Courant Institute of Mathematical Sciences
New York University
October 23, 2012
Parameter-free statistical model invalidation for biochemical reaction networks
The problem of model selection is pervasive in computational biology. Standard methods typically involve some form of parameter estimation, which often requires optimization or exploration over the parameter space. This can be difficult for complex models due to the nonlinearity and high dimensionality of the problem. Here, we present a statistical model invalidation technique for mass-action chemical reaction networks that does not require any such parameter estimation. If our algorithm rejects a proposed model on the basis of observed data, then that model cannot fit the data under *any* possible choice of parameters. The main novelty is a 'lifting' procedure that exposes low-dimensional structures that persist independently of parameter values. We discuss this as well as more recent results for the special case of complex-balanced networks. Our work complements conventional inference schemes and has connections with many areas of mathematics, including algebraic geometry, graph theory, linear algebra, and classical statistics.