Summer Program
Summer Course 2019
GR8201(1) – Topics in Statistics:
An introduction to Approximate Bayesian Computation (ABC)
Simon Tavaré, Department of Statistics
Held on June 5, 7, 10, 11, 12, 14, 17, 18
11.40 am-12.55pm
Room: 903 SSW
Lectures:
Lecture 4: Slides Notes Primates
Lecture 5: Slides
Statistical inference for complex probability models is often complicated by intractable or computationally intensive likelihoods. This has led to the development of simulation-based and likelihood-free methods, and ABC – approximate Bayesian computation. ABC evolved in population genetics, where the stochastic process underlying the likelihood calculations is easy to simulate, but the appropriate likelihood cannot be computed. There are at least three basic flavours of ABC, including those based on rejection methods, on Markov chain Monte Carlo, and on population Monte Carlo.
Loosely speaking, ABC methods work as follows. A parameter value is simulated, and a data set is simulated with that parameter. A decision to retain this value as an approximate draw from the posterior is made by comparing the simulated data and the true data. This raises a number of important issues, such as how the simulated data should be used, how the data are to be summarized (related to notions of approximate sufficiency), and how a subset of useful summary statistics might be chosen.
In the course we will explore these methods in some detail, identify a number of unresolved issues, and describe a number of applications in genetics and cancer biology. We will have some practical R- based sessions to illustrate the methods, and discuss other applications in a student-led reading group format.