7.3.3 Processing steps

The model-fitting process follows the following steps (decribed in detail in Holl et al. (2023b)):

1. 1.

   A period search is first performed by each module. Given the nature of the astrometric dataset, the application of standard tools for the periodogram analysis of unevenly sampled time-series (e.g. the Generalized Lomb-Scargle periodogram, Zechmeister and Kürster 2009) is not possible. For any given source, both the DE-MCMC and GA modules draw a large sample of initial trial periods for sinusoidal signals projected along the scan directions of the time-series. For DE-MCMC this is a uniform grid up to twice the observations time span. For GA this is random period sample uniformly drawn in log10(period) between roughly the shorted and longest time-intervals in the observations as derived from repeated bootstrap sampling of the observations. One may note that when running the GA algorithm it is allowed to explore periods up to twice the observations time span through its mutation operators. For both DE-MCMC and GA, a sparsely sampled selection of periods corresponding to local ${\chi }^2$ minima becomes the seed for the initialisation of the DE-MCMC chains and GA genome population;

2. 2.

   Each algorithm is allowed to determine its best-fit parameters for a maximum of 60 s of single-threaded wall-clock CPU computation time.

3. 3.

   Finally, the best-fitting model parameters are determined by evaluating the Bayesian Information Criterion (Schwarz 1978) metric: $\mathrm{BIC}=k\ln (n)-2\ln ℒ$ (where $k$ is the number of parameters estimated by the model and $n$ is the number of data points). The solution with the lowest BIC is selected as the best-fit solution. The published solution therefore originates from either the DE-MCMC or GA approaches, but the information on which was chosen for a given source is not published;

4. 4.

   Symmetric estimates of the parameter uncertainties are obtained by reconstructing the covariance matrix directly from the Jacobians of all parameters for all observations.