### Lecture Notes Published In Applications of Data Assimilation and Inverse Problems in the Earth Sciences

20 Jun 2023
My lecture notes,
**A Tutorial on Bayesian Data Assimilation**, are now published in
**Applications of Data Assimilation and Inverse Problems in the Earth Sciences**.
This chapter provides a broad introduction to Bayesian data assimilation that will be useful
to practitioners in interpreting algorithms and results, and for theoretical studies developing
novel schemes with an understanding of the rich history of geophysical data assimilation and its
current directions. The simple case of data assimilation in a 'perfect' model is primarily
discussed for pedagogical purposes. Some mathematical results are derived at a high level in
order to illustrate key ideas about different estimators. However, the focus of this chapter
is on the intuition behind these methods, where more formal and detailed treatments of the data
assimilation problem can be found in the various references. In surveying a variety of widely
used data assimilation schemes, the key message of this chapter is how the Bayesian analysis
provides a consistent framework for the estimation problem and how this allows one to formulate
its solution in a variety of ways to exploit the operational challenges in the geosciences.