Likelihood methods in biology - Spring 2019

The course provides an introduction to likelihood-based inference in Biology. We will cover both theoretical and practical aspects of maximum likelihood and Bayesian inference.

Meeting: Monday and Wednesday 10:00-10:50AM in 2025 Haworth

The syllabus is available as a pdf by clicking here .

Instructors (office hours by appointment):

John Kelly 864-3706 5005 Haworth
Mark Holder 864-5789 6031 Haworth

Grades will be based on class participation and homework assignments. We will have approximately one homework assignment per week. The git repo for MTH's notes is at


Date Topic and Links Assignments
Week 1 Jan 23 Probability, random variables, distributions
Notes on probability by Bálint Tóth
Homework 1: HW1_2019.doc
data: PoissonCounts.xls
Week 2 Jan 28, Jan 29 Random samples, sample distributions, likelihood.
Week 3 Feb 04, Feb 06 Explicitly specifying variability: likelihood examples.
notes on allele freq estimation
Homework 2: HW2_2019.doc (frogs)
Week 4 Feb 11, Feb 13 more Maximum likelihood estimation
notes on population size estimation from sequences
Week 5 Feb 18, Feb 20 Likelihood ratio test statistic and Model Selection
notes on the counter CI vs Bayesian statement example
Notes on Bayesian inference with conjugate priors
Homework 3: HW3_2019.pdf Due Monday, 25 Feb.
Week 6 Feb 25, Feb 27 notes on two parameters and feasiblility constraints Homework 4: HW4_2019.pdf
Week 7 Mar 04, Mar 06 Likelihood ratio test statistic and Model Selection
Some notes on Markov chains and their stationary distributions
Week 8 Mar 18, Mar 20 Numerical optimization example code Homework 5: HW5_2019.doc
Week 9 Mar 25, Mar 27 Fisher's Information and more code. one-param-k2p.R (one and two parameter version despite the name) and (two parameter version).
mar-27-2019.pdf notes
Week 10 Apr 01, Apr 03 MCMC
Notes on MCMC for Bayesian inference and the script
code MTH used to get numbers for key
HW6_2019.pdf Due Wednesday, 17 Apr.
Week 11 Apr 08, Apr 10 Markov chain Monte Carlo (MCMC)
Week 12 Apr 15, Apr 17 Hastings ratio and model jumping
Week 13 Apr 22, Apr 24 Hastings ratio and model jumping
See nice slides by Patrick Lam on convergence diagnostics at
Some slides on Bayes' factors (ignore the irrelevant title slide)
HW7_2019.pdf Due Monday, 6 May
Week 14 Apr 29, May 01 Hidden Markov Models
Week 15 May 06, May 08 HiSSE and imputation. See Gelman's chapter