**Course description: **

Bayesian statistics is concerned with inference on variables that are not directly observable, the unknowns of primary interest, based a priori information about them plus observation of other quantities that depend indirectly on the variables of interest. The connection between Bayesian inference and inverse problems, the science of estimating variables from noisy indirect measurements is clear, and presently Bayesian methods in inverse problems are widely used. The interplay between ideas from scientific computing for inverse problems and Bayesian methods for inference gives rise to Bayesian scientific computing, which the topic of this course.

\nThe lectured will focus on basic techniques in Bayesian methods, including probability distributions, Bayes' formula, conditioning, hierarchical models, estimation problems arising in this context, as well as certain numerical techniques for inverse problems, including regularization and iterative methods for solving large systems. In the lectures the connections between computational inverse problems and Bayesian inference will be highlighted. The Bayesian methods developed in the course will be used to solve inverse problems with sparsity constraints and dynamically update estimates with classical filtering techniques such as Kalman filtering.

\nThe course consists of lectures and MATLAB based exercises, and is based on the book: D. Calvetti and E. Somersalo, *Introduction to Bayesian Scientific Computing*, Springer, 2007, as well as a preliminary new edition of it.

Ects: 2.5.

\nTime: December 9-13, 2019 (one full week).

\nTeacher: Professor Daniela Calvetti and Professor Erkki Somersalo, both from Case Western Reserve University, Cleveland, Ohio.

\nCourse responsible, contact: Professor Per Christian Hansen, DTU.

\nMore details: link to course description (DTU course 02962).

Sign up for the course by sending an email to Per Christian Hansen: pcha@dtu.dk.

\nPlease be advised that all participants are responsible themselves for finding accommodation (we do not have the resources to help with this).

URL:https://www.dtu.dk/Service/Kalender/2019/12/PhD-course-Bayesian-Scientific-Computing DTSTAMP:20200125T082500Z UID:{D34DDDB5-9F15-4DF0-B90D-78614674B06F}-20191209T070000Z-20191209T070000Z LOCATION: DTU Lyngby Campus END:VEVENT END:VCALENDAR