Fitting large number of parameters

In an ideal world, a transmission spectrum would be made up of very many light curve observations, at many filters and epochs. Fitting all of these observations simultaneously would result in a very high-dimensioned parameter space, which leads to instabilities in the nested sampling.

In order to avoid this, TransitFit has modes for dealing with large numbers of parameter sets: 'batched', and 'folded', which can be set with the fitting_mode argument of run_retrieval(). There is also 'all' mode, which can be set to manually force all parameters to be fitted simultaneously.

‘Batched’ fitting

This mode groups the light curves by filter, and then splits the retrieval into multi-filter ‘batches,’ fitting each of these batches one at a time. The batches are chosen to allow a maximum number of parameters to be fitted simultaneously, which can be controlled with the max_batch_parameters argument of run_retrieval(). Final best-fit values are then calculated from weighted means of the best-fit values from each batch.

The batches are generally constructed to have at least one filter in common with at least one other batch. This ensures that there is still some coupling of information between the batches. The exception to this is when there is one filter in particular which has a very high number of observations. In this case, we recommend using the 'folded' mode.

It is suggested to run the model twice if using ‘batched’ mode. For the second run, use the output from first run as the priors for the wavelength independent parameters (P, t0, a, inc). The error limits, standard deviation on these priors should be narrowed down to not allow for much variation in individual batches/lightcurves.

‘Folded’ fitting

With the launch of large surveys such as TESS, many exoplanets have multiple-epoch observations in a single filter. TransitFit can make use of these through a two-step retrieval process.

  1. TransitFit runs a retrieval on each filter independently, and uses the results to produce a phase-folded light curve for each filter.

  2. TransitFit runs a standard multi-wavelength retrieval using the batched algorithm above.

This mode of retrieval allows for the production of high-quality folded light curves from non-detrended data, as well as providing a method where observations from long-term, single-waveband surveys such as TESS can be easily combined with single-epoch observations at multiple wavelengths, such as from ground-based spectrographic follow-up.

Automatic mode selection

By default, TransitFit will try and detect which fitting mode is most appropriate for your data. It first works out how many parameters are required to fit everything simultaneously, which we will call max_n_params. Then if:

  1. max_n_params <= max_batch_parameters - all parameters are fitted simultaneously ('all' mode).

  2. If any filter has 3 or more epochs observed, then 'folded' mode is used.

  3. Otherwise, 'batched' mode is used.