Dr. Massimiliano Tamborrino
Tel.: +43 732 2468 4168
- Statistical inference for (partially/full observed) stochastic processes.
- Monte-Carlo methods and simulation.
- First passage times.
- Point processes and dependence measures.
- Stochastic modelling in neuroscience.
- Neural network connectivity.
- Mathematical modeling of physiological systems.
- Mathematical modeling of visual attention.
In particular, I have been (and still am) working on first passage times of multivariate diffusion processes from a statistic (cf. ), probabilistic and numerical point of view (cf. , , ). I am also interested in dependence measures between point processes (assuming that each event is in fact a passage time), with application to neural network connectivity (cf.  ,  ).
One of my favorite topic is the statistical inference from perturbed stochastic processes, i.e. stochastic processes in presence of a stimulus onset which modifies the model parameters (cf. , , , , , ). I started working on this topic during my PhD, and then I developed it thanks to two consecutive 2-years bilateral Projects between Austria and Czech-Republic (Czech PI: Prof. Lansky), for 2015-2016 (PI, 3875€) and 2017-2018. The ongoing project is titled "Perturbed stochastic point processes as a novel tool for neural coding analysis" (PI, 6790 €).
Recently I got interested in multi-timescale adapting threshold models, i.e. diffusion processes in presence of time-varying thresholds, having a jump after each crossing time, yielding non-renewal processes of hitting times. A preliminary step in this direction is represented by , where I investigated the first passage time density of a Wiener process in presence of exponentially decaying threshold (no jumps occur). Together with Dr. Kobayashi from Japan, I plan to investigate them from a modelling, probabilistic, statistical and numerical point of view. The model under consideration requires the development of techniques to deal with systems of recursive integral equations, non-renewal point processes and analytical methods for considers systems of MTATMs.
In 2017 and 2018 I have been founded for a 2-years bilateral Project between Austria and France (French PI: Prof. Samson) titled "Statistical inference for multivariate partially observed stochastic processes with application to neuroscience" (PI, 6840€). The model under consideration does not fall into the well-known class of Hidden Markov models, requiring further statistical developments.