**A PhD position is available for this project. Scroll down to the recruitment section to apply.**

You will research new exciting methods, merging computer simulations,
Bayesian inference, deep learning and more generally machine learning,
to infer model parameters in stochastic models and quantify
uncertainties. Goal is to extract knowledge and perform predictions in challenging scenarios.

Mathematical and statistical models for real-world applications are complex. When constructing statistical and machine learning methodology to fit the model to data, we wish to obtain a realistic mathematical representation of the experiment under study. This means finding the "best" model parameters and quantify their uncertainties in a probabilistic way. However, what we typically face with realistically complex models is the inability to perform statistical inference exactly. This is typically due to the lack of a closed-form expression for the likelihood function of the model parameters. This affects both frequentist and Bayesian procedures. A change of paradigm is given by simulation-based "likelihood-free" approaches. In this case, the only requirement is the ability to simulate artificial data from am arbitrarily complex "computer simulator", which is a software implementation of the mathematical model. An important simulation-based approach is the class of Approximate Bayesian Computation (ABC) algorithms.

The goal of this project is to marry modern machine learning methodology such as deep neuronal networks, with simulation-based inference methods. This implies constructing new methodology for both areas, with the goal of creating novel "plug-and-play" engines for parameter inference and uncertainty quantification.

Special interest is geared towards learning the parameters of stochastic dynamical models (though not exclusively) such as stochastic differential equations and hidden Markov models (state space models). Moreover, while the project is of methodological nature, applications to real data case studies are foreseen, such as protein folding data, epidemic data and smart-city data such as such as precipitation, pollution data, temperature and humidity.

Here is a slightly more extended description with references.

PI is Umberto Picchini and the project is an international collaboration with Jes Frellsen (DTU Copenhagen), Andrew Golightly (Newcastle University, UK) and Samuel Wiqvist (Lund, Sweden).

The project is funded by the Chalmers AI Research centre and by the Swedish Research Council (Vetenskapsrådet).

**PhD student recruitment**

Interested in this project?

Please contact Umberto Picchini (link below) for further information or questions.

**Essential requirements:**

- strong interest in statistical inference and machine learning;
- having taken courses in (or knowing elements of) Bayesian inference methods;
- The student should be proficient with at least one programming language for data-science (e.g. R, Python, MATLAB, Julia);
- Proficiency with oral and written English.

**Additional points of merit**(NOT essential requirements. Please feel free to apply even without the experience below)

- experience with inference for stochastic differential equations;
- experience with inference via particle filters (sequential Monte Carlo);
- experience with software libraries such as TensorFlow or PyTorch.

Below is a link to the official University page of the supervisor Umberto Picchini. However a more informative page is his personal one.