Toric geometry and maximum likelihood estimation in quasi-independence models

We investigate the toric fibre product (TFP) structure of a family of log-linear statistical models called quasi-independence models. This is useful for understanding the geometry of parameter inference in these models because the maximum likelihood degree is multiplicative under the TFP. We define the notion of a coordinate toric fibre product, or cTFP, and give necessary and sufficient conditions under which a quasi-independence model is a cTFP of lower-order models. Our main result is that the vanishing ideal of every 2-way quasi-independence model with ML-degree 1 can be realised as an iterated toric fibre product of linear ideals.

Joint work with Jane Coons and Heather Harrington.