The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data

by Brock D. Sherlock, Marko A.A. Boon, Maria Vlasiou, Adelle C.F. Coster

Experimental data is often in the form of time-series data with multiple measurements taken at a number of time points. In biological datasets the number of measurements at each time point is often small. So, it can be useful to consider data from multiple experimental protocols to constrain model parameters. In this study, we identify distance metrics for the comparison of stochastic model outputs and time-evolving stochastic measurements of a system. Our distance is across three scales: that of the data at each time point of each type of experiment; a combined distance across the time course of each experiment; and a combined distance across all the experiments. The distances identified offer a means to fit a wide range of models to data.

The algorithm to produce a hierarchical distance measure over three scales: individual time points, across a time course of a single experiment, and a combined distance over all experiments. This combined distance can then be used for parameter inference, model or other comparisons.