Chapter 1: Introduction to uncertainty, priors, and Bayesian inverse problems

The goal of this introductory chapter is to set the stage for the book. We give brief introductions to the main concepts and tools that we are going to use throughout. There is nothing new here; a reader who is already familiar with Bayesian inverse problems and uncertainty quantification, and is mainly interested in the use of CUQIpy, can easily skip this chapter.

Learning objectives: ¶

By the end of the chapter you will be able to explain:

• What is error, uncertainty, and quantification.

• What is a inverse problem and an ill-posed problem.

• What is a Bayesian inverse problem.

• What are the ingredients in Bayes’ theorem for a Bayesian inverse problem.

• What is the connection between Gaussian priors and Tikhonov regularization.