4.10. Generic Priors¶

Although Phosphoros provides some default prior functionality, pre-computed user-defined priors are also allowed. In this way, users can try different ideas without having to modify the Phosphoros code. Currently two types of generic priors are allowed, axes priors and multi-dimensional generic priors.

Note

Currently, generic priors can only be used via the CLI.

Warning

Generic priors are applied after the full likelihood grid has been computed. This means that if a prior defines big areas of zero probability, the computations for these areas will still be done, slowing down the Phosphoros execution. In this case, instead of using the generic priors functionality, a sparse grid should be considered.

4.10.1. Axes Priors¶

Axes priors are applied on a single axis of the parameter space, meaning that the likelihood of all models with the same value of the axis will be scaled with the same prior value.

Phosphoros reads axes priors from files located in the directory:

> $PHOSPHOROS_ROOT/AuxiliaryData/AxisPriors/<axis_name>/

where axis_name is one of the following names: sed, red-curve, ebv or z. The files in these directories are expected to be ASCII tables with two columns, the axis value and the prior value (for more details see Axes Priors Format).

Axes priors can be defined in two different ways, depending on the type of axes:

Numerical axes

Color excess E_(B-V) and redshift are numerical parameters. Phosphoros uses interpolation to compute prior values for the exact axis knots. So axis values at which the prior is computed do not have to match exactly the axis knots, and the same prior file can be used for multiple grids.

Warning

If an axis knot is outside the range of the given prior table, Phosphoros will assign a prior of zero value to it and all models belonging to this slice of the parameter space will get zero probability.

Numerical axes priors are applied in the compute_redshifts (or CR) action using the action parameters:
```
axis-function-prior-ebv=<filename>
axis-function-prior-z=<filename>
```
where the argument is the file containing the prior values (in the directory $PHOSPHOROS_ROOT/AuxiliaryData/AxisPriors/ebv or z). For example, if you want to use a prior which will penalize high E_(B-V) values, you set axis-function-prior-ebv=ebv_prior and create a file ebv_prior.txt like:
```
0.0         0.988813044611
0.2         0.998750780925
0.4         0.969233234476
0.6         0.903707077873
0.8         0.809571648668
1.0         0.696804775496
1.2         0.576229073672
1.4         0.457833361772
1.6         0.3495006002
1.8         0.256340151415
2.0         0.180639851619
```
Note

The filename of prior functions is provided without the extension.
Categorical axes

SEDs and reddening curves are categorical parameters, and Phosphoros cannot use the same approach as for numerical parameters. The priors of these two axes are provided again as tables, but now the first column is a string, and it must match exactly the name of the axis knots. Tables must contain entries for all the knots of your axis (extra entries are instead allowed).

To use these priors, users should call the compute_redshifts action with the parameters:
```
axis-weight-prior-sed=<filename>
axis-weight-prior-red-curve=<filename>
```
For example, if three different variations of the Calzetti law for reddening have been used, users might want to apply a prior to balance this fact. In this case, they can create a redcurve_prior.txt file in the directory $Phosphoros_Root/AuxiliaryData/AxisPriors/red-curve like:
```
SB_calzetti         1.
SB_calzetti_bump1   1.
SB_calzetti_bump2   1.
SMC_prevot          3.
```
and set axis-weight-prior-red-curve=redcurve_prior.

Note

Again, the filename is provided without the extension.

4.10.2. Multi-dimensional Priors¶

The axes priors described above cannot express priors which depend on multiple parameters. For example, it is not possible to describe priors on E_(B-V) that are different for different SED templates. In this case, Phosphoros allows for multi-dimensional generic priors, which provide a prior value for each cell of the parameter space.

Multi-dimensional priors must be provided in FITS files, whose format is described in the Priors Format Reference. Phosphoros searches for these files in the Phosphoros_Root/AuxiliaryData/GenericPriors directory.

The prior parameter space must match exactly the parameter space of the grid of models that will be used to compute photometric redshifts. As constructing these prior FITS files from scratch can be quite complicated, Phosphoros provides a tool, the create_flat_grid_prior (or CFGP for short) action, that gets as input a grid of models and constructs a prior FITS file with all the cells set to 1.

For example, users can generate a flat prior (named multi_priors.fits) with the command:

Phosphoros CFGP --out-grid-name=multi_priors.fits --model-grid-file=<path>/<model grid name>

where the --model-grid-file parameter asks for the qualified filename of the grid of models.

The file multi_priors.fits will be created in the correct directory, i.e. AuxilaryData/GenericPriors/. Users can then use their favorite tool for editing FITS arrays and for setting the actual prior values.

Tip

We recommend Astropy, a Python library for astronomy, to manage FITS files 1 .

Once you have build the prior FITS file, you can use it when computing the photometric redshifts by including in the configuration file the action parameter:

generic-grid-prior=multi_priors.fits

Note

The argument of the --generic-grid-prior option is the filename with the .FITS extension.

Warning

Building the multi-dimensional generic prior is a cumbersome task and the FITS files you produce are not reusable for different parameter spaces. For this reason, users should always favor the axes priors over the multi-dimensional ones.

Footnotes

1: See the web page: https://docs.astropy.org/en/stable/io/fits/