Fitting algorithm

This page contains information about the fit wrappers

• fit spectrum
• fit
• fit track
• fit cluster

Detailed information about the fitting process is provided here. At a high level, there are three primary uses for BrainTrak

• Computation of the random walk and generation of the chain is performed by chain.m and chain_parallel.m
• A minimal fit is generated by fit_spectrum.m which calls chain.m. This function takes in a spectrum

Typically, you would not use the core functions directly. Instead, you would write other scripts and functions that use these core routines. For example

• +bt/fit.m shows a minimal fitting example, taking in a model, a spectrum, and optionally the length of the chain (i.e., how long to run the routine for)
• +bt/fit_track.m shows common usage of BrainTrak, where a data set is automatically loaded and preprocessed, and then a sequence of spectra is fitted with incremental prior updates.

Additional wrappers for these routines are provided in braintrak/data_examples (for fitting various data sets), and braintrak/published/Abeysuriya_2015 which contains wrappers used to generate the fits published in Abeysuriya (2015).

MCMC fitting consists of the following steps

• Get some initial parameter values (manually specified, or automatically given by model.initialize_fit)
• Simulate a random walk (chain.m)
• Pick the most likely parameters (fit.m)
• Compute the posterior marginal distributions (model.make_posterior)

These steps are all driven by fit.m. The steps in fit.m are

1. You specify the model, the target power spectrum, and the priors and initial conditions. If you don't have any priors or initial conditions e.g., because this is the first fit in a series of fits, you should use model.initialize_fit beforehand, like in fit_single.m
2. model.prepare_for_fit is called, which loads the power spectrum into the model object and calls model.set_cache to do any one-off computations
3. The chain is simulated using mcmc.chain or mcmc.chain_parallel depending on whether a parpool is open
4. The output from the chain is analyzed, producing the fit_data struct which stores information about the posteriors and the optimum fit, and plot_data struct which contains the XYZ cloud data (only used for plotting)