Defining the prior

The MCMC based searches (i.e. pyfstat.MCMC*) require a prior specification for each model parameter, implemented via a python dictionary. This is best explained through a simple example, here is the prior for a directed search with a uniform prior on the frequency and a normal prior on the frequency derivative:

theta_prior = {'F0': {'type': 'unif',
                      'lower': 29.9,
                      'upper': 30.1},
               'F1': {'type': 'norm',
                      'loc': 0,
                      'scale': 1e-10},
               'F2': 0,
               'Alpha': 2.3,
               'Delta': 1.8
               }

For the sky positions Alpha and Delta, we give the fixed values (i.e. they are considered 'known' by the MCMC simulation), the same is true for F2, the second derivative of the frequency which we fix at 0. Meanwhile, for the frequency F0 and first frequency derivative F1 we give a dictionary specifying their prior distribution. This dictionary must contain three arguments: the type (in this case either unif or norm) which specifies the type of distribution, then two shape arguments. The shape parameters will depend on the type of distribution, but here we use lower and upper, required for the unif prior while loc and scale are required for the norm prior.

Currently, two other types of prior are implemented: halfnorm, neghalfnorm (both of which require loc and scale shape parameters). Further priors can be added by modifying pyfstat.MCMCSearch._generic_lnprior.