
A reference of probabilistic methods of sequence analysis.
I can recommend 3 really good books, SICP-level good:
1. Biological Sequence Analysis by Durbin et al.
How to model DNA, RNA and proteins as probabilistic languages / generative models. There is also a companion book with all exercises solved.
2. Physical Biology of the Cell by Phillips et al.
A massive amount of quantitative cell biology models that use simple undergrad physics.
Originated from a Caltech course. After reading this book, all other intro to biology books look like a bag of tricks.
3. An Introduction to Systems Biology: Design Principles of Biological Circuits by Alon.
Bacterial circuits from the perspective of an electrical engineer.
Sadly, NSF discontinued funding for a totally epic Cold Spring Harbor Summer school for postdocs that taught [2,3].
A shame, we need more quantitative biology and less bags of tricks.
I've had this argument with folks before and some people seem fine learning in other ways, but I really prefer the textbook approach, especially textbooks which are basically just summaries of the current understanding of the field, with direct links to the detailed review articles.
If you want an overview of Markov chains as statistical models in their own right, Durbin et al.'s Biological Sequence Analysis is a well-motivated overview.
It's a really good way to get a good overview of the field, and what some of the problems have been already solved in bioinformatics. It's definitely best to combine it with a more traditional textbook such as "Introduction to Computational Biology" (Haubold and Wiehe) or "Biological Sequence Analysis" (Mitchison, Krogh, Durbin, and Eddy).
Hope that helps!