Tim Litwin

Inferring model parameters from measured data, i.e. the “inverse problem”, is a necessary step in evaluating virtually any quantitative model. For linear models, there are already many theoretical results established for parameter inference. Specifically, uniquely estimating the maximum likelihood parameters in a linear model is known to be impossible if there are less data points available than parameters in the model. This is conventionally thought to be also true for non-linear models, setting a threshold for the minimum number of data points necessary to uniquely estimate all the model parameters. However, it is possible to construct examples in which more parameters than data points can be uniquely estimated, i.e. with a unique best estimate and finite 95%-confidence intervals. This is demonstrated on a model with three unknown parameters which can be estimated from just two data points. This talk introduces the basic problem and discusses the two-data-points-three-parameters example, providing background and intuition as well as possible explanations of why this seems to work.