests me, but it is also a consequence of my PhD work.

Umberto did his master’s thesis in Rome. During that time, a biomathematics unit led by Dr. Andrea De Gaetano and financed by the Italian research council was looking for young researchers who could help with data analysis. Umberto did some work for them, and shortly after, his PhD at Sapienza Università di Roma was performed in collaboration with the biomathematics laboratory.

Simulation methods in statistical inference

From Rome Umberto continued to Copenhagen, where a co-supervisor from his PhD years, Prof. Susanne Ditlevsen, had invited him to a one-year postdoctoral appointment. He was then a lecturer at Durham University but missed the lifestyle and good work life balance of Scandinavia and got an Assistant Professorship at Lund University. Since 2018 he has been an Associated Professor at the University of Gothenburg.

In the last decade, Umberto has focused on advancing methodology for Bayesian inference, especially for complex models that can be simulated but not analytically treated. This research area is known as simulation-based inference. Several of his publications also consider models using stochastic differential equations.

Many modern research questions are not tractable analytically with pen and paper, and so statistical and machine learning methods based on computer simulations are essential. These models must not only be accurate, but also computationally efficient to run.

Design of experiments

In the future I would like to be more involved with “designs of experiments”, which is a methodological branch of statistics that aims at optimising the planning of real-world scientific experiments so that the most informative data are obtained.

As an example of this, Umberto describes the design of medical drugs. You may want to observe the effect of a certain drug on human subjects and need blood samples taken at certain intervals, for example every hour. This is an effort in time, costs, and not least the discomfort of the subjects. If the methodology could show that blood samples obtained every sixth hour instead would be informative enough, it would be a huge gain overall.

 

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