LECTURE: 

"An introduction to Bayesian data analysis for model selection and other applications"

We present an introduction to some concepts of Bayesian statistics for the analysis of atomic spectra. Starting from basic rules of probability, we present the Bayes’ theorem and its applications. We discuss the limits of standard (frequentist) statistical methods and in which cases a Bayesian analysis is mandatory. In particular, we present how to deal with some common problems, like a) how to correctly fit models with parameters with constraints to data, b) how to deal with multimodal problems, and, more importantly, c) how to assign probability to different possible models (different numbers of spectral contributions, type of peak profile, etc.) from the analysis of the same set of experimental data. Contrary to standard model testing methods, generally based on criteria, the attribution of a quantitative probability to models (or hypotheses) allows to deal with cases not presenting a clear favour for a particular working hypothesis. Weighted averages between models of a given parameter can be thus calculated (to determine a peak position, but not its specific shape), and the uncertainty resulting from the model choice can be quantified.

TUTORIAL: 

"How many lines are there? A training with the Nested_fit code"

In this hands-on tutorial, we will show how to evaluate probabilities of different models for the description of the same simple data set. The tutorial is based on the use of the Nested_fit code, a polyvalent program specially designed for spectroscopy applications, and based on the nested sampling algorithm. We will see how to extract the probability distribution of the parameters of the models, how to choose the more adapted model, and how to deal with likelihood function multimodality. For the latter, a number of unsupervised clustering techniques will be used, and their efficiency will be evaluated.

The tutorial is based on a Python Jupyter notebook that can be run remotely via a web browser (in Google Colab). Alternatively, the code (based on Python/Fortran and C++) can be installed on local machines (via Git) and called from Python or run independently. This is the recommended way for high-performance computing, where one can take advantage of the full code parallelization (via OpenMP).

The tutorial itself is already available on the main page of the program website: https://github.com/martinit18/nested_fit

SEMINAR: 

"Testing quantum electrodynamics in extreme fields without using lasers"

Transition energy measurements in heavy, few-electron atoms are a unique tool to test bound-state QED in extremely strong Coulomb fields. In such strong fields, QED effects of the quantum vacuum fluctuations on the atomic energies are enhanced by several orders of magnitude with respect to light atoms, but perturbative methods cannot be implemented. These systems are extremely challenging to study experimentally as well: almost no laser spectroscopy measurements can be performed and most high-resolution spectra come from acquisitions that take several days. Up to now, higher-order (two-loop) QED effects in this strong regime could not conclusively be tested. Here we present a novel multi-reference method based on Doppler-tuned x-ray emission from fast uranium ions stored at relativistic velocities. By accurately measuring the relative energies between 2p3/2 -> 2s1/2 transitions in two-, three-, and four-electron uranium ions, we were able, for the first time in this regime, to disentangle and test separately high-order (two-loop) one-electron and two-electron QED effects, setting a new important benchmark. Moreover, the achieved accuracy of 37 parts per million allows us to discriminate between different theoretical approaches developed throughout the last decades for describing He-like systems.

BIOGRAPHY:

Martino TRASSINELLI is a CNRS researcher since 2007 and part of the ASUR team (French acronym for Clusters and Surfaces under Intense Excitation) at the Institute of NanoSciences of Paris. His primary area of study is the physics of highly charged ions for Quantum Electrodynamics tests in strong fields and dynamical collisional processes. He is collaborating with several international centres, and in particular with the FAIR accelerator/GSI Helmholtzzentrum. Since several years, he has been developing a series of tools based on Bayesian statistics for the analysis of complex and/or few-count data sets. In particular, he is developing the nested_fit code, specially orientated for model testing for atomic spectra, which is based on the nested sampling algorithm, widely implemented in other research fields.
More information can be found in https://w3.insp.upmc.fr/en/insp-page-perso/trassinelli-martino