Extended BASCS algorithm: MCMC for separating overlapping sources

Luis F. Campos and David E. Jones

This is an extension of the model described in: ``Disentangling Overlapping Astronomical Sources using Spatial and Spectral Information" Jones, Kashyap, van Dyk (ApJ 2015).

Follow the writeup for model details in Overleaf

Description

The algorithm uses the spatial, temporal and spectral information of a fixed number of sources to find the joint posterior distribution of their spatial, temporal and spectral parameters.

File Descriptions

• simulate_data_two_sources.R: contains code for simulating data from the model for two sources. You can change the distance between them, relative intensities and background level. On the energy side, you we've pre-specified four settings of interest

  1. equalE: Equal Energy distributions Gamma(4, 4/1000) across time and sources
  2. varyE_bySource: Varying Energy distributions Gamma(4, 4/1000) and Gamma(3, 3/600) for sources, same dist'n across time
  3. varyE_byTime_Source: Vary Energy dist'ns across source, bright typically higher than the dim, but vary both across time as well Gamma(~5, ~5/~1000) and Gamma(~3, ~3/~600)
  4. varyE_byTime_Source_same_Marginal: Vary Energy dist'n across time for bright source, keep same for dim source -- but marginally will be the ~same. The file can be run using the command shell (with optional settings) or manually.

• Three files to run three different models

  1. run_BASCS_fixedk.R: runs BASCS with a fixed number of sources (k), so BASCS without reversible jump.
  2. run_eBASCS_full_fixedk.R: runs eBASCS described in the paper. The energy distributions vary across sources and across time.
  3. run_eBASCS_full_marginal_fixedk.R: runs a simplified version of eBASCS where we do not allow the energy distribution to vary across time, but it may vary across sources.

These files source a number of setting files. We did this to simplify the coding and ensure runs across models have the same settings. These are

• _clean_data.R: This formats the data to a form appropriate for the mcmc functions
• _init.sim.R: Initializes parameters for BASCS mcmc
• _init.time.sim.R: Initializes parameters for eBASCS mcmc
• _mcmc_options.R: Sets parameters for mcmc including the proposal distribution parameters, chain length and burn-in period
• _model_options.R: sets model parameter options including spectral model (full or extended), time spacing model (multinomial Dirichlet, equally spaced), psf model.
• _prior_options.R: sets parameters for prior distributions on energy, spatial, etc.