UBC Math Colloquium: Dr Bamdad Hosseini

Inverse problems (the problem of inferring an unknown parameter from indirect and noisy measurements) are ubiquitous in science and engineering. The Bayesian approach to inverse problems provides a probabilistic framework in which prior knowledge about the unknown parameter is combined with indirect measurements to give an improved estimate of the unknown. Furthermore, the Bayesian approach allows for rigorous estimation of uncertainties associated with the estimated value of the unknown. In this talk we give a brief introduction to Bayesian inverse problems with a focus on modelling of prior knowledge with non-Guassian probability measures. We will discuss theoretical aspects of Bayesian inverse problems such as their well-posedness as well as applications and algorithms for their solution.