Inference in complex systems

Abstract

The interface between life and physical sciences provides an abundant habitat for mathematical models. These are often complex to our feeble minds yet ridiculously simplistic in comparison with nature's subtlety. They nevertheless often succeed in extracting important insights into, and sometimes quantitative measures of, nature's ways. The effectiveness of mathematics in the natural sciences was dubbed 'unreasonable' in the title of a famous essay over 50 years ago [1], and is no less so today. The models come in a range of flavours, with elements from deterministic and stochastic mathematics, and from algebra, combinatorics and graph theory among other branches of the mathematical tree. To evaluate the hypotheses about how nature works embodied in such models, their properties-most obviously the outcomes they predict-must be compared with observations. At a minimum, the observations can be at the level of qualitative descriptions of natural systems, but increasingly today models are evaluated on the basis of detailed comparisons with carefully measured data. Moreover, rather than coming at the end of a process of model building and computation, comparisons with data are today usually integrated into every level of the model building process, from choosing the broad features of the model to fine-tuning of parameter values.This issue of Interface Focus is devoted to showcasing some of the many possibilities for innovative approaches to inference in complex models. The emphasis here is not on fully general exposition of methods or rigorous proofs of validity. There is of course some introduction and review of advanced techniques that are more fully developed elsewhere. However, our focus is on application to cutting edge scientific problems. For this showcase, we have selected an unusually broad range of scientific areas, the unifying features being complex models and challenging inference problems tackled by novel techniques.This year marks the centenary of the death of Francis Galton, the great Victorian polymath who has a claim to be regarded as the first applied statistician in the modern sense. He enthusiastically collected and analysed data to illuminate a range of scientific problems from climate to human psychology and morphology, the latter including fingerprints for forensic use. His bequest generated another important centenary this year-the founding of the world's first academic department of statistics at University College London. Academic statistics has flourished in the intervening century, but the number of card-carrying statisticians remains far too small to address the ubiquitous challenges of inference in every branch of science. The toolkit of inference methods available to scientists has constantly been enriched by contributions from other disciplines, including students of insurance, games of chance, psychology, agriculture and genetics. In recent decades, entire schools of inferential thought have evolved in various engineering and informatics disciplines, largely independent of mainstream...

Complexity in Neurobiology: Perspectives from the study of noise in human motor systems

“…The second theme we explored was how changes in expertise after skill acquisition can be shown as the nature of changes in a Lévy distribution. 29,35 The quantification of noise in terms of its distributional properties is useful in determining the nature of corrective processes and learning. The short and long time-scale corrective movements revealed by intermittency have provided insight about the discontinuous nature of the control system that is governing a system in which time delays make it impossible to rely on feedback control alone.…”

“…This approach, which consists of inferring information about the internal organization and functioning of the system from the statistical properties of its outcome variables, represents an exciting challenge. 29 In the following sections, we highlight briefly what we think to be some of the most exciting developments in complex systems approaches to neurobiology, in addition to the other excellent papers published in this volume.…”

“…To fully understand the control strategies used by the CNS, we need to establish methods that distinguish purposeful variability from noise. The stochastic optimal feedback control models 29,31 have been very successful at promoting the idea that the CNS works well in the presence of fluctuations. However, noise has always been treated in these models as random variation that does not have structure.…”

Ensemble Bayesian Analysis of Bistability in a Synthetic Transcriptional Switch

“…Our results support the notion that Bayesian ensemble techniques, by virtue of approximating important marginal distributions of high-dimensional probability distributions generated by complex models, make mechanistic biochemical models useable for prediction and inference. 73 Nonetheless, because the "stiffness" of parameters, the precision with which the combined parameter values can be inferred, depends on the number, precision, and type of experimental data available, careful experimental design and cautious interpretation of modeling and analysis results would be required. Beyond analysis, Bayesian inference could be used in design tools that specify "design objectives" for synthetic biology applications.…”

Machines of life: catalogue, stochastic process modeling, probabilistic reverse engineering and the PIs- from Aristotle to Alberts

“…The "inverse problem" of inferring the model from the observed experimental data has to be based on the theory of probability. Such "statistical inference" [166] can be drawn by following methods developed by statisticians over the last one century. Inferring the complete network of mechano-chemical states and kinetic scheme of a molecular machine from its observed properties is reminiscent of inferring the operational mechanism of a given functioning macroscopic machine by "reverse engineering".…”