Many natural, social, financial phenomena can be better understood using mathematical and statistical models. These models typically contain unknown parameters that we need to calibrate using data. If such calibration (estimation) of the parameters is successful, these models can be used to perform predictions and help us in better understanding the experiment under study. However, dealing with models that are "realistic", as opposed to "simplistic" though amenable to analytic derivations, means that often some computations cannot be performed
exactly, as analytically and closed-form formulas are unavailable. For example, in many cases, statistical inference can be challenging (analytically impossible or computationally expensive) because the likelihood function may be unavailable to the statistician.
What you will study in this project are simulation-based inference methods. These are approaches relying on the ability to simulate ("generate") artificial data from a computer implementation of the postulated model, a so-called "generative model". The catch is that producing simulated data from a computer/generative model is typically possible, even when the associated likelihood is unknown, and by using the simulated data we can construct procedures to learn the unknown parameters, given some data.
In the end it will also be possible to quantify the uncertainty around the estimated quantities, which is something always desirable to understand the limitations of the model and the limitations of what we can learn from the given data.
Range of possibilities is wide:
- you can experiment with inference for dynamic models: say ODEs, or stochastic differential equations (SDEs);
- model simulators for financial data or stochastic chemical reactions;
- other models of your choice depending on your interests.
In the end you will learn a lot about Bayesian inference, without the need for having studied it first and without needing to know anything about it.
The project will be written in English.
Gruppstorlek 3-4 studenter
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Matematisk statistik (MSG900/MSG910).
Projektspecifika förkunskapskrav Basic knowledge in statistics, probability theory and some programming. You should have some experience in coding with some language for data-science (examples are R/Matlab/Python/Julia).
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare Umberto Picchini, firstname.lastname@example.org, https://umbertopicchini.github.io/
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper