Available methods

This implementation includes a two parameter Milky Way galaxy model with an arbitrary number of components. The stars have single-band luminosities. These data are binned and the parameters are inferred by posterior simulation.

Overall, this inference of course is the main goal of this project and to test our approach we proceed as follows:

• Begin with some number of data bins in each dimension.

• Choose a prior distribution of parameters for the components.

• The likelihood is the joint probability of the model in all of the bins according to the Poisson process

• We simulation the posterior using Markov Chain Monte Carlo either straight Metropolis-Hastings or Reversible Jump transitions.

• The default simulation uses a single chain. In addition, one may Radford Neal's Tempered Transtions method. This is a hierarchy of chains at successively larger temperatures. A single step consists of proposals to exchange states between adjacent temperature states sequentially from coldest to hotest and back again.

• There are two parallel chain algorithms (Parallel Chains), again based on tempering. These include Geyer's (1991) parallel tempering and a new hierarchical tempering scheme. The number of chains is chosen by the maximum temperature and the dimension of the model. In the former method, each step consists of either updates of each chain of a proposal to swap the states of adjacent chains. In the latter, one proposes to exchange the cold (fiducial) chain with one of the warmer chains and the remaining chains are updated with a the chosen MCMC algorithm (e.g. Metropolis-Hastings or Reversible Jump).

• Convergence is monitored. Either after a preset number of iterations or after the Markov chain appears converged at the present level, the data is regridded on a finer scale, bins per dimension and the simulation is restarted. Now the prior distribution is the posterior at the previous level and the likelihood is the likelihood ratio of the current likelihood to the likelihood at the previous level (see Multiresolution).

• Parallel chain monitoring is planned.

A discussion of basic results for a test with is described in Sample.