Approximate Bayesian Computation for Parameter Estimation of Complex Stochastic Models
speaker: Yannik Schaelte (Helmholtz Muenchen)abstract: Mathematical models are widely used in computational biology to describe and analyze dynamical systems. These models are commonly subject to unknown parameters, which have to be inferred by fitting the model to measured data. Frequently, this is done in a Bayesian setting by formulating a likelihood function quantifying the support parameters lend to data. However, as models get more complex and stochastic, it can become infeasible to compute a likelihood function at all. Examples of such models include agent-based, stochastic differential equation, or Markov process models, which are used in computational biology to describe e.g. multi-scale gene expression, signal transduction, or multi-cellular processes. In these situations, it is often still possible to simulate data from the model. Approximate Bayesian Computation (ABC) methods have been developed to perform reliable analysis in this situation. All that is required is some model black-box, which takes parameters and returns simulated data. In a nutshell, in ABC data are simulated from the model for sampled parameters, and then compared via some distance function to measured data. Accepted parameters then realize a sample from an approximation to the posterior distribution. To tackle low acceptance rates and improve performance, ABC is frequently combined with a Sequential Monte Carlo (SMC) scheme, where the posterior approximation is iteratively improved throughout multiple particle populations. ABC has become quite popular in the last years and found applications in many different research areas.
In this talk, I will discuss the fundamentals of ABC, but also show its successful application to biological problems, e.g. to a study of tumor growth using a multi-scale hybrid discrete-continuum model. While ABC methods are broadly applicable, they are computationally expensive, since the computation time scales with the model simulations. Several toolboxes have been developed to make the use of ABC possible. Here, I will present pyABC, a distributed ABC-SMC framework for parameter estimation and model selection, which implements various state-of-the-art methods. These include e.g.\ a runtime-minimizing dynamic parallelization strategy for multi-core and distributed environments, and a scheme for the automatic adaptation of population size. Further, the toolbox offers multiple extension and customization possibilities for expert users, including early rejection, adaptive acceptance thresholds, transition kernels, and distance functions. The source code is hosted on https:/github.comicb-dcmpyabc.
timetable:
Wed 3 Oct, 11:45 - 13:00, Aula Dini
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