### Kenneth Ho

Visiting Scholar

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.