Abstract
We discuss how statistical inference techniques can be applied in the context of designing novel biological systems. Bayesian techniques have found widespread application and acceptance in the systems biology community, where they are used for both parameter estimation and model selection. Here we show that the same approaches can also be used in order to engineer synthetic biological systems by inferring the structure and parameters that are most likely to give rise to the dynamics that we require a system to exhibit. Problems that are shared between applications in systems and synthetic biology include the vast potential spaces that need to be searched for suitable models and model parameters; the complex forms of likelihood functions; and the interplay between noise at the molecular level and nonlinearity in the dynamics owing to often complex feedback structures. In order to meet these challenges, we have to develop suitable inferential tools and here, in particular, we illustrate the use of approximate Bayesian computation and unscented Kalman filtering-based approaches. These partly complementary methods allow us to tackle a number of recurring problems in the design of biological systems. After a brief exposition of these two methodologies, we focus on their application to oscillatory systems.