Math 227C: Stochastic modeling and statistical modeling for the life sciences

• The repository will be updated throughout the course, including with lecture notes. A convenient way to rapidly synchronize a copy onto your computer is using git, available openly online.
• In the second part of the course, we will make use of Jupyter notebooks and the R programming language. We plan to start using Jupyter around the 5th week of class. There are (at least) three ways to run Jupyter R notebooks.
  • Install Jupyter and R on your machine is through Anaconda, available openly online, by first installing Anaconda and then installing R.
  • Use Google Colab
  • For UCI students, use our local high-performance computing facility, hpc3, which has a Jupyter notebook server called biojhub. See some instructions from rcic.
  • Use R-lang Jupyter in VSCode (a free text editor made by Microsoft).
• In the first part of the course, a good tool for typesetting mathematical homeworks is LaTeX. A good tutorial to learn LaTeX is here.
• R learning resources
  • R Tutorial from W3C
  • R cheatsheet with loops, if statements, lapply, etc.

Premise

This course follows MATH 227A and 227B in establishing mathematical and computational tools that are useful in modeling the dynamics of biological systems. This course, MATH 227C, is in two parts: the first covers stochastic processes, where randomness plays a role in the system behavior; the second covers statistical modeling, where models, including their attributes such as parameters, are learned from data in the presence of noise or inherent randomness in the model.

Lecture notes

• In-class hand notes

• In-class Jupyter notebooks

Problem sets

1. Discrete probability. Fair dice.

2. Discrete-state Markov chains, base pairs

3. Discrete-state Markov chains, MFPTs and a biologist in the rain

4. Poisson rates, my advisor is always late, viral DNA

5. Receptors, continuous-time Markov chains, and MFPTs

6. Parametric noise in an ODE

7. Fitting linear and nonlinear regression to a power law

8. Variance-bias tradeoff of k-Nearest-Neighbors classification

9. Gut microbiome and the elastic net

10. Bootstrap and the Standard Error of the Mean, bootstrap on linear regression

11. MCMC and chemical kinetics

Scheduling

Special dates

• There will be no lecture Wednesday, April 17th (wk 3).
• There will be no lecture Monday, May 13th (wk 7).
• Instead we will have out-of-class recorded lectures that you will be responsible for watching. These will be released throughout the quarter.